Solved: Calculating Equilibrium Constants

(a) Based on the following energy profile, predict whether kf 7 kr or kf 6 kr.

(b) Using Equation 15.5, predict whether the equilibrium constant for the process is greater than 1 or less than 1. [Section 15.1] Reaction progress Potential energy Reactants Products

The following diagrams represent a hypothetical reaction A B, with A represented by red spheres and B represented by blue spheres. The sequence from left to right represents the system as time passes. Does the system reach equilibrium? If so, in which diagram is the system in equilibrium? [Sections 15.1 and 15.2] 1 2 3 4 5

The following diagram represents an equilibrium mixture produced for a reaction of the type A + X AX. Is K greater or smaller than 1 if the volume is 1 L and each atom/ molecule in the diagram represents 1 mol? [Section 15.2]

The following diagram represents a reaction shown going to completion. Each molecule in the diagram represents 0.1 mol and the volume of the box is 1.0 L. (a) Letting A = red spheres and B = blue spheres, write a balanced equation for the reaction. (b) Write the equilibrium-constant expression for the reaction. (c) Calculate the value of Kc. (d) Assuming that all of the molecules are in the gas phase, calculate n, the change in the number of gas molecules that accompanies the reaction. (e) Calculate the value of Kp. [Section 15.2

Snapshots of two hypothetical reactions, A1g2 +B1g2 AB1g2 and X1g2 + Y1g2 XY1g2 at five different times are shown here. Which reaction has a larger equilibrium constant? [Sections 15.1 and 15.2] t = 10 s 20 s 30 s 40 s 50 s X(g) + Y(g) XY(g) t = 10 s 20 s 30 s 40 s 50 s A(g) + B(g) AB(g)

Ethene 1C2H42 reacts with halogens 1X22 by the following reaction: C2H41g2 + X21g2 C2H4X21g2 The following figures represent the concentrations at equilibrium at the same temperature when X2 is Cl2 (green), Br2 (brown), and I2 (purple). List the equilibria from smallest to largest equilibrium constant. [Section 15.3] (a) (b) (c)

When lead (IV) oxide is heated above 300 C it decomposes according to the following reaction PbO21s2 PbO1s2 + O21g2. Consider the two sealed vessels of PbO2 shown here. If both vessels are heated to 400 C and allowed to come to equilibitum which of the following statements is true? (a) There will be less PbO2 remaining in vessel A, (b) There will be less PbO2 remaining in vessel B, (c) The amount of PbO2 remaining in each vessel will be the same. [Section 15.4] 5.0 g PbO2(g) in both vessels Vessel A V = 50 mL Vessel B V = 100 mL

The reaction A2 + B2 2 AB has an equilibrium constant Kc = 1.5. The following diagrams represent reaction mixtures containing A2 molecules (red), B2 molecules (blue), and AB molecules. (a) Which reaction mixture is at equilibrium? (b) For those mixtures that are not at equilibrium, how will the reaction proceed to reach equilibrium? [Sections 15.5 and 15.6] (i) (ii) (iii)

The reaction A21g2 + B1g2 A1g2 + AB1g2 has an equilibrium constant of Kp = 2. The accompanying diagram shows a mixture containing A atoms (red), A2 molecules, and AB molecules (red and blue). How many B atoms should be added to the diagram to illustrate an equilibrium mixture? [Section 15.6]

The diagram shown here represents the equilibrium state for the reaction A21g2 + 2 B1g2 2AB1g2. (a) Assuming the volume is 2 L, calculate the equilibrium constant Kc for the reaction. (b) If the volume of the equilibrium mixture is decreased, will the number of AB molecules increase or decrease? [Sections 15.5 and 15.7]

The following diagrams represent equilibrium mixtures for the reaction A2 + B A + AB at 300 K and 500 K. The A atoms are red, and the B atoms are blue. Is the reaction exothermic or endothermic? [Section 15.7] 300 K 500 K

The following graph represents the yield of the compound AB at equilibrium in the reaction A1g2 + B1g2 AB1g2 at two different pressures, x and y, as a function of temperature. Temperature [AB] P=x P=y (a) Is this reaction exothermic or endothermic? (b) Is P = x greater or smaller than P = y? [Section 15.7]

Suppose that the gas-phase reactions A B and B A are both elementary processes with rate constants of 4.7 * 10-3 s -1 and 5.8 * 10-1 s -1 , respectively. (a) What is the value of the equilibrium constant for the equilibrium A1g2 B1g2? (b) Which is greater at equilibrium, the partial pressure of A or the partial pressure of B?

Consider the reaction A + B C + D. Assume that both the forward reaction and the reverse reaction are elementary processes and that the value of the equilibrium constant is very large. (a) Which species predominate at equilibrium, reactants or products? (b) Which reaction has the larger rate constant, the forward or the reverse?

Write the expression for Kc for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) 3 NO1g2 N2O1g2 + NO21g2 (b) CH41g2 + 2 H2S1g2 CS21g2 + 4 H21g2 (c) Ni1CO241g2 Ni1s2 + 4 CO1g2 (d) HF1aq2 H+1aq2 + F-1aq2 (e) 2 Ag1s2 + Zn2+1aq2 2 Ag+1aq2 + Zn1s2 (f) H2O1l2 H+1aq2 + OH-1aq2 (g) 2 H2O1l2 2 H+1aq2 + 2 OH-1aq2

Write the expressions for Kc for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) 2 O31g2 3 O21g2 (b) Ti1s2 + 2 Cl21g2 TiCl41l2 (c) 2 C2H41g2 + 2 H2O1g2 2 C2H61g2 + O21g2 (d) C1s2 + 2 H21g2 CH41g2 (e) 4 HCl1aq2 + O21g2 2 H2O1l2 + 2 Cl21g2 (f) 2 C8H181l2 + 25 O21g2 16 CO21g2 + 18 H2O1g2 (g) 2 C8H181l2 + 25 O21g2 16 CO21g2 + 18 H2O1l2

When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products? (a) N21g2 + O21g2 2 NO1g2; Kc = 1.5 * 10-10 (b) 2 SO21g2 + O21g2 2 SO31g2; Kp = 2.5 * 109

Which of the following reactions lies to the right, favoring the formation of products, and which lies to the left, favoring formation of reactants? (a) 2 NO1g2 + O21g2 2 NO21g2; Kp = 5.0 * 1012 (b) 2 HBr1g2 H21g2 + Br21g2; Kc = 5.8 * 10-18

Which of the following statements are true and which are false? (a) The equilibrium constant can never be a negative number. (b) In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero. (c) As the value of the equilibrium constant increases the speed at which a reaction reaches equilibrium increases.

Which of the following statements are true and which are false? (a) For the reaction 2 A1g2 + B1g2 A2B1g2 Kc and Kp are numerically the same. (b) It is possible to distinguish Kc from Kp by comparing the units used to express the equilibrium constant. (c) For the equilibrium in (a), the value of Kc increases with increasing pressure.

If Kc = 0.042 for PCl31g2 + Cl21g2 PCl51g2 at 500 K, what is the value of Kp for this reaction at this temperature?

Calculate Kc at 303 K for SO21g2 + Cl21g2 SO2Cl21g2 if Kp = 34.5 at this temperature

The equilibrium constant for the reaction 2 NO1g2 + Br21g2 2 NOBr1g2 is Kc = 1.3 * 10-2 at 1000 K. (a) At this temperature does the equilibrium favor NO and Br2, or does it favor NOBr? (b) Calculate Kc for 2 NOBr1g2 2 NO1g2 + Br21g2. (c) Calculate Kc for NOBr1g2 NO1g2 + 1 2 Br21g2.

Consider the following equilibrium: 2 H21g2 + S21g2 2 H2S1g2 Kc = 1.08 * 107 at 700 C (a) Calculate Kp. (b) Does the equilibrium mixture contain mostly H2 and S2 or mostly H2S? (c) Calculate the value of Kc if you rewrote the equation H21g2 + 1 2 S21g2 H2S1g2.

At 1000 K, Kp = 1.85 for the reaction SO21g2 + 1 2 O21g2 SO31g2 (a) What is the value of Kp for the reaction SO31g2 SO21g2 + 1 2 O21g2? (b) What is the value of Kp for the reaction 2 SO21g2 + O21g2 2 SO31g2? (c) What is the value of Kc for the reaction in part (b)?

Consider the following equilibrium, for which Kp = 0.0752 at 480 C: 2 Cl21g2 + 2 H2O1g2 4 HCl1g2 + O21g2 (a) What is the value of Kp for the reaction 4 HCl1g2 + O21g2 2 Cl21g2 + 2 H2O1g2? (b) What is the value of Kp for the reaction Cl21g2 + H2O1g2 2 HCl1g2 + 1 2 O21g2? (c) What is the value of Kc for the reaction in part (b)?

The following equilibria were attained at 823 K: CoO1s2 + H21g2 Co1s2 + H2O1g2 Kc = 67 CoO1s2 + CO1g2 Co1s2 + CO21g2 Kc = 490 Based on these equilibria, calculate the equilibrium constant for H21g2 + CO21g2 CO1g2 + H2O1g2 at 823 K.

Consider the equilibrium N21g2 + O21g2 + Br21g2 2 NOBr1g2 Calculate the equilibrium constant Kp for this reaction, given the following information (at 298 K): 2 NO1g2 + Br21g2 2 NOBr1g2 Kc = 2.0 2 NO1g2 N21g2 + O21g2 Kc = 2.1 * 1030

Mercury(I) oxide decomposes into elemental mercury and elemental oxygen: 2 Hg2O1s2 4 Hg1l2 + O21g2. (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Suppose you run this reaction in a solvent that dissolves elemental mercury and elemental oxygen. Rewrite the equilibrium-constant expression in terms of molarities for the reaction, using (solv) to indicate solvation

Consider the equilibrium Na2O1s2 + SO21g2 Na2SO31s2. (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) All the compounds in this reaction are soluble in water. Rewrite the equilibriumconstant expression in terms of molarities for the aqueous reaction.

Methanol 1CH3OH2 is produced commercially by the catalyzed reaction of carbon monoxide and hydrogen: CO1g2 + 2 H21g2 CH3OH1g2. A n e q u i l i b r i u m mixture in a 2.00-L vessel is found to contain 0.0406 mol CH3OH, 0.170 mol CO, and 0.302 mol H2 at 500 K. Calculate Kc at this temperature.

Gaseous hydrogen iodide is placed in a closed container at 425 C, where it partially decomposes to hydrogen and iodine: 2 HI1g2 H21g2 + I21g2. At equilibrium it is found that 3HI4 = 3.53 * 10-3 M, 3H24 = 4.79 * 10-4 M, and 3I24 = 4.79 * 10-4 M. What is the value of Kc at this temperature?

The equilibrium 2 NO1g2 + Cl21g2 2 NOCl1g2 is established at 500 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (a) Calculate Kp for this reaction at 500.0 K. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl31g2 + Cl21g2 PCl51g2. A 7.5-L gas vessel is charged with a mixture of PCl31g2 and Cl21g2, which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are PPCl3 = 0.124 atm, PCl2 = 0.157 atm, and PPCl5 = 1.30 atm. (a) What is the value of Kp at this temperature? (b) Does the equilibrium favor reactants or products? (c) Calculate Kc for this reaction at 450 K.

A mixture of 0.10 mol of NO, 0.050 mol of H2, and 0.10 mol of H2O is placed in a 1.0-L vessel at 300 K. The following equilibrium is established: 2 NO1g2 + 2 H21g2 N21g2 + 2 H2O1g2 At equilibrium 3NO4 = 0.062 M. (a) Calculate the equilibrium concentrations of H2, N2, and H2O. (b) Calculate Kc.

A mixture of 1.374 g of H2 and 70.31 g of Br2 is heated in a 2.00-L vessel at 700 K. These substances react according to H21g2 + Br21g2 2 HBr1g2 At equilibrium, the vessel is found to contain 0.566 g of H2. (a) Calculate the equilibrium concentrations of H2, Br2, and HBr. (b) Calculate Kc.

A mixture of 0.2000 mol of CO2, 0.1000 mol of H2, and 0.1600 mol of H2O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO21g2 + H21g2 CO1g2 + H2O1g2 (a) Calculate the initial partial pressures of CO2, H2, and H2O. (b) At equilibrium PH2O = 3.51 atm. Calculate the equilibrium partial pressures of CO2, H2, and CO. (c) Calculate Kp for the reaction. (d) Calculate Kc for the reaction

A flask is charged with 1.500 atm of N2O41g2 and 1.00 atm NO21g2 at 25 C, and the following equilibrium is achieved: N2O41g2 2 NO21g2 After equilibrium is reached, the partial pressure of NO2 is 0.512 atm. (a) What is the equilibrium partial pressure of N2O4? (b) Calculate the value of Kp for the reaction. (c) Calculate Kc for the reaction.

Two different proteins X and Y are dissolved in aqueous solution at 37 C. The proteins bind in a 1:1 ratio to form XY. A solution that is initially 1.00 mM in each protein is allowed to reach equilibrium. At equilibrium, 0.20 mM of free X and 0.20 mM of free Y remain. What is Kc for the reaction?

A chemist at a pharmaceutical company is measuring equilibrium constants for reactions in which drug candidate molecules bind to a protein involved in cancer. The drug molecules bind the protein in a 1:1 ratio to form a drug protein complex. The protein concentration in aqueous solution at 25 C is 1.50 * 10-6 M. Drug A is introduced into the protein solution at an initial concentration of 2.00 * 10-6 M. Drug B is introduced into a separate, identical protein solution at an initial concentration of 2.00 * 10-6 M. At equilibrium, the drug A-protein solution has an A-protein complex concentration of 1.00 * 10-6 M, and the drug B solution has a B-protein complex concentration of 1.40 * 10-6 M. Calculate the Kc value for the A-protein binding reaction and for the Bprotein binding reaction. Assuming that the drug that binds more strongly will be more effective, which drug is the better choice for further research?

(a) If Qc 6 Kc, in which direction will a reaction proceed in order to reach equilibrium?

(b) What condition must be satisfied so that Qc = Kc?

(a) If Qc 7 Kc, how must the reaction proceed to reach equilibrium?

(b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of Qc at this point in the reaction?

At 100 C, the equilibrium constant for the reaction COCl21g2 CO1g2 + Cl21g2 has the value Kc = 2.19 * 10-10 . Are the following mixtures of COCl2, CO, and Cl2 at 100 C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium. (a) 3COCl24 = 2.00 * 10- 3 M, 3CO4 = 3.3 * 10-6 M, 3Cl24 = 6.62 * 10-6 M (b) 3COCl24 = 4.50 * 10-2 M, 3CO4 = 1.1 * 10-7 M, 3Cl24 = 2.25 * 10-6 M (c) 3COCl24 = 0.0100 M, 3CO4 = 3Cl24 = 1.48 * 10-6 M

As shown in Table 15.2, Kp for the equilibrium N21g2 + 3 H21g2 2 NH31g2 is 4.51 * 10-5 at 450 C. For each of the mixtures listed here, indicate whether the mixture is at equilibrium at 450 C. If it is not at equilibrium, indicate the direction (toward product or toward reactants) in which the mixture must shift to achieve equilibrium. (a) 98 atm NH3, 45 atm N2, 55 atm H2 (b) 57 atm NH3, 143 atm N2, no H2 (c) 13 atm NH3, 27 atm N2, 82 atm H2

At 100 C, Kc = 0.078 for the reaction SO2Cl21g2 SO21g2 + Cl21g2 In an equilibrium mixture of the three gases, the concentrations of SO2Cl2 and SO2 are 0.108 M and 0.052 M, respectively. What is the partial pressure of Cl2 in the equilibrium mixture?

At 900 K, the following reaction has Kp = 0.345: 2 SO21g2 + O21g2 2 SO31g2 In an equilibrium mixture the partial pressures of SO2 and O2 are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO3 in the mixture?

At 1285 C, the equilibrium constant for the reaction Br21g2 2 Br1g2 is Kc = 1.04 * 10-3 . A 0.200-L vessel containing an equilibrium mixture of the gases has 0.245 g Br21g2 in it. What is the mass of Br1g2 in the vessel?

For the reaction H21g2 + I21g2 2 HI1g2, Kc = 55.3 at 700 K. In a 2.00-L flask containing an equilibrium mixture of the three gases, there are 0.056 g H2 and 4.36 g I2. What is the mass of HI in the flask?

At 800 K, the equilibrium constant for I21g2 2 I1g2 is Kc = 3.1 * 10-5 . If an equilibrium mixture in a 10.0-L vessel contains 2.67 * 10-2 g of I(g), how many grams of I2 are in the mixture?

For 2 SO21g2 + O21g2 2 SO31g2, Kp = 3.0 * 104 at 700 K. In a 2.00-L vessel, the equilibrium mixture contains 1.17 g of SO3 and 0.105 g of O2. How many grams of SO2 are in the vessel?

At 2000 C, the equilibrium constant for the reaction 2 NO1g2 N21g2 + O21g2 is Kc = 2.4 * 103 . If the initial concentration of NO is 0.175 M, what are the equilibrium concentrations of NO, N2, and O2?

For the equilibrium Br21g2 + Cl21g2 2 BrCl1g2 at 400 K, Kc = 7.0. If 0.25 mol of Br2 and 0.55 mol of Cl2 are introduced into a 3.0-L container at 400 K, what will be the equilibrium concentrations of Br2, Cl2, and BrCl?

At 373 K, Kp = 0.416 for the equilibrium 2 NOBr1g2 2 NO1g2 + Br21g2 If the pressures of NOBr(g) and NO(g) are equal, what is the equilibrium pressure of Br21g2?

At 218 C, Kc = 1.2 * 10-4 for the equilibrium NH4SH1s2 NH31g2 + H2S1g2 Calculate the equilibrium concentrations of NH3 and H2S if a sample of solid NH4SH is placed in a closed vessel at 218 C and decomposes until equilibrium is reached.

Consider the reaction CaSO41s2 Ca 2+1aq2 + SO4 2-1aq2 At 25 C, the equilibrium constant is Kc = 2.4 * 10-5 for this reaction. (a) If excess CaSO41s2 is mixed with water at 25 C to produce a saturated solution of CaSO4, what are the equilibrium concentrations of Ca2+ and SO4 2-? (b) If the resulting solution has a volume of 1.4 L, what is the minimum mass of CaSO41s2 needed to achieve equilibrium?

At 80 C, Kc = 1.87 * 10-3 for the reaction PH3BCl31s2 PH31g2 + BCl31g2 (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80 C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH3BCl31s2 that must be added to the flask to achieve equilibrium?

At 80 C, Kc = 1.87 * 10-3 for the reaction PH3BCl31s2 PH31g2 + BCl31g2 (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80 C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH3BCl31s2 that must be added to the flask to achieve equilibrium?

At 25 C, the reaction CaCrO41s2 Ca 2+1aq2 + CrO4 2-1aq2 has an equilibrium constant Kc = 7.1 * 10-4 . What are the equilibrium concentrations of Ca 2 + and CrO4 2- in a saturated solution of CaCrO4?

Methane, CH4, reacts with I2 according to the reaction CH41g2 + l21g2 CH3l1g2 + HI1g2. At 630 K, Kp for this reaction is 2.26 * 10-4 . A reaction was set up at 630 K with initial partial pressures of methane of 105.1 torr and of 7.96 torr for I2. Calculate the pressures, in torr, of all reactants and products at equilibrium

The reaction of an organic acid with an alcohol, in organic solvent, to produce an ester and water is commonly done in the pharmaceutical industry. This reaction is catalyzed by strong acid (usually H2SO4). A simple example is the reaction of acetic acid with ethyl alcohol to produce ethyl acetate and water: CH3COOH1solv2 + CH3CH2OH1solv2 CH3COOCH2CH31solv2 + H2O1solv2 where (solv) indicates that all reactants and products are in solution but not an aqueous solution. The equilibrium constant for this reaction at 55 C is 6.68. A pharmaceutical chemist makes up 15.0 L of a solution that is initially 0.275 M in acetic acid and 3.85 M in ethanol. At equilibrium, how many grams of ethyl acetate are formed?

Consider the following equilibrium for which H 6 0 2 SO21g2 + O21g2 2 SO31g2 How will each of the following changes affect an equilibrium mixture of the three gases: (a) O21g2 is added to the system; (b) the reaction mixture is heated; (c) the volume of the reaction vessel is doubled; (d) a catalyst is added to the mixture; (e) the total pressure of the system is increased by adding a noble gas; (f) SO31g2 is removed from the system?

Consider the reaction 4 NH31g2 + 5 O21g2 4 NO1g2 + 6 H2O1g2, H = -904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (a) increase 3NH34; (b) increase 3H2O4; (c) decrease 3O24; (d) decrease the volume of the container in which the reaction occurs; (e) add a catalyst; (f) increase temperature.

How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant, (b) removal of a product, (c) decrease in the volume, (d) decrease in the temperature, (e) addition of a catalyst?

For a certain gas-phase reaction, the fraction of products in an equilibrium mixture is increased by either increasing the temperature or by increasing the volume of the reaction vessel. (a) Is the reaction exothermic or endothermic? (b) Does the balanced chemical equation have more molecules on the reactant side or product side?

Consider the following equilibrium between oxides of nitrogen 3 NO1g2 NO21g2 + N2O1g2 (a) Use data in Appendix C to calculate H for this reaction. (b) Will the equilibrium constant for the reaction increase or decrease with increasing temperature? (c) At constant temperature, would a change in the volume of the container affect the fraction of products in the equilibrium mixture?

Methanol 1CH3OH2 can be made by the reaction of CO with H2: CO1g2 + 2 H21g2 CH3OH1g2 (a) Use thermochemical data in Appendix C to calculate H for this reaction. (b) To maximize the equilibrium yield of methanol, would you use a high or low temperature? (c) To maximize the equilibrium yield of methanol, would you use a high or low pressure?

Ozone, O3, decomposes to molecular oxygen in the stratosphere according to the reaction 2 O31g2 3 O21g2. Would an increase in pressure favor the formation of ozone or of oxygen?

The watergas shift reaction CO1g2 + H2O1g2 CO21g2 + H21g2 is used industrially to produce hydrogen. The reaction enthalpy is H = -41 kJ. (a) To increase the equilibrium yield of hydrogen would you use high or low temperature? (b) Could you increase the equilibrium yield of hydrogen by controlling the pressure of this reaction? If so would high or low pressure favor formation of H21g2?

Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps: CO1g2 + Cl21g2 COCl1g2 + Cl1g2 At 25 C, the rate constants for the forward and reverse reactions are 1.4 * 10-28 M-1 s -1 and 9.3 * 1010 M-1 s -1 , respectively. (a) What is the value for the equilibrium constant at 25 C? (b) Are reactants or products more plentiful at equilibrium?

If Kc = 1 for the equilibrium 2 A1g2 B1g2, what is the relationship between [A] and [B] at equilibrium?

A mixture of CH4 and H2O is passed over a nickel catalyst at 1000 K. The emerging gas is collected in a 5.00-L flask and is found to contain 8.62 g of CO, 2.60 g of H2, 43.0 g of CH4, and 48.4 g of H2O. Assuming that equilibrium has been reached, calculate Kc and Kp for the reaction CH41g2 + H2O1g2 CO1g2 + 3 H21g2.

When 2.00 mol of SO2Cl2 is placed in a 2.00-L flask at 303 K, 56% of the SO2Cl2 decomposes to SO2 and Cl2: SO2Cl21g2 SO21g2 + Cl21g2 (a) Calculate Kc for this reaction at this temperature. (b) Calculate Kp for this reaction at 303 K. (c) According to Le Chteliers principle, would the percent of SO2Cl2 that decomposes increase, decrease or stay the same if the mixture were transferred to a 15.00-L vessel? (d) Use the equilibrium constant you calculated above to determine the percentage of SO2Cl2 that decomposes when 2.00 mol of SO2Cl2 is placed in a 15.00-L vessel at 303 K.

A mixture of H2, S, and H2S is held in a 1.0-L vessel at 90 C and reacts according to the equation: H21g2 + S1s2 H2S1g2 At equilibrium, the mixture contains 0.46 g of H2S and 0.40 g H2. (a) Write the equilibrium-constant expression for this reaction. (b) What is the value of Kc for the reaction at this temperature?

A mixture of H2, S, and H2S is held in a 1.0-L vessel at 90 C and reacts according to the equation: H21g2 + S1s2 H2S1g2 At equilibrium, the mixture contains 0.46 g of H2S and 0.40 g H2. (a) Write the equilibrium-constant expression for this reaction. (b) What is the value of Kc for the reaction at this temperature?

Consider the hypothetical reaction A1g2 2 B1g2. A flask is charged with 0.75 atm of pure A, after which it is allowed to reach equilibrium at 0 C. At equilibrium, the partial pressure of A is 0.36 atm. (a) What is the total pressure in the flask at equilibrium? (b) What is the value of Kp? (c) What could we do to maximize the yield of B?

As shown in Table 15.2, the equilibrium constant for the reaction N21g2 + 3 H21g2 2 NH31g2 is Kp = 4.34 * 10-3 at 300 C. Pure NH3 is placed in a 1.00-L flask and allowed to reach equilibrium at this temperature. There are 1.05 g NH3 in the equilibrium mixture. (a) What are the masses of N2 and H2 in the equilibrium mixture? (b) What was the initial mass of ammonia placed in the vessel? (c) What is the total pressure in the vessel?

For the equilibrium 2 IBr1g2 I21g2 + Br21g2 Kp = 8.5 * 10-3 at 150 C. If 0.025 atm of IBr is placed in a 2.0-L container, what is the partial pressure of all substances after equilibrium is reached?

For the equilibrium PH3BCl31s2 PH31g2 + BCl31g2 Kp = 0.052 at 60 C. (a) Calculate Kc. (b) After 3.00 g of solid PH3BCl3 is added to a closed 1.500-L vessel at 60 C, the vessel is charged with 0.0500 g of BCl31g2. What is the equilibrium concentration of PH3?

Solid NH4SH is introduced into an evacuated flask at 24 C. The following reaction takes place: NH4SH1s2 NH31g2 + H2S1g2 At equilibrium, the total pressure (for NH3 and H2S taken together) is 0.614 atm. What is Kp for this equilibrium at 24 C?

A 0.831-g sample of SO3 is placed in a 1.00-L container and heated to 1100 K. The SO3 decomposes to SO2 and O2: 2 SO31g2 2 SO21g2 + O21g2 At equilibrium, the total pressure in the container is 1.300 atm. Find the values of Kp and Kc for this reaction at 1100 K.

Nitric oxide (NO) reacts readily with chlorine gas as follows: 2 NO1g2 + Cl21g2 2 NOCl1g At 700 K, the equilibrium constant Kp for this reaction is 0.26. Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) PNO = 0.15 atm, PCl2 = 0.31 atm, PNOCl = 0.11 atm (b) PNO = 0.12 atm, PCl2 = 0.10 atm, PNOCl = 0.050 atm (c) PNO = 0.15 atm, PCl2 = 0.20 atm, PNOCl = 5.10 * 10-3 atm

At 900 C, Kc = 0.0108 for the reaction CaCO31s2 CaO1s2 + CO21g2 A mixture of CaCO3, CaO, and CO2 is placed in a 10.0-L vessel at 900 C. For the following mixtures, will the amount of CaCO3 increase, decrease, or remain the same as the system approaches equilibrium? (a) 15.0 g CaCO3, 15.0 g CaO, and 4.25 g CO2 (b) 2.50 g CaCO3, 25.0 g CaO, and 5.66 g CO2 (c) 30.5 g CaCO3, 25.5 g CaO, and 6.48 g CO2

When 1.50 mol CO2 and 1.50 mol H2 are placed in a 3.00-L container at 395 C, the following reaction occurs: CO21g2 + H21g2 CO1g2 + H2O1g2. If Kc = 0.802, what are the concentrations of each substance in the equilibrium mixture?

The equilibrium constant Kc for C1s2 + CO21g2 2 CO1g2 is 1.9 at 1000 K and 0.133 at 298 K. (a) If excess C is allowed to react with 25.0 g of CO2 in a 3.00-L vessel at 1000 K, how many grams of CO are produced? (b) How many grams of C are consumed? (c) If a smaller vessel is used for the reaction, will the yield of CO be greater or smaller? (d) Is the reaction endothermic or exothermic?

NiO is to be reduced to nickel metal in an industrial process by use of the reaction NiO1s2 + CO1g2 Ni1s2 + CO21g2 At 1600 K, the equilibrium constant for the reaction is Kp = 6.0 * 102 . If a CO pressure of 150 torr is to be employed in the furnace and total pressure never exceeds 760 torr, will reduction occur?

Le Chtelier noted that many industrial processes of his time could be improved by an understanding of chemical equilibria. For example, the reaction of iron oxide with carbon monoxide was used to produce elemental iron and CO2 according to the reaction Fe2O31s2 + 3 CO1g2 2 Fe1s2 + 3 CO21g2 Even in Le Chteliers time, it was noted that a great deal of CO was wasted, expelled through the chimneys over the furnaces. Le Chtelier wrote, Because this incomplete reaction was thought to be due to an insufficiently prolonged contact between carbon monoxide and the iron ore [oxide], the dimensions of the furnaces have been increased. In England, they have been made as high as 30 m. But the proportion of carbon monoxide escaping has not diminished, thus demonstrating, by an experiment costing several hundred thousand francs, that the reduction of iron oxide by carbon monoxide is a limited reaction. Acquaintance with the laws of chemical equilibrium would have permitted the same conclusion to be reached more rapidly and far more economically. What does this anecdote tell us about the equilibrium constant for this reaction?

At 700 K, the equilibrium constant for the reaction CCl41g2 C1s2 + 2 Cl21g2 is Kp = 0.76. A flask is charged with 2.00 atm of CCl4, which then reaches equilibrium at 700 K. (a) What fraction of the CCl4 is converted into C and Cl2? (b) What are the partial pressures of CCl4 and Cl2 at equilibrium?

The reaction PCl31g2 + Cl21g2 PCl51g2 has Kp = 0.0870 at 300 C. A flask is charged with 0.50 atm PCl3, 0.50 atm Cl2, and 0.20 atm PCl5 at this temperature. (a) Use the reaction quotient to determine the direction the reaction must proceed to reach equilibrium. (b) Calculate the equilibrium partial pressures of the gases. (c) What effect will increasing the volume of the system have on the mole fraction of Cl2 in the equilibrium mixture? (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of Cl2 in the equilibrium mixture?

An equilibrium mixture of H2, I2, and HI at 458 C contains 0.112 mol H2, 0.112 mol I2, and 0.775 mol HI in a 5.00-L vessel. What are the equilibrium partial pressures when equilibrium is reestablished following the addition of 0.200 mol of HI?

Consider the hypothetical reaction A1g2 + 2 B1g2 2 C1g2, for which Kc = 0.25 at a certain temperature. A 1.00-L reaction vessel is loaded with 1.00 mol of compound C, which is allowed to reach equilibrium. Let the variable x represent the number of mol>L of compound A present at equilibrium. (a) In terms of x, what are the equilibrium concentrations of compounds B and C? (b) What limits must be placed on the value of x so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of x) into the equilibriumconstant expression, derive an equation that can be solved for x. (d) The equation from part (c) is a cubic equation (one that has the form ax3 + bx2 + cx + d = 0). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of x that you specified in part (b). The point at which the cubic equation crosses the x-axis is the solution. (e) From the plot in part (d), estimate the equilibrium concentrations of A, B, and C. (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

At 1200 K, the approximate temperature of automobile exhaust gases (Figure 15.15), Kp for the reaction 2 CO21g2 2 CO1g2 + O21g2 is about 1 * 10-13 . Assuming that the exhaust gas (total pressure 1 atm) contains 0.2% CO, 12% CO2, and 3% O2 by volume, is the system at equilibrium with respect to the CO2 reaction? Based on your conclusion, would the CO concentration in the exhaust be decreased or increased by a catalyst that speeds up the CO2 reaction? Recall that at a fixed pressure and temperature, volume % = mol %.

Suppose that you worked at the U.S. Patent Office and a patent application came across your desk claiming that a newly developed catalyst was much superior to the Haber catalyst for ammonia synthesis because the catalyst led to much greater equilibrium conversion of N2 and H2 into NH3 than the Haber catalyst under the same conditions. What would be your response?

Consider the reaction IO4 -1aq2 + 2 H2O1l2 H4IO6 -1aq2; Kc = 3.5 * 10-2 . If you start with 25.0 mL of a 0.905 M solution of NaIO4, and then dilute it with water to 500.0 mL, what is the concentration of H4IO6 - at equilibrium?

Silver chloride, AgCl(s), is an insoluble strong electrolyte. (a) Write the equation for the dissolution of AgCl(s) in H2O1l2. (b) Write the expression for Kc for the reaction in part (a). (c) Based on the thermochemical data in Appendix C and Le Chteliers principle, predict whether the solubility of AgCl in H2O increases or decreases with increasing temperature. (d) The equilibrium constant for the dissolution of AgCl in water is 1.6 * 10-10 at 25 C. In addition, Ag+1aq2 can react with Cl -1aq2 according to the reaction Ag+1aq2 + 2 Cl -1aq2 AgCl2 -1aq2 where Kc = 1.8 * 105 at 25 C. Although AgCl is not soluble in water, the complex AgCl2 - is soluble. At 25 C, is the solubility of AgCl in a 0.100 M NaCl solution greater than the solubility of AgCl in pure water, due to the formation of soluble AgCl2 - ions? Or is the AgCl solubility in 0.100 M NaCl less than in pure water because of a Le Chtelier-type argument? Justify your answer with calculations. (Hint: Any form in which silver is in solution counts as solubility.)

Consider the equilibrium A B in which both the forward and reverse reactions are elementary (single- step) reactions. Assume that the only effect of a catalyst on the reaction is to lower the activation energies of the forward and reverse reactions, as shown in Figure 15.14. Using the Arrhenius equation (Section 14.5), prove that the equilibrium constant is the same for the catalyzed reaction as for the uncatalyzed one.

The phase diagram for SO2 is shown here. (a) What does this diagram tell you about the enthalpy change in the reaction SO21l2 SO21g2? (b) Calculate the equilibrium constant for this reaction at 100 C and at 0 C. (c) Why is it not possible to calculate an equilibrium constant between the gas and liquid phases in the supercritical region? (d) At which of the three points marked in red does SO21g2 most closely approach ideal-gas behavior? (e) At which of the three red points does SO21g2 behave least ideally? Gas Critical point Supercritical region Liquid Temperature (C) Pressure (atm) 0 100 200 300 102 10 1 101

Write the equilibrium-constant expression for the equilibrium C1s2 + CO21g2 2 CO1g2 The table that follows shows the relative mole percentages of CO21g2 and CO(g) at a total pressure of 1 atm for several temperatures. Calculate the value of Kp at each temperature. Is the reaction exothermic or endothermic? Temperature 1C2 Co2 1mol %2 Co 1mol %2 850 6.23 93.77 950 1.32 98.68 1050 0.37 99.63 1200 0.06 99.94

In Section 11.5, we defined the vapor pressure of a liquid in terms of an equilibrium. (a) Write the equation representing the equilibrium between liquid water and water vapor and the corresponding expression for Kp. (b) By using data in Appendix B, give the value of Kp for this reaction at 30 C. (c) What is the value of Kp for any liquid in equilibrium with its vapor at the normal boiling point of the liquid?

Water molecules in the atmosphere can form hydrogenbonded dimers, 1H2O22. The presence of these dimers is thought to be important in the nucleation of ice crystals in the atmosphere and in the formation of acid rain. (a) Using VSEPR theory, draw the structure of a water dimer, using dashed lines to indicate intermolecular interactions. (b) What kind of intermolecular forces are involved in water dimer formation? (c) The Kp for water dimer formation in the gas phase is 0.050 at 300 K and 0.020 at 350 K. Is water dimer formation endothermic or exothermic?

The protein hemoglobin (Hb) transports O2 in mammalian blood. Each Hb can bind 4 O2 molecules. The equilibrium constant for the O2 binding reaction is higher in fetal hemoglobin than in adult hemoglobin. In discussing protein oxygen-binding capacity, biochemists use a measure called the P50 value, defined as the partial pressure of oxygen at which 50% of the protein is saturated. Fetal hemoglobin has a P50 value of 19 torr, and adult hemoglobin has a P50 value of 26.8 torr. Use these data to estimate how much larger Kc is for the aqueous reaction 4 O21g2 + Hb1aq2 3Hb1O2241aq24.

The reaction between hydrogen and iodine to form hydrogen iodide was used to illustrate Beer’s law in Chapter 14 (Figure 14.5). The reaction can be monitored using visible-light spectroscopy because \(I_{2}\) has a violet color while \(H_{2} \text { and } H I\) are colorless. At \(300 K\), the equilibrium constant for the reaction \(H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \text { is } K_{c}=794\). To answer the following questions assume you have access to hydrogen, iodine, hydrogen iodide, a transparent reaction vessel, a visible-light spectrometer, and a means for changing the temperature. (a) Which gas or gases concentration could you readily monitor with the spectrometer? (b) To use Beer’s law (Equation 14.5) you need to determine the extinction coefficient, \(\varepsilon\) , for the substance in question. How would you determine \(\varepsilon\)? (c) Describe an experiment for determining the equilibrium constant at \(600 K\). (d) Use the bond enthalpies in Table 8.4 to estimate the enthalpy of this reaction. (e) Based on your answer to part (d), would you expect \(K_{c} \text { at } 600 K\) to be larger or smaller than at \(300 K\)? Equation Transcription: ? Text Transcription: I_{2} H_{2} \text { and } H I 300 K H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \text { is } K_{c}=794 \varepsilon \varepsilon 600 K K_{c} \text { at } 600 K 300 K

(a) Based on the following energy profile, predict whether \(k_{f}>k_{r} \text { or } k_{f}<k_{r}\) (b) Using Equation 15.5, predict whether the equilibrium constant for the process is greater than 1 or less than 1. [Section 15.1] Equation Transcription: Text Transcription: k_{f}>k_{r} \text { or } k_{f}<k_{r}

The following diagram represents an equilibrium mixture produced for a reaction of the type \(A+X \rightleftharpoons A X\). Is K greater or smaller than 1 if the volume is 1 L and each atom/ molecule in the diagram represents 1 mol? [Section 15.2] Equation Transcription: ? Text Transcription: A+X \rightleftharpoons A X

The following diagrams represent a hypothetical reaction \(A \rightarrow B\), with A represented by red spheres and B represented by blue spheres. The sequence from left to right represents the system as time passes. Does the system reach equilibrium? If so, in which diagram is the system in equilibrium? [Sections 15.1 and 15.2] Equation Transcription: Text Transcription: A \rightarrow B

Problem 4E Visualizing Concepts The following diagram represents a reaction shown going to completion. Each molecule in the diagram represents 0.1 mol and the volume of the box is 1.0L (a) Letting A = red spheres and B = blue spheres, write a balanced equation for the reaction (b) Write the equilibrium-constant expression for the reaction (c) Calculate the value of Kc (d) Assuming that all of the molecules are in the gas phase, calculate , the change in the number of gas molecules that accompanies the reaction (e) Calculate the value of Kp.

Snapshots of two hypothetical reactions, \(A(g)+B(g) \rightleftharpoons A B(g) \text { and } X(g)+Y(g) \rightleftharpoons X Y(g)\) at five different times are shown here. Which reaction has a larger equilibrium constant? [Sections 15.1 and 15.2] Equation Transcription: ?? ? ? Text Transcription: A(g)+B(g) \rightleftharpoons A B(g) \text { and } X(g)+Y(g) \rightleftharpoons X Y(g) t=10 \mathrm{~s} A(g)+B(g) \rightleftharpoons A B(g) t=10 \mathrm{~s} X(g)+Y(g) \rightleftharpoons X Y(g)

Ethene (C2H4) reacts with halogens (X2) by the following reaction: C2H4(g) + X2(g) ? C2H4X2(g) The following figures represent the concentrations at equilibrium at the same temperature when X2 is Cl2 (green), Br2 (brown), and I2 (purple). List the equilibria from smallest to largest equilibrium constant. [Section 15.3]

When lead (IV) oxide is heated above \(300^{\circ} \mathrm{C}\) it decomposes according to the following reaction \(\mathrm{PbO}_{2}(s) \rightleftharpoons P b O(s)+O_{2}(g)\). Consider the two sealed vessels of \(\mathrm{PbO}_{2}\) shown here. If both vessels are heated to \(400^{\circ} \mathrm{C}\) and allowed to come to equilibitum which of the following statements is true? (a) There will be less \(\mathrm{PbO}_{2}\) remaining in vessel A, (b) There will be less \(\mathrm{PbO}_{2}\) remaining in vessel B, (c) The amount of \(\mathrm{PbO}_{2}\) remaining in each vessel will be the same. [Section 15.4] Equation Transcription: ? Text Transcription: 300°C PbO}_{2}(s) \rightleftharpoons P b O(s)+O_{2}(g) PbO}_{2} 400°C PbO}_{2} PbO}_{2} PbO}_{2}

The reaction \(A_{2}+B_{2} \rightleftharpoons 2 A B\) has an equilibrium constant \(K_{c}=1.5\). The following diagrams represent reaction mixtures containing \(A_{2}\) molecules (red), \(B_{2}\) molecules (blue), and AB molecules. (a) Which reaction mixture is at equilibrium? (b) For those mixtures that are not at equilibrium, how will the reaction proceed to reach equilibrium? [Sections 15.5 and 15.6] Equation Transcription: ? Text Transcription: A_{2}+B_{2} \rightleftharpoons 2 A B K_{c}=1.5 A_{2} B_{2}

The reaction \(A_{2}(g)+B(g) \rightleftharpoons A(g)+A B(g)\) has an equilibrium constant of \(K_{p}=2\). The accompanying diagram shows a mixture containing A atoms (red), \(A_{2}\) molecules, and AB molecules (red and blue). How many B atoms should be added to the diagram to illustrate an equilibrium mixture? [Section 15.6] Equation Transcription: ? Text Transcription: A_{2}(g)+B(g) \rightleftharpoons A(g)+A B(g) K_{p}=2 A_{2}

The diagram shown here represents the equilibrium state for the reaction \(A_{2}(g)+2 B(g) \leftrightarrow 2 A B(g)\). (a) Assuming the volume is 2 L, calculate the equilibrium constant \(K_{0}\) for the reaction. (b) If the volume of the equilibrium mixture is decreased, will the number of AB molecules increase or decrease? [Sections 15.5 and 15.7] Equation transcription: Text transcription: A_{2}(g)+2 B(g) \leftrightarrow 2 A B(g) K_{0}

The following diagrams represent equilibrium mixtures for the reaction \(A_{2}+B \rightleftharpoons A+A B\) at 300 K and 500 K. The A atoms are red, and the B atoms are blue. Is the reaction exothermic or endothermic? [Section 15.7] Equation transcription: Text transcription: A_{2}+B rightleftharpoons A+A B

The following graph represents the yield of the compound AB at equilibrium in the reaction A(g) + B(g) ? AB(g) at two different pressures, x and y, as a function of temperature. (a) Is this reaction exothermic or endothermic? (b) Is P = x greater or smaller than P = y? [Section 15.7] Equation transcription: Text transcription: A(g)+B(g) \rightarrow A B(g)

Problem 13E Equilibrium; The Equilibrium Constant (Sections) Suppose that the gas-phase reactions A. B and B . A are both elementary processes with rate constants of 4.7 x 10-3 s-1 and 5.8 x 10—1 s-1, respectively (a) What is the value of the equilibrium constant for the equilibrium A(g) = 8(g)? (b) Which is greater at equilibrium, the partial pressure of A or the partial pressure of 8?

Problem 14E Equilibrium; The Equilibrium Constant (Sections) Consider the reaction A + B - C + D. Assume that both the forward reaction and the reverse reaction are elementary processes and that the value of the equilibrium constant is very large (a) Which species predominate at equilibrium, reactants or products? (b) Which reaction has the larger rate constant, the forward or the reverse?

Problem 15E Equilibrium; The Equilibrium Constant (Sections) Write the expression for Kc for the following reactions. In each case Indicate whether the reaction is homogeneous or heterogeneous. (a) 3 NO(g) = N20(g) + N02(g) (b) CH4(g) + 2 H2S(g) = CS2(g) + 4 H2(g) (c) Ni(CO)4(g) = Ni(s) + 4 CO(g) (d) HF(ag) = H+(ag) + F-(ag) (e) 2 Ag(s) + Zn2+(ag) = 2 Ag+(ag) + Zn(s) (f) H20(/) = H+(ag) + OH-(ag) (g) 2 H2O(0 = 2 H+(ag) + 2 OH-(ag)

Problem 16E Equilibrium; The Equilibrium Constant (Sections) Write the expressions for Kc for the following reactions. In each case Indicate whether the reaction is homogeneous or heterogeneous. (a) 2 03(g) = 3 02(g) (b) Ti(s) + 2 012(g) = TiCI4(/) (C) 2 C2H4(g) + 2 H20(g) = 2 C2H6(g) + 02(g) (d) C(S) + 2 H2(g) = CH4(g) (e) 4 HCI(ag) + 02(g) = 2 H20(/) + 2 012(g) (f) 2 C8H18(/) + 25 02(g) = 16 002(g) + 18 H20(g) (g) 2 C8H18(/) + 25 02(g) = 16 002(g) + 18 H20(/)

Problem 17E Equilibrium; The Equilibrium Constant (Sections) When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products? (a) N2(g) + 02(g) = 2 NO(g); Kc= 1,5 * 10-10 (b) 2 S02(g) + 02(g) = 2 S03(g); Kp = 2,5 X 109

Problem 18E Equilibrium; The Equilibrium Constant (Sections) Which of the following reactions lies to the right, favoring the formation of products, and which lies to the left, favoring formation of reactants? (a) 2 NO(g) + 02(g) - 2 N02(g); Kp = 5.0 x 1012 (b) 2 HBr(g) - H2(g) + Br2(g); Kc = 5.8 x 10-18

Problem 19E Equilibrium; The Equilibrium Constant (Sections) Which of the following statements are true and which are false? (a) The equilibrium constant can never be a negative number, (b) In reactions that we draw with a single-headed arrow, the equilibrium constant has a value that is very close to zero, (c) As the value of the equilibrium constant increases the speed at which a reaction reaches equilibrium increases.

Problem 20E Equilibrium; The Equilibrium Constant (Sections) Which of the following statements are true and which are false? (a) For the reaction 2 A(g) + B(g) - A2B(g) Kc and Kp are numerically the same (b) It is possible to distinguish Kc from Kp by comparing the units used to express the equilibrium constant (c) For the equilibrium in (a), the value of Kc increases with increasing pressure

Problem 21E Equilibrium; The Equilibrium Constant (Sections) If Kc = 0.042 for PCI3(gr) + CI2(g) - PCI5(g) at 500 K, what is the value of Kp for this reaction at this temperature?

Problem 22E Equilibrium; The Equilibrium Constant (Sections) Calculate Kc at 303 K for SQ2(g) + CI2(g) -S02CI2(g) if Kp = 34.5 at this temperature.

Problem 23E Equilibrium; The Equilibrium Constant (Sections) The equilibrium constant for the reaction 2 NO(g) + Br2(g) - 2 NOBr(g) is Kc =1.3x10-2 at 1000 K (a) At this temperature does the equilibrium favor NO and Br2, or does it favor NOBr? (b) Calculate Kc for 2 NOBr(g) -2 NO(g) + Br2(g). (c) Calculate Kc for NOBr(g).NO(g) + !4 Br2(g).

Problem 24E Equilibrium; The Equilibrium Constant (Sections) Consider the following equilibrium: 2 H2(g) + S2(g) - 2 H2S(g) Kc = 1.08 * 107at 700 °C (a) Calculate Kp(b) Does the equilibrium mixture contain mostly H2 and S2 or mostly H2S? (c) Calculate the value of Kc if you rewrote the equation H2(g) + % S2(g) - H2S(g).

Problem 25E Equilibrium; The Equilibrium Constant (Sections) At 1000 K, Kp = 1.85 for the reaction S02(g) + y2 02(g) - S03(g) (a) What is the value of Kp for the reaction S03(g) - S02(g) + !4 02(g)? (b) What is the value of Kp for the reaction 2 S02(g) + 02(g) - 2 S03(g)? (c) What is the value of Kc for the reaction in part (b)?

Problem 26E Equilibrium; The Equilibrium Constant (Sections) Consider the following equilibrium, for which Kp = 0.0752 at 480 °C: 2 CI2(g) + 2 H20(g) s± 4 HCI(g) + 02(g) (a) What is the value of Kp for the reaction 4 HCI(g) + 02(g) - 2 CI2(g) + 2 H20(g)? (b) What is the value of Kp for the reaction CI2(g) + H20(g) - 2 HCI(g) + 7202(g)? (c) What is the value of Kc for the reaction in part (b)?

Problem 27E Equilibrium; The Equilibrium Constant (Sections) The following equilibria were attained at 823 K: CoO(s) + H2(g) 5± Co(s) + H20(g) Kc = 67 CoO(s) + CO(g) - Co(s) + C02(g) Kc = 490 Based on these equilibria, calculate the equilibrium constant for H2(g) + C02(g) - CO(g) + H20(g) at 823 K.

Problem 28E Equilibrium; The Equilibrium Constant (Sections) Consider the equilibrium N2(g) + 02(g) + Br2(g) - 2 NOBr(gj Calculate the equilibrium constant Kp for this reaction, given the following information (at 298 K): 2 NO(g) + Br2(g)-2 NOBr(g) Kc = 2.0 2 NO(g)-N2(g) + 02(g) Kc = 2.1 x 1030

Problem 29E Equilibrium; The Equilibrium Constant (Sections) Mercury(l) oxide decomposes into elemental mercury and elemental oxygen: 2 Hg20(s) - 4 Hg(0 + 02(g) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures (b) Suppose you run this reaction in a solvent that dissolves elemental mercury and elemental oxygen. Rewrite the equilibrium-constant expression in terms of molarities for the reaction, using (solv) to indicate solvation.

Problem 30E Equilibrium; The Equilibrium Constant (Sections) Consider the equilibrium Na20(s) + S02(g)-Na2S03(s) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures (b) All the compounds in this reaction are soluble in water. Rewrite the equilibrium constant expression in terms of molarities for the aqueous reaction.

Problem 31E Calculating Equilibrium Constants (Section) Methanol (CH30H) is produced commercially by the catalyzed reaction of carbon monoxide and hydrogen: CO(g) + 2 H2(g) - CH30H(g). An equ i I ibr ium mixture in a 2.00-L vessel is found to contain 0.0406 mol CH30H, 0.170 mol CO, and 0.302 mol H2 at 500 K. Calculate Kc at this temperature.

Problem 32E Calculating Equilibrium Constants (Section) Gaseous hydrogen iodide is placed in a closed container at 425 °C, where it partially decomposes to hydrogen and iodine: 2 Hl(gr) - H2(g) + 12(g). At equilibrium it is found that [HI] = 3.53 x 10-3 M, [H2] = 4.79 x 10-4 M, and [I2] = 4.79 x 10-4 M. What is the value of Kc at this temperature?

Problem 33E Calculating Equilibrium Constants (Section) The equilibrium 2 NO(g) + CI2(g) - 2 NOCI(g) is established at 500 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, CI2, and NOCI. respectively (a) Calculate Kp for this reaction at 500.0 K (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.

Problem 34E Calculating Equilibrium Constants (Section) Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCI3(g) + CI2(g) - PCI5(g). A 7.5-L gas vessel is charged with a mixture of PCI3(g) and CI2(g), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are PPCI3 = 0.124 atm, PCI2 = 0.157 atm, and PPCI5 = 1.30 atm (a) What is the value of Kp at this temperature? (b) Does the equilibrium favor reactants or products? (c) Calculate Kc for this reaction at 450 K.

Problem 35E Calculating Equilibrium Constants (Section) A mixture of 0.10 mol of NO, 0.050 mol of H2, and 0.10 mol of H20 is placed in a 1 0-L vessel at 300 K. The following equilibrium is established: 2 NO(g) + 2 H2(g) - N2(g) + 2 H20(g) At equilibrium [NO] = 0.062 M (a) Calculate the equilibrium concentrations of H2, N2, and H20 (b) Calculate Kc

Problem 36E Calculating Equilibrium Constants (Section) A mixture of 1.374 g of H2 and 70.31 g of Br2 is heated in a 2.00-L vessel at 700 K. These substances react according to H2(g) + Br2(g) - 2 HBr(g) At equilibrium, the vessel is found to contain 0.566 g of H2 (a) Calculate the equilibrium concentrations of H2, Br2, and HBr (b) Calculate Kc..

Problem 37E Calculating Equilibrium Constants (Section) A mixture of 0.2000 mol of C02, 0.1000 mol of H2, and 0.1600 mol of H20 is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: C02(g) + H2(g) - CO(g) + H20(g) (a) Calculate the initial partial pressures of C02, H2, and H20. (b) At equilibrium PH20 = 3.51 atm. Calculate the equilibrium partial pressures of C02, H2, and CO (c) Calculate Kp for the reaction (d) Calculate Kc for the reaction.

Problem 38E Calculating Equilibrium Constants (Section) A flask is charged with 1.500 atm of N204(g) and 1.00 atm N02(g) at 25 °C, and the following equilibrium is achieved: N204(g) ss 2 N02(g) After equilibrium is reached, the partial pressure of N02 is 0.512 atm (a) What is the equilibrium partial pressure of N204? (b) Calculate the value of Kp for the reaction (c) Calculate Kc for the reaction.

Problem 39E Calculating Equilibrium Constants (Section) Two different proteins X and Y are dissolved in aqueous solution at 37 °C. The proteins bind in a 1:1 ratio to form XY. A solution that is initially 1.00 mM in each protein is allowed to reach equilibrium. At equilibrium, 0.20 mM of free X and 0.20 mM of free Y remain. What is Kc for the reaction?

Problem 40E Calculating Equilibrium Constants (Section) A chemist at a pharmaceutical company is measuring equilibrium constants for reactions in which drug candidate molecules bind to a protein involved in cancer. The drug molecules bind the protein in a 1:1 ratio to form a drug-protein complex. The protein concentration in aqueous solution at 25 °C is 1.50 x 10-6M. Drug A is introduced into the protein solution at an initial concentration of 2.00 x 10-6M. Drug B is introduced into a separate, identical protein solution at an initial concentration of 2.00 x 10-6M. At equilibrium, the drug A-protein solution has an A-protein complex concentration of 1.00 x 10-6M, and the drug B solution has a B-protein complex concentration of 1.40 x 10-6M. Calculate the Kc value for the A-protein binding reaction and for the Bprotein binding reaction. Assuming that the drug that binds more strongly will be more effective, which drug is the better choice for further research?

Problem 41E Applications of Equilibrium Constants (Section) (a) If Qc6 Kc, in which direction will a reaction proceed in order to reach equilibrium? (b) What condition must be satisfied so that Qc = Kc?

Problem 42E Applications of Equilibrium Constants (Section) (a) If Qc7 Kc, how must the reaction proceed to reach equilibrium? (b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of Qc at this point in the reaction?

Problem 43E Applications of Equilibrium Constants (Section) At 100 °C. the equilibrium constant for the reaction COCI2(g) - CO(g) + CI2(g) has the value Kc = 2.19 x 10-10. Are the following mixtures of COCI2, CO, and CI2 at 100 °C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium. (a) [COCI2] = 2.00 x 10-3 M, [CO] = 3.3 x 10-6 M, [CI2] = 6.62 x 10-6 M (b) [COCI2] = 4.50 x 10-2 M, [CO] = 1.1 x 10-7 M, [CI2] = 2.25 x 10-6 M (C) [COCI2] = 0.0100 M, [CO] = [CI2] = 1.48 x 10-6 M

As shown in Table 15.2, \(K_{p}\) for the equilibrium \(N_{2}(g)+3 H_{2}(g) \leftrightarrow 2 N H_{2}(g)\) is \(4.51 x 10^{-5}\) at \(450^{0} \mathrm{C}\). For each of the mixtures listed here, indicate whether the mixture is at equilibrium at \(450^{0} \mathrm{C}\). If it is not at equilibrium, indicate the direction (toward product or toward reactants) in which the mixture must shift to achieve equilibrium. (a) 98 atm \(\mathrm{NH}_{3}\), 45 atm \(N_{2}\) , 55 atm \(H_{2}\) (b) 57 atm \(\mathrm{NH}_{3}\), 143 atm \(N_{2}\) , no \(H_{2}\) (c) 13 atm \(\mathrm{NH}_{3}\), 27 atm \(N_{2}\) , 82 atm \(H_{2}\) Equation transcription Text transcription: K_{p} N_{2}(g)+3 H_{2}(g) \leftrightarrow 2 N H_{2}(g) 4.51 x 10^{-5} 450^{0}{C} {NH}_{3} H{2} N{2}

Problem 45E Applications of Equilibrium Constants (Section) At 100 °C, Kc = 0.078 for the reaction S02CI2(g) 5* S02(g) + CI2(g) In an equilibrium mixture of the three gases, the concentrations of S02CI2 and S02 are 0.108 M and 0.052 M, respectively. What is the partial pressure of CI2 in the equilibrium mixture?

Problem 46E Applications of Equilibrium Constants (Section) At 900 K, the following reaction has Kp = 0.345: 2 S02(g) + 02(g) - 2 S03(g) In an equilibrium mixture the partial pressures of S02 and 02 are 0.135 atm and 0.455 atm. respectively. What is the equilibrium partial pressure of S03 in the mixture?

Problem 47E Applications of Equilibrium Constants (Section) At 1285 °C, the equilibrium constant for the reaction Br2(g) - 2 Br(g) is Kc = 1.04 x 10-3. A 0.200-L vessel containing an equilibrium mixture of the gases has 0.245 g Br2(g) in it. What is the mass of Br(g) in the vessel?

Problem 48E Applications of Equilibrium Constants (Section) For the reaction H2(g) + 12(g) - 2 Hl(g), Kc= 55.3 at 700 K. In a 2.00-L flask containing an equilibrium mixture of the three gases, there are 0.056 g H2 and 4.36 g 12. What is the mass of HI in the flask?

Problem 49E Applications of Equilibrium Constants (Section) At 800 K, the equilibrium constant for 12(g) - 2 1(g) is Kc = 3.1 x 10-5. If an equilibrium mixture in a 10.0-L vessel contains 2.67 x 10-2 g of l(g), how many grams of I2 are in the mixture?

Problem 50E For 2 S02(g) + 02(g) - 2 S03(g), Kp = 3.0 x 104 at 700 K. In a 2.00-L vessel, the equilibrium mixture contains 1.17 g of S03 and 0.105 g of 02. How many grams of S02 are in the vessel?

Problem 51E Applications of Equilibrium Constants (Section) At 2000 °C, the equilibrium constant for the reaction 2 NO(g) - N2(g) + 02(g) is Kc = 2.4 x 103. If the initial concentration of NO is 0.175 M, what are the equilibrium concentrations of NO, N2, and 02?

Problem 52E Applications of Equilibrium Constants (Section) For the equilibrium Br2(g) + C\2(g) «± 2 BrCI(g) at 400 K, Kc = 7.0. If 0.25 mol of Br2 and 0.55 mol of CI2 are introduced into a 3.0-L container at 400 K, what will be the equilibrium concentrations of Br2, CI2, and BrCI?

Problem 53E Applications of Equilibrium Constants (Section) At 373 K, Kp = 0.416 for the equilibrium 2 NOBr(g) = 2 NO(g) + Br2(g) If the pressures of NOBr(g) and NO(g) are equal, wbat is the equilibrium pressure of Br2(g)?

Problem 55E Applications of Equilibrium Constants (Section) Consider the reaction CaS04(s) -Ca2+(ag) + S042-(aq) At 25 °C, the equilibrium constant is Kc = 2 A x 10-5 for this reaction (a) If excess CaS04(s) is mixed with water at 25 °C to produce a saturated solution of CaS04, what are the equilibrium concentrations of Ca2+ and S042-? (b) If the resulting solution has a volume of 1.4 L, what is the minimum mass of CaSQ4(s) needed to achieve equilibrium?

Problem 54E Applications of Equilibrium Constants (Section) At 218 °C, Kc= 1.2 x 10-4 for the equilibrium NH4SH(s) NH3(g) + H2S(g) Calculate the equilibrium concentrations of NH3 and H2S if a sample of solid NH4SH is placed in a closed vessel at 218 °C and decomposes until equilibrium is reached.

Problem 56E Applications of Equilibrium Constants (Section) At 80 °C, Kc = 1.87 x 10-3 for the reaction PH3BCI3(s) PH3(g) + BCI3(fif) (a) Calculate the equilibrium concentrations of PH3 and BCI3 if a solid sample of PH3BCI3 is placed in a closed vessel at 80 °C and decomposes until equilibrium is reached (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH3BCI3(s) that must be added to the flask to achieve equilibrium?

Problem 57E Applications of Equilibrium Constants (Section) For the reaction 12 + Br2(g)-2 IBr(g), Kc = 280 at 150 °C. Suppose that 0.500 mol IBr in a 2.00-L flask is allowed to reach equilibrium at 150 °C. What are the equilibrium concentrations of IBr, I2, and Br2?

Problem 58E At 25 °C, the reaction CaCr04(s)-Ca2+(aq) + Cr042-(aq) has an equilibrium constant Kc = 7.1 x 10-4. What are the equilibrium concentrations of Ca2+ and Cr042- in a saturated solution of CaCr04?

Problem 59E Applications of Equilibrium Constants (Section) Methane, CH4, reacts with 12 according to the reaction CH4(g) + 12(g) - CH3l(g) + Hl(g). At 630 K, Kp for this reaction is 2.26 x 10-4. A reaction was set up at 630 K with initial partial pressures of methane of 105.1 torr and of 7.96 torr for I2. Calculate the pressures, in torr, of all reactants and products at equilibrium.

Problem 60E Applications of Equilibrium Constants (Section) The reaction of an organic acid with an alcohol, in organic solvent, to produce an ester and water is commonly done in the pharmaceutical industry. This reaction is catalyzed by strong acid (usually H2S04). A simple example is the reaction of acetic acid with ethyl alcohol to produce ethyl acetate and water: CH3COOH (so/v) + CH3CH20H (so/v) = CH3COOCH2CH3 (so/v) + H20 (so/v) where “(so/v)" indicates that all reactants and products are in solution but not an aqueous solution. The equilibrium constant for this reaction at 55 °C is 6.68. A pharmaceutical chemist makes up 15.0 L of a solution that is initially 0.275 M in acetic acid and 3.85 M in ethanol. At equilibrium, how many grams of ethyl acetate are formed?

Problem 61E Le Chatelier’s Principle (Section) Consider the following equilibrium for which AH< 0 2 S02(g) + 02(g) - 2 S03(g) How will each of the following changes affect an equilibrium mixture of the three gases: (a) 02(g) is added to the system; (b) the reaction mixture is heated: (c) the volume of the reaction vessel is doubled: (d) a catalyst is added to the mixture; (e) the total pressure of the system is increased by adding a noble gas: (f) S03(g) is removed from the system?

Problem 62E Le Chatelier’s Principle (Section) Consider the reaction 4 NH3(g) + 5 02(g) -4 NO(g) + 6 H20(g), AH = -904.4 kJ Does each of the following increase, decrease, or leave unchanged the yield of NO at equilibrium? (a) increase [NH3]; (b) increase [H20]; (c) decrease [02]; (d) decrease the volume of the container in which the reaction occurs; (e) add a catalyst; (f) increase temperature

Problem 63E Le Chatelier’s Principle (Section) How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant (b) removal of a product (c) decrease in the volume (d) decrease in the temperature (e) addition of a catalyst?

Problem 64E For a certain gas-phase reaction, the fraction of products in an equilibrium mixture is increased by either increasing the temperature or by increasing the volume of the reaction vessel, (a) Is the reaction exothermic or endothermic? (b) Does the balanced chemical equation have more molecules on the reactant side or product side?

Problem 65E Le Chatelier’s Principle (Section) Consider the following equilibrium between oxides of nitrogen 3 NO(g) - N02(g) + N20(g; (a) Use data in Appendix C to calculate AH° for this reaction, (b) Will the equilibrium constant for the reaction increase or decrease with increasing temperature? (c) At constant temperature, would a change in the volume of the container affect the fraction of products in the equilibrium mixture?

Problem 66E Le Chatelier’s Principle (Section) Methanol (CH30H) can be made by the reaction of CO with H2: CO(g) + 2 H2(g) - CH30H(g) (a) Use thermochemical data in Appendix C to calculate AH° for this reaction (b) To maximize the equilibrium yield of methanol, would you use a high or low temperature? (c) To maximize the equilibrium yield of methanol, would you use a high or low pressure?

Problem 67E Le Chatelier’s Principle (Section) Ozone, 03, decomposes to molecular oxygen in the stratosphere according to the reaction 2 03(g).3 02(g). Would an increase in pressure favor the formation of ozone or of oxygen?

Problem 68E Le Chatelier’s Principle (Section) The water-gas shift reaction CO(g) + H20(g)- C02(g) + H2(g) is used industrially to produce hydrogen. The reaction enthalpy is AH° = -41 kJ (a) To increase the equilibrium yield of hydrogen would you use high or low temperature? (b) Could you increase the equilibrium yield of hydrogen by controlling the pressure of this reaction? If so would high or low pressure favor formation of H2(g)?

Problem 69AE Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps: CO(g) + CI2(g) ^ COCI(g) + Cl(g) At 25 °C, the rate constants for the forward and reverse reactions are 1.4 x 10-28 /W-1 s-1 and 9.3 x 1010 M-1 s-1, respectively, (a) What is the value for the equilibrium constant at 25 °C? (b) Are reactants or products more plentiful at equilibrium?

Problem 71AE A mixture of CH4 and H20 is passed over a nickel catalyst at 1000 K. The emerging gas is collected in a 5.00-L flask and is found to contain 8.62 g of CO, 2.60 g of H2, 43.0 g of CH4, and 48.4 g of H20. Assuming that equilibrium has been reached, calculate Kc and Kp for the reaction CH4(g) + H2C)(g) - CO(g) + 3 H2(g).

Problem 70AE If Kc = 1 for the equilibrium 2 A(g) - B(g), what is the relationship between [A] and [B] at equilibrium?

Problem 73AE A mixture of H2, S, and H2S is held in a 1 0-L vessel at 90 °C and reacts according to the equation: H2(g) + S(s) - H2S(g) At equilibrium, the mixture contains 0.46 g of H2S and 0.40 g H2. (a) Write the equilibrium-constant expression for this reaction, (b) What is the value of Kc for the reaction at this temperature?

Problem 72AE When 2.00 mol of S02CI2 is placed in a 2.00-L flask at 303 K, 56% of the S02CI2 decomposes to S02 and CI2: S02CI2(g) - S02(g) + CI2(g) (a) Calculate Kc for this reaction at this temperature, (b) Calculate Kp for this reaction at 303 K. (c) According to Le Chatelier's principle, would the percent of S02CI2 that decomposes increase, decrease or stay the same if the mixture were transferred to a 15.00-L vessel? (d) Use the equilibrium constant you calculated above to determine the percentage of S02CI2 that decomposes when 2.00 mol of SQ2CI2 is placed in a 15.00-L vessel at 303 K.

Problem 74AE A sample of nitrosyl bromide (NOBr) decomposes according to the equation 2 NOBr(g) - 2 NO(g) + Br2(g) An equilibrium mixture in a 5.00-L vessel at 100 °C contains 3.22 g of NOBr. 3.08 g of NO. and 4.19 g of Br2. (a) Calculate Kc. (b) What is the total pressure exerted by the mixture of gases? (c) What was the mass of the original sample of NOBr?

Problem 75AE Consider the hypothetical reaction A(g) - 2 B(g). A flask is charged with 0.75 atm of pure A, after which it is allowed to reach equilibrium at 0 °C. At equilibrium, the partial pressure of A is 0.36 atm. (a) What is the total pressure in the flask at equilibrium? (b) What is the value of Kp? (c) What could we do to maximize the yield of B?

As shown in Table 15.2, the equilibrium constant for the reaction \(\mathrm{N}_{2}(g) \leftrightarrow 2 \mathrm{NH}_{3}(g)\) is \(K_{p}=4.34 \times 10^{-3}\) at 300°C. Pure \(\mathrm{NH}_{3}\) is placed in a 1.00-L flask and allowed to reach equilibrium at this temperature. There are 1.05 g \(\mathrm{NH}_{3}\) in the equilibrium mixture. (a) What are the masses of \(N_{2}\) and \(H_{2}\) in the equilibrium mixture? (b) What was the initial mass of ammonia placed in the vessel? (c) What is the total pressure in the vessel? Equation transcription: Text transcription: {N}_{2}(g) \leftrightarrow 2{NH}_{3}(g) K{p}=4.34 \times 10^{-3} {NH}_{3} N_{2} H_{2}

Problem 77AE For the equilibrium 2 IBr(g) - 12(g) + Br2(g) Kp = 8.5 x 10-3 at 150 °C. If 0.025 atm of IBr is placed in a 2.0-L container, what is the partial pressure of all substances after equilibrium is reached?

Problem 78AE PH3BCI3(s) PH3(g) + BCI3(g) Kp = 0.052 at 60 °C. (a) Calculate Kc. (b) After 3.00 g of solid PH3BCI3 is added to a closed 1 500-L vessel at 60 °C, the vessel is charged with 0.0500 g of BCI3(g). What is the equilibrium concentration of PH3?

Problem 79AE Solid NH4SH is introduced into an evacuated flask at 24 °C. The following reaction takes place: NH4SH(s) NH3(g) + H2S(g) At equilibrium, the total pressure (for NH3 and H2S taken together) is 0.614 atm. What is Kp for this equilibrium at 24 °C?

Problem 81AE Nitric oxide (NO) reacts readily with chlorine gas as follows: 2 NO(g) + CI2(g) - 2 NOCI(g) At 700 K, the equilibrium constant Kp for this reaction is 0.26. Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) PNO = 0.15 atm, PCI2 = 0.31 atm, PNOCI = 0.11 atm (b) PNO = 0.12 atm. PCI2 = 0.10 atm. PNOCI = 0.050 atm (c) PNO = 0.15 atm. PCI2 = 0.20 atm. PNOCI = 5.10 x 10-3 atm

Problem 80AE A 0.831-g sample of S03 is placed in a 1 00-L container and heated to 1100 K. The S03 decomposes to S02 and 02: 2 S03(g) - 2 S02(g) + 02(g) At equilibrium, the total pressure in the container is 1.300 atm. Find the values of Kp and Kc for this reaction at 1100 K.

Problem 82AE At 900 °C, Kc = 0.0108 for the reaction CaC03(s) - CaO(s) + C02(g) A mixture of CaC03, CaO. and C02 is placed in a 10.0-L vessel at 900 °C. For the following mixtures, will the amount of CaC03 increase, decrease, or remain the same as the system approaches equilibrium? (a) 15.0 g CaC03, 15.0 g CaO, and 4.25 g C02 (b) 2.50 g CaC03, 25.0 g CaO, and 5.66 g C02 (c) 30.5 g CaC03, 25.5 g CaO, and 6.48 g C02

Problem 84AE The equilibrium constant Kc for C(s) + C02(g) - 2 CO(g) is 1.9 at 1000 K and 0.133 at 298 K. (a) If excess C is allowed to react with 25.0 g of C02 in a 3.00-L vessel at 1000 K, how many grams of CO are produced? (b) How many grams of C are consumed? (c) If a smaller vessel is used for the reaction, will the yield of CO be greater or smaller? (d) Is the reaction endothermic or exothermic?

Problem 85AE NiO is to be reduced to nickel metal in an industrial process by use of the reaction NiO(s) + CO(g) - Ni(s) + C02(g) At 1600 K, the equilibrium constant for the reaction is Kp = 6.0 x 102. If a CO pressure of 150 torr is to be employed in the furnace and total pressure never exceeds 760 torr, will reduction occur?

Problem 83AE When 1.50 mol C02 and 1.50 mol H2 are placed in a 3.00-L container at 395 °C, the following reaction occurs: C02(g) + H2(g) - CO(g) + H20(g). If Kc = 0.802, what are the concentrations of each substance in the equilibrium mixture?

Problem 86AE Le Chatelier noted that many industrial processes of his time could be improved by an understanding of chemical equilibria. For example, the reaction of iron oxide with carbon monoxide was used to produce elemental iron and C02 according to the reaction Fe203(s) + 3 CO(g) - 2 Fe(s) + 3 C02(g) Even in Le Chatelier's time, it was noted that a great deal of CO was wasted, expelled through the chimneys over the furnaces. Le Chatelier wrote, “Because this incomplete reaction was thought to be due to an insufficiently prolonged contact between carbon monoxide and the iron ore [oxide], the dimensions of the furnaces have been increased. In England, they have been made as high as 30 m. But the proportion of carbon monoxide escaping has not diminished, thus demonstrating, by an experiment costing several hundred thousand francs, that the reduction of iron oxide by carbon monoxide is a limited reaction. Acquaintance with the laws of chemical equilibrium would have permitted the same conclusion to be reached more rapidly and far more economically." What does this anecdote tell us about the equilibrium constant for this reaction?

Problem 87AE At 700 K, the equilibrium constant for the reaction CCI4(fif) - C(s) + 2 CI2(fif) is Kp = 0.76. A flask is charged with 2.00 atm of CCI4, which then reaches equilibrium at 700 K. (a) What fraction of the CCI4 is converted into C and CI2? (b) What are the partial pressures of CCI4 and CI2 at equilibrium?

Problem 88AE The reaction PCI3(gr) + CI2(g) - PCI5(g) has Kp = 0.0870 at 300 °C. A flask is charged with 0.50 atm PCI3, 0.50 atm CI2, and 0.20 atm PCI5 at this temperature, (a) Use the reaction quotient to determine the direction the reaction must proceed to reach equilibrium, (b) Calculate the equilibrium partial pressures of the gases, (c) What effect will increasing the volume of the system have on the mole fraction of CI2 in the equilibrium mixture? (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of CI2 in the equilibrium mixture?

Problem 89AE An equilibrium mixture of H2,12, and HI at 458 °C contains 0.112 mol H2, 0.112 mol I2, and 0.775 mol HI in a 5.00-L vessel. What are the equilibrium partial pressures when equilibrium is reestablished following the addition of 0.200 mol of HI?

Problem 90AE Consider the hypothetical reaction A(g) + 2 B(g) - 2 C(g), for which Kc = 0.25 at a certain temperature. A 1.00-L reaction vessel is loaded with 1.00 mol of compound C, which is allowed to reach equilibrium. Let the variable x represent the number of mol/L of compound A present at equilibrium, (a) In terms of x, what are the equilibrium concentrations of compounds B and C? (b) What limits must be placed on the value of x so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of x) into the equilibriumconstant expression, derive an equation that can be solved for x. (d) The equation from part (c) is a cubic equation (one that has the form ax3 + 0x2 + cx + d = 0). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of x that you specified in part (b). The point at which the cubic equation crosses the x-axis is the solution, (e) From the plot in part (d), estimate the equilibrium concentrations of A, B. and C. (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

At 1200 K, the approximate temperature of automobile exhaust gases (Figure 15.15), \(K_{p}\) for the reaction \(2 C O_{2}(g) \leftrightarrow 2 C O(g)+O_{2}(g)\) is about \(1 \times 10^{-13}\). Assuming that the exhaust gas (total pressure 1 atm) contains 0.2% CO, 12% \(\mathrm{CO}_{2}\), and 3% \(\mathrm{CO}_{2}\) by volume, is the system at equilibrium with respect to the \(\mathrm{CO}_{2}\) reaction? Based on your conclusion, would the CO concentration in the exhaust be decreased or increased by a catalyst that speeds up the \(\mathrm{CO}_{2}\) reaction? Recall that at a fixed pressure and temperature, volume % = mol %. Equation transcription: Text transcription: K_{p} 2 C O_{2}(g) \leftrightarrow 2 C O(g)+O_{2}(g) 1 \times 10^{-13} \mathrm{CO}_{2}

Problem 92AE Suppose that you worked at the U S. Patent Office and a patent application came across your desk claiming that a newly developed catalyst was much superior to the Haber catalyst for ammonia synthesis because the catalyst led to much greater equilibrium conversion of N2 and H2 into NH3 than the Haber catalyst under the same conditions. What would be your response?

Problem 93IE Consider the reaction 104 -(aq) + 2 H20(/) - H4I06 -(aq); Kc = 3.5 x 10-2. If you start with 25.0 mL of a 0.905 M solution of Nal04, and then dilute it with water to 500.0 mL, what is the concentration of H4I06 - at equilibrium?

Problem 94IE Silver chloride, AgCI(s), is an "insoluble" strong electrolyte (a) Write the equation for the dissolution of AgCI(s) in H20(/). (b) Write the expression for Kc for the reaction in part (a), (c) Based on the thermochemical data in Appendix C and Le Chatelier's principle, predict whether the solubility of AgCI in H20 increases or decreases with increasing temperature, (d) The equilibrium constant for the dissolution of AgCI in water is 1.6 x 10-10 at 25 °C. In addition, Ag+(aq) can react with Cl-(ag) according to the reaction Ag+(ag) + 2 Cl-(ag) - AgCI2 -(aq) where Kc= 1.8 x 105 at 25 °C. Although AgCI is "not soluble" in water, the complex AgCI2 - is soluble. At 25 °C, is the solubility of AgCI in a 0.100 M NaCI solution greater than the solubility of AgCI in pure water, due to the formation of soluble AgCI2 - ions? Or is the AgCI solubility in 0.100 M NaCI less than in pure water because of a Le Chatelier-type argument? Justify your answer with calculations. (Hint Any form in which silver is in solution counts as "solubility ")

Consider the equilibrium \(A \leftrightarrow B\) in which both the forward and reverse reactions are elementary (single-step) reactions. Assume that the only effect of a catalyst on the reaction is to lower the activation energies of the forward and reverse reactions, as shown in Figure 15.14. Using the Arrhenius equation (Section 14.5), prove that the equilibrium constant is the same for the catalyzed reaction as for the uncatalyzed one. Equation transcription: Text transcription: A \leftrightarrow B

Write the equilibrium-constant expression for the equilibrium \(C(s)+C O_{2}(g) \leftrightarrow 2 C O(g)\) The table that follows shows the relative mole percentages of \(\mathrm{CO}_{2}(g)\) and CO(g) at a total pressure of 1 atm for several temperatures. Calculate the value of \(K_{p}\) at each temperature. Is the reaction exothermic or endothermic? Equation transcription: Text transcription: C(s)+C O_{2}(g) leftrightarrow 2 C O(g) {CO}{2}(g) K{p}

The phase diagram for \(\mathrm{SO}_{2}) is shown here. (a) What does this diagram tell you about the enthalpy change in the reaction \(\mathrm{SO}_{2}(\mathrm{I}) \rightarrow \mathrm{SO}_{2}(g)\)? (b) Calculate the equilibrium constant for this reaction at 100°C and at 0°C. (c) Why is it not possible to calculate an equilibrium constant between the gas and liquid phases in the supercritical region? (d) At which of the three points marked in red does \(\mathrm{SO}_{2}\)(g) most closely approach ideal-gas behavior? (e) At which of the three red points does \(\mathrm{SO}_{2}\)(g) behave least ideally? Equation transcription: Text transcription: {SO}_{2} {SO}_{2}({I}) \rightarrow{SO}_{2}(g)

Problem 100IE The protein hemoglobin (Hb) transports 02 in mammalian blood. Each Hb can bind 4 02 molecules. The equilibrium constant for the 02 binding reaction is higher in fetal hemoglobin than in adult hemoglobin. In discussing protein oxygen-binding capacity, biochemists use a measure called the P50 value, defined as the partial pressure of oxygen at which 50% of the protein is saturated. Fetal hemoglobin has a P50 value of 19 torr. and adult hemoglobin has a P50 value of 26.8 torr. Use these data to estimate how much larger Kc is for the aqueous reaction 4 02(g) + Hb(ag) -»? [Hb(02)4(ag)] in the fetal bloodstream.

Problem 98IE In Section, we defined the vapor pressure of a liquid in terms of an equilibrium, (a) Write the equation representing the equilibrium between liquid water and water vapor and the corresponding expression for Kp (b) By using data in Appendix B, give the value of Kp for this reaction at 30 °C. (c) What is the value of Kp for any liquid in equilibrium with its vapor at the normal boiling point of the liquid?

Problem 99IE Water molecules in the atmosphere can form hydrogenbonded dimers, (H20)2. The presence of these dimers is thought to be important in the nucleation of ice crystals in the atmosphere and in the formation of acid rain. (a) Using VSEPR theory, draw the structure of a water dimer, using dashed lines to indicate intermolecular interactions, (b) What kind of intermolecular forces are involved in water dimer formation? (c) The Kp for water dimer formation in the gas phase is 0.050 at 300 K and 0.020 at 350 K. Is water dimer formation endothermic or exothermic?