Solved: The equilibrium constant for the reaction 4X 1 Y

Define equilibrium. Give two examples of a dynamic equilibrium

Explain the difference between physical equilibrium and chemical equilibrium. Give two examples of each.

What is the law of mass action?

Briefly describe the importance of equilibrium in the study of chemical reactions.

Define homogeneous equilibrium and heterogeneous equilibrium. Give two examples of each.

What do the symbols Kc and KP represent?

Write the expressions for the equilibrium constants KP of the following thermal decomposition reactions: (a) 2NaHCO3(s) Na2CO3(s) 1 CO2(g) 1 H2O(g) (b) 2CaSO4(s) 2CaO(s) 1 2SO2(g) 1 O2(g)

Write equilibrium constant expressions for Kc, and for KP, if applicable, for the following processes: (a) 2CO2(g) 2CO(g) 1 O2(g) (b) 3O2(g) 2O3(g) (c) CO(g) 1 Cl2(g) COCl2(g) (d) H2O(g) 1 C(s) CO(g) 1 H2(g) (e) HCOOH(aq) H1 (aq) 1 HCOO2 (aq) (f) 2HgO(s) 2Hg(l) 1 O2(g)

Write the equilibrium constant expressions for Kc and KP, if applicable, for the following reactions: (a) 2NO2(g) 1 7H2(g) 2NH3(g) 1 4H2O(l) (b) 2ZnS(s) 1 3O2(g) 2ZnO(s) 1 2SO2(g) (c) C(s) 1 CO2(g) 2CO(g) (d) C6H5COOH(aq) C6H5COO2(aq) 1 H1(aq)

Write the equation relating Kc to KP, and define all the terms.

What is the rule for writing the equilibrium constant for the overall reaction involving two or more reactions?

Give an example of a multiple equilibria reaction

The equilibrium constant for the reaction A B is Kc 5 10 at a certain temperature. (1) Starting with only reactant A, which of the diagrams shown here best represents the system at equilibrium? (2) Which of the diagrams best represents the system at equilibrium if Kc 5 0.10? Explain why you can calculate Kc in each case without knowing the volume of the container. The gray spheres represent the A molecules and the green spheres represent the B molecules. (a) (b) (c) (d)

The following diagrams represent the equilibrium state for three different reactions of the type A 1 X AX (X 5 B, C, or D): A B AB wx wx wx A C AC A D AD (a) Which reaction has the largest equilibrium constant? (b) Which reaction has the smallest equilibrium constant? 1

The equilibrium constant (Kc) for the reaction 2HCl(g) H2(g) 1 Cl2(g) is 4.17 3 10234 at 25C. What is the equilibrium constant for the reaction H2(g) 1 Cl2(g) 2HCl(g) at the same temperature?

Consider the following equilibrium process at 700C: 2H2(g) 1 S2(g) 2H2S(g) Analysis shows that there are 2.50 moles of H2, 1.35 3 1025 mole of S2, and 8.70 moles of H2S present in a 12.0-L flask. Calculate the equilibrium constant Kc for the reaction

What is KP at 1273C for the reaction 2CO(g) 1 O2(g) 2CO2(g) if Kc is 2.24 3 1022 at the same temperature?

The equilibrium constant KP for the reaction 2SO3(g) 2SO2(g) 1 O2(g) is 1.8 3 1025 at 350C. What is Kc for this reaction?

Consider the following reaction: N2(g) 1 O2(g) 2NO(g) If the equilibrium partial pressures of N2, O2, and NO are 0.15 atm, 0.33 atm, and 0.050 atm, respectively, at 2200C, what is KP?

A reaction vessel contains NH3, N2, and H2 at equilibrium at a certain temperature. The equilibrium concentrations are [NH3] 5 0.25 M, [N2] 5 0.11 M, and [H2] 5 1.91 M. Calculate the equilibrium constant Kc for the synthesis of ammonia if the reaction is represented as (a) N2(g) 1 3H2(g) 2NH3(g) (b) 1 2N2(g) 1 3 2H2(g) NH3(g)

The equilibrium constant Kc for the reaction I2(g) 2I(g) is 3.8 3 1025 at 727C. Calculate Kc and KP for the equilibrium 2I(g) I2(g) at the same temperature

At equilibrium, the pressure of the reacting mixture CaCO3(s) CaO(s) 1 CO2(g) is 0.105 atm at 350C. Calculate KP and Kc for this reaction.

The equilibrium constant KP for the reaction PCl5(g) PCl3(g) 1 Cl2(g) is 1.05 at 250C. The reaction starts with a mixture of PCl5, PCl3, and Cl2 at pressures 0.177 atm, 0.223 atm, and 0.111 atm, respectively, at 250C. When the mixture comes to equilibrium at that temperature, which pressures will have decreased and which will have increased? Explain why.

Ammonium carbamate, NH4CO2NH2, decomposes as follows: NH4CO2NH2(s) 2NH3(g) 1 CO2(g) Starting with only the solid, it is found that at 40C the total gas pressure (NH3 and CO2) is 0.363 atm. Calculate the equilibrium constant KP.

Consider the following reaction at 1600C. Br2(g) 2Br(g) When 1.05 moles of Br2 are put in a 0.980-L flask, 1.20 percent of the Br2 undergoes dissociation. Calculate the equilibrium constant Kc for the reaction

Pure phosgene gas (COCl2), 3.00 3 1022 mol, was placed in a 1.50-L container. It was heated to 800 K, and at equilibrium the pressure of CO was found to be 0.497 atm. Calculate the equilibrium constant KP for the reaction CO(g) 1 Cl2(g) COCl2(g)

Consider the equilibrium 2NOBr(g) 2NO(g) 1 Br2(g) If nitrosyl bromide, NOBr, is 34 percent dissociated at 25C and the total pressure is 0.25 atm, calculate KP and Kc for the dissociation at this temperature

A 2.50-mole quantity of NOCl was initially in a 1.50-L reaction chamber at 400C. After equilibrium was established, it was found that 28.0 percent of the NOCl had dissociated: 2NOCl(g) 2NO(g) 1 Cl2(g) Calculate the equilibrium constant Kc for the reaction.

The following equilibrium constants have been determined for hydrosulfuric acid at 25C: H2S(aq) H1 (aq) 1 HS2 (aq) K c 5 9.5 3 1028 HS2 (aq) H1 (aq) 1 S22 (aq) Kc 5 1.0 3 10219 Calculate the equilibrium constant for the following reaction at the same temperature: H2S(aq) 2H1 (aq) 1 S22 (aq)

The following equilibrium constants have been determined for oxalic acid at 25C: H2C2O4(aq) H1 (aq) 1 HC2O2 4 (aq) K c 5 6.5 3 1022 HC2O4 2 (aq) H1 (aq) 1 C2O22 4 (aq) Kc 5 6.1 3 1025 Calculate the equilibrium constant for the following reaction at the same temperature: H2C2O4(aq) 2H1 (aq) 1 C2O22 4 (aq)

The following equilibrium constants were determined at 1123 K: C(s) 1 CO2(g) 2CO(g) KP 5 1.3 3 1014 CO(g) 1 Cl2(g) COCl2(g) KP 5 6.0 3 1023 Write the equilibrium constant expression KP, and calculate the equilibrium constant at 1123 K for C(s) 1 CO2(g) 1 2Cl2(g) 2COCl2(g)

At a certain temperature the following reactions have the constants shown: S(s) 1 O2(g) SO2(g) K c 5 4.2 3 1052 2S(s) 1 3O2(g) 2SO3(g) Kc 5 9.8 3 10128 Calculate the equilibrium constant Kc for the following reaction at that temperature: 2SO2(g) 1 O2(g) 2SO3(g)

Based on rate constant considerations, explain why the equilibrium constant depends on temperature.

Explain why reactions with large equilibrium constants, such as the formation of rust (Fe2O3), may have very slow rates.

Water is a very weak electrolyte that undergoes the following ionization (called autoionization): H2O(l) k1 k 1 H (aq) OH ( 1 aq) 1 2 (a) If k1 5 2.4 3 1025 s21 and k21 5 1.3 3 1011/M ? s, calculate the equilibrium constant K where K 5 [H1][OH2]/[H2O]. (b) Calculate the product [H1][OH2] and [H1] and [OH2].

Consider the following reaction, which takes place in a single elementary step: 2A B k1 k 1 1 A2B If the equilibrium constant Kc is 12.6 at a certain temperature and if kr 5 5.1 3 1022 s21 , calculate the value of kf.

Define reaction quotient. How does it differ from equilibrium constant?

Outline the steps for calculating the concentrations of reacting species in an equilibrium reaction.

The equilibrium constant KP for the reaction 2SO2(g) 1 O2(g) 2SO3(g) is 5.60 3 104 at 350C. The initial pressures of SO2 and O2 in a mixture are 0.350 atm and 0.762 atm, respectively, at 350C. When the mixture equilibrates, is the total pressure less than or greater than the sum of the initial pressures (1.112 atm)?

For the synthesis of ammonia N2(g) 1 3H2(g) 2NH3(g) the equilibrium constant Kc at 375C is 1.2. Starting with [H2]0 5 0.76 M, [N2]0 5 0.60 M, and [NH3]0 5 0.48 M, which gases will have increased in concentration and which will have decreased in concentration when the mixture comes to equilibrium?

For the reaction H2(g) 1 CO2(g) H2O(g) 1 CO(g) at 700C, Kc 5 0.534. Calculate the number of moles of H2 that are present at equilibrium if a mixture of 0.300 mole of CO and 0.300 mole of H2O is heated to 700C in a 10.0-L container

At 1000 K, a sample of pure NO2 gas decomposes: 2NO2(g) 2NO(g) 1 O2(g) The equilibrium constant KP is 158. Analysis shows that the partial pressure of O2 is 0.25 atm at equilibrium. Calculate the pressure of NO and NO2 in the mixture

The equilibrium constant Kc for the reaction H2(g) 1 Br2(g) 2HBr(g) is 2.18 3 106 at 730C. Starting with 3.20 moles of HBr in a 12.0-L reaction vessel, calculate the concentrations of H2, Br2, and HBr at equilibrium

The dissociation of molecular iodine into iodine atoms is represented as I2(g) 2I(g) At 1000 K, the equilibrium constant Kc for the reaction is 3.80 3 1025 . Suppose you start with 0.0456 mole of I2 in a 2.30-L flask at 1000 K. What are the concentrations of the gases at equilibrium?

The equilibrium constant Kc for the decomposition of phosgene, COCl2, is 4.63 3 1023 at 527C: COCl2(g) CO(g) 1 Cl2(g) Calculate the equilibrium partial pressure of all the components, starting with pure phosgene at 0.760 atm.

Consider the following equilibrium process at 686C: CO2(g) 1 H2(g) CO(g) 1 H2O(g) The equilibrium concentrations of the reacting species are [CO] 5 0.050 M, [H2] 5 0.045 M, [CO2] 5 0.086 M, and [H2O] 5 0.040 M. (a) Calculate Kc for the reaction at 686C. (b) If we add CO2 to increase its concentration to 0.50 mol/L, what will the concentrations of all the gases be when equilibrium is reestablished?

Consider the heterogeneous equilibrium process: C(s) 1 CO2(g) 2CO(g) At 700C, the total pressure of the system is found to be 4.50 atm. If the equilibrium constant KP is 1.52, calculate the equilibrium partial pressures of CO2 and CO.

The equilibrium constant Kc for the reaction H2(g) 1 CO2(g) H2O(g) 1 CO(g) is 4.2 at 1650C. Initially 0.80 mol H2 and 0.80 mol CO2 are injected into a 5.0-L flask. Calculate the concentration of each species at equilibrium

Explain Le Chteliers principle. How can this principle help us maximize the yields of reactions?

Use Le Chteliers principle to explain why the equilibrium vapor pressure of a liquid increases with increasing temperature

List four factors that can shift the position of an equilibrium. Only one of these factors can alter the value of the equilibrium constant. Which one is it?

Does the addition of a catalyst have any effects on the position of an equilibrium?

Consider the following equilibrium system involving SO2, Cl2, and SO2Cl2 (sulfuryl dichloride): SO2(g) 1 Cl2(g) SO2Cl2(g) Predict how the equilibrium position would change if (a) Cl2 gas were added to the system; (b) SO2Cl2 were removed from the system; (c) SO2 were removed from the system. The temperature remains constant

Heating solid sodium bicarbonate in a closed vessel establishes the following equilibrium: 2NaHCO3(s) Na2CO3(s) 1 H2O(g) 1 CO2(g) What would happen to the equilibrium position if (a) some of the CO2 were removed from the system; (b) some solid Na2CO3 were added to the system; (c) some of the solid NaHCO3 were removed from the system? The temperature remains constant

Consider the following equilibrium systems: (a) A 2B H 5 20.0 kJ/mol (b) A 1 B C H 5 25.4 kJ/mol (c) A B H 5 0.0 kJ/mol Predict the change in the equilibrium constant Kc that would occur in each case if the temperature of the reacting system were raised.

What effect does an increase in pressure have on each of the following systems at equilibrium? The temperature is kept constant and, in each case, the reactants are in a cylinder fitted with a movable piston. (a) A(s) 2B(s) (b) 2A(l) B(l) (c) A(s) B(g) (d) A(g) B(g) (e) A(g) 2B(g)

Consider the equilibrium 2I(g) I2(g) What would be the effect on the position of equilibrium of (a) increasing the total pressure on the system by decreasing its volume; (b) adding gaseous I2 to the reaction mixture; and (c) decreasing the temperature at constant volume?

PCl5(g) PCl3(g) 1 Cl2(g) H 5 92.5 kJ/mol Predict the direction of the shift in equilibrium when (a) the temperature is raised; (b) more chlorine gas is added to the reaction mixture; (c) some PCl3 is removed from the mixture; (d) the pressure on the gases is increased; (e) a catalyst is added to the reaction mixture.

Consider the reaction 2SO2(g) 1 O2(g) 2SO3(g) H 5 2198.2 kJ/mol Comment on the changes in the concentrations of SO2, O2, and SO3 at equilibrium if we were to (a) increase the temperature; (b) increase the pressure; (c) increase SO2; (d) add a catalyst; (e) add helium at constant volume

In the uncatalyzed reaction N2O4(g) 2NO2(g) the pressure of the gases at equilibrium are PN2O4 5 0.377 atm and PNO2 5 1.56 atm at 100C. What would happen to these pressures if a catalyst were added to the mixture?

Consider the gas-phase reaction 2CO(g) 1 O2(g) 2CO2(g) Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture (a) at constant pressure and (b) at constant volume.

Consider the following equilibrium reaction in a closed container: CaCO3(s) CaO(s) 1 CO2(g) What will happen if (a) the volume is increased; (b) some CaO is added to the mixture; (c) some CaCO3 is removed; (d) some CO2 is added to the mixture; (e) a few drops of a NaOH solution are added to the mixture; (f) a few drops of a HCl solution are added to the mixture (ignore the reaction between CO2 and water); (g) temperature is increased?

Consider the statement: The equilibrium constant of a reacting mixture of solid NH4Cl and gaseous NH3 and HCl is 0.316. List three important pieces of information that are missing from this statement.

Pure nitrosyl chloride (NOCl) gas was heated to 240C in a 1.00-L container. At equilibrium the total pressure was 1.00 atm and the NOCl pressure was 0.64 atm. 2NOCl(g) 2NO(g) 1 Cl2(g) (a) Calculate the partial pressures of NO and Cl2 in the system. (b) Calculate the equilibrium constant KP.

Determine the initial and equilibrium concentrations of HI if the initial concentrations of H2 and I2 are both 0.16 M and their equilibrium concentrations are both 0.072 M at 430C. The equilibrium constant (Kc) for the reaction H2(g) 1 I2(g) 2HI(g) is 54.2 at 430C.

Diagram (a) shows the reaction A2(g) 1 B2(g) 2AB(g) at equilibrium at a certain temperature, where the blue spheres represent A and the yellow spheres represent B. If each sphere represents 0.020 mole and the volume of the container is 1.0 L, calculate the concentration of each species when the reaction in (b) reaches equilibrium. (a) (b)

The equilibrium constant (KP) for the formation of the air pollutant nitric oxide (NO) in an automobile engine at 530C is 2.9 3 10211: N2(g) 1 O2(g) 2NO(g) (a) Calculate the partial pressure of NO under these conditions if the partial pressures of nitrogen and oxygen are 3.0 atm and 0.012 atm, respectively. (b) Repeat the calculation for atmospheric conditions where the partial pressures of nitrogen and oxygen are 0.78 atm and 0.21 atm and the temperature is 25C. (The KP for the reaction is 4.0 3 10231 at this temperature.) (c) Is the formation of NO endothermic or exothermic? (d) What natural phenomenon promotes the formation of NO? Why?

Baking soda (sodium bicarbonate) undergoes thermal decomposition as follows: 2NaHCO3(s) Na2CO3(s) 1 CO2(g) 1 H2O(g) Would we obtain more CO2 and H2O by adding extra baking soda to the reaction mixture in (a) a closed vessel or (b) an open vessel?

Consider the following reaction at equilibrium: A(g) 2B(g) From the data shown here, calculate the equilibrium constant (both KP and Kc) at each temperature. Is the reaction endothermic or exothermic? Temperature (C) [A] (M) [B] (M) 200 0.0125 0.843 300 0.171 0.764 400 0.250 0.724

The equilibrium constant KP for the reaction 2H2O(g) 2H2(g) 1 O2(g) is 2 3 10242 at 25C. (a) What is Kc for the reaction at the same temperature? (b) The very small value of KP (and Kc) indicates that the reaction overwhelmingly favors the formation of water molecules. Explain why, despite this fact, a mixture of hydrogen and oxygen gases can be kept at room temperature without any change.

Consider the following reacting system: 2NO(g) 1 Cl2(g) 2NOCl(g) What combination of temperature and pressure (high or low) would maximize the yield of nitrosyl chloride (NOCl)? [Hint: Hf(NOCl) 5 51.7 kJ/mol. You will also need to consult Appendix 3.]

At a certain temperature and a total pressure of 1.2 atm, the partial pressures of an equilibrium mixture 2A(g) B(g) are PA 5 0.60 atm and PB 5 0.60 atm. (a) Calculate the KP for the reaction at this temperature. (b) If the total pressure were increased to 1.5 atm, what would be the partial pressures of A and B at equilibrium?

The decomposition of ammonium hydrogen sulfide NH4HS(s) NH3(g) 1 H2S(g) is an endothermic process. A 6.1589-g sample of the solid is placed in an evacuated 4.000-L vessel at exactly 24C. After equilibrium has been established, the total pressure inside is 0.709 atm. Some solid NH4HS remains in the vessel. (a) What is the KP for the reaction? (b) What percentage of the solid has decomposed? (c) If the volume of the vessel were doubled at constant temperature, what would happen to the amount of solid in the vessel?

Consider the reaction 2NO(g) 1 O2(g) 2NO2(g) At 430C, an equilibrium mixture consists of 0.020 mole of O2, 0.040 mole of NO, and 0.96 mole of NO2. Calculate KP for the reaction, given that the total pressure is 0.20 atm.

When heated, ammonium carbamate decomposes as follows: NH4CO2NH2(s) 2NH3(g) 1 CO2(g) At a certain temperature the equilibrium pressure of the system is 0.318 atm. Calculate KP for the reaction.

A mixture of 0.47 mole of H2 and 3.59 moles of HCl is heated to 2800C. Calculate the equilibrium partial pressures of H2, Cl2, and HCl if the total pressure is 2.00 atm. For the reaction H2(g) 1 Cl2(g) 2HCl(g) KP is 193 at 2800C

When heated at high temperatures, iodine vapor dissociates as follows: I2(g) 2I(g) In one experiment, a chemist finds that when 0.054 mole of I2 was placed in a flask of volume 0.48 L at 587 K, the degree of dissociation (that is, the fraction of I2 dissociated) was 0.0252. Calculate Kc and KP for the reaction at this temperature.

One mole of N2 and three moles of H2 are placed in a flask at 375C. Calculate the total pressure of the system at equilibrium if the mole fraction of NH3 is 0.21. The KP for the reaction is 4.31 3 1024 .

At 1130C the equilibrium constant (Kc) for the reaction 2H2S(g) 2H2(g) 1 S2(g) is 2.25 3 1024 . If [H2S] 5 4.84 3 1023 M and [H2] 5 1.50 3 1023 M, calculate [S2]

A quantity of 6.75 g of SO2Cl2 was placed in a 2.00-L flask. At 648 K, there is 0.0345 mole of SO2 present. Calculate Kc for the reaction SO2Cl2(g) SO2(g) 1 Cl2(g)

The formation of SO3 from SO2 and O2 is an intermediate step in the manufacture of sulfuric acid, and it is also responsible for the acid rain phenomenon. The equilibrium constant KP for the reaction 2SO2(g) 1 O2(g) 2SO3(g) is 0.13 at 830C. In one experiment 2.00 mol SO2 and 2.00 mol O2 were initially present in a flask. What must the total pressure at equilibrium be in order to have an 80.0 percent yield of SO3?

Consider the dissociation of iodine: I2(g) 2I(g) A 1.00-g sample of I2 is heated to 1200C in a 500-mL flask. At equilibrium the total pressure is 1.51 atm. Calculate KP for the reaction. [Hint: Use the result in 14.117(a). The degree of dissociation can be obtained by first calculating the ratio of observed pressure over calculated pressure, assuming no dissociation.]

Eggshells are composed mostly of calcium carbonate (CaCO3) formed by the reaction Ca21 (aq) 1 CO3 22 (aq) CaCO3(s) The carbonate ions are supplied by carbon dioxide produced as a result of metabolism. Explain why eggshells are thinner in the summer when the rate of panting by chickens is greater. Suggest a remedy for this situation.

The equilibrium constant KP for the following reaction is 4.31 3 1024 at 375C: N2(g) 1 3H2(g) 2NH3(g) In a certain experiment a student starts with 0.862 atm of N2 and 0.373 atm of H2 in a constant-volume vessel at 375C. Calculate the partial pressures of all species when equilibrium is reached.

A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: C(s) 1 CO2(g) 2CO(g) Under these conditions, the average molar mass of the gases was 35 g/mol. (a) Calculate the mole fractions of CO and CO2. (b) What is KP if the total pressure is 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.)

When dissolved in water, glucose (corn sugar) and fructose (fruit sugar) exist in equilibrium as follows: fructose glucose A chemist prepared a 0.244 M fructose solution at 25C. At equilibrium, it was found that its concentration had decreased to 0.113 M. (a) Calculate the equilibrium constant for the reaction. (b) At equilibrium, what percentage of fructose was converted to glucose?

At room temperature, solid iodine is in equilibrium with its vapor through sublimation and deposition (see p. 502). Describe how you would use radioactive iodine, in either solid or vapor form, to show that there is a dynamic equilibrium between these two phases.

At 1024C, the pressure of oxygen gas from the decomposition of copper(II) oxide (CuO) is 0.49 atm: 4CuO(s) 2Cu2O(s) 1 O2(g) (a) What is KP for the reaction? (b) Calculate the fraction of CuO that will decompose if 0.16 mole of it is placed in a 2.0-L flask at 1024C. (c) What would the fraction be if a 1.0 mole sample of CuO were used? (d) What is the smallest amount of CuO (in moles) that would establish the equilibrium?

A mixture containing 3.9 moles of NO and 0.88 mole of CO2 was allowed to react in a flask at a certain temperature according to the equation NO(g) 1 CO2(g) NO2(g) 1 CO(g) At equilibrium, 0.11 mole of CO2 was present. Calculate the equilibrium constant Kc of this reaction.

The equilibrium constant Kc for the reaction H2(g) 1 I2(g) 2HI(g) is 54.3 at 430C. At the start of the reaction there are 0.714 mole of H2, 0.984 mole of I2, and 0.886 mole of HI in a 2.40-L reaction chamber. Calculate the concentrations of the gases at equilibrium

When heated, a gaseous compound A dissociates as follows: A(g) B(g) 1 C(g) In an experiment, A was heated at a certain temperature until its equilibrium pressure reached 0.14P, where P is the total pressure. Calculate the equilibrium constant KP of this reaction.

When a gas was heated under atmospheric conditions, its color deepened. Heating above 150C caused the color to fade, and at 550C the color was barely detectable. However, at 550C, the color was partially restored by increasing the pressure of the system. Which of the following best fits the above description? Justify your choice. (a) A mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color and nitrogen dioxide is a brown gas. The other gases are colorless.)

In this chapter we learned that a catalyst has no effect on the position of an equilibrium because it speeds up both the forward and reverse rates to the same extent. To test this statement, consider a situation in which an equilibrium of the type 2A(g) B(g) is established inside a cylinder fitted with a weightless piston. The piston is attached by a string to the cover of a box containing a catalyst. When the piston moves upward (expanding against atmospheric pressure), the cover is lifted and the catalyst is exposed to the gases. When the piston moves downward, the box is closed. Assume that the catalyst speeds up the forward reaction (2A B) but does not affect the reverse process (B 2A). Suppose the catalyst is suddenly exposed to the equilibrium system as shown here. Describe what would happen subsequently. How does this thought experiment convince you that no such catalyst can exist? String Catalyst 2A B

The equilibrium constant Kc for the following reaction is 1.2 at 375C. N2(g) 1 3H2(g) 2NH3(g) (a) What is the value of KP for this reaction? (b) What is the value of the equilibrium constant Kc for 2NH3(g) N2(g) 1 3H2(g)? (c) What is the value of Kc for 1 2N2(g) 1 3 2H2(g) NH3(g)? (d) What are the values of KP for the reactions described in (b) and (c)?

A sealed glass bulb contains a mixture of NO2 and N2O4 gases. Describe what happens to the following properties of the gases when the bulb is heated from 20C to 40C: (a) color, (b) pressure, (c) average molar mass, (d) degree of dissociation (from N2O4 to NO2), (e) density. Assume that volume remains constant. (Hint: NO2 is a brown gas; N2O4 is colorless.)

At 20C, the vapor pressure of water is 0.0231 atm. Calculate KP and Kc for the process H2O(l) H2O(g)

Industrially, sodium metal is obtained by electrolyzing molten sodium chloride. The reaction at the cathode is Na1 1 e2 Na. We might expect that potassium metal would also be prepared by electrolyzing molten potassium chloride. However, potassium metal is soluble in molten potassium chloride and therefore is hard to recover. Furthermore, potassium vaporizes readily at the operating temperature, creating hazardous conditions. Instead, potassium is prepared by the distillation of molten potassium chloride in the presence of sodium vapor at 892C: Na(g) 1 KCl(l) NaCl(l) 1 K(g) In view of the fact that potassium is a stronger reducing agent than sodium, explain why this approach works. (The boiling points of sodium and potassium are 892C and 770C, respectively.)

In the gas phase, nitrogen dioxide is actually a mixture of nitrogen dioxide (NO2) and dinitrogen tetroxide (N2O4). If the density of such a mixture is 2.3 g/L at 74C and 1.3 atm, calculate the partial pressures of the gases and KP for the dissociation of N2O4

The equilibrium constant for the reaction A 1 2B 3C is 0.25 at a certain temperature. Which diagram shown here corresponds to the system at equilibrium? If the system is not at equilibrium, predict the direction of the net reaction to reach equilibrium. Each molecule represents 0.40 mole and the volume of the container is 2.0 L. The color codes are A 5 green, B 5 red, C 5 blue. (a) (b) (c)

The equilibrium constant for the reaction 4X 1 Y 3Z is 33.3 at a certain temperature. Which diagram shown here corresponds to the system at equilibrium? If the system is not at equilibrium, predict the direction of the net reaction to reach equilibrium. Each molecule represents 0.20 mole and the volume of the container is 1.0 L. The color codes are X 5 blue, Y 5 green, and Z 5 red. (a) (b) (c)

About 75 percent of hydrogen for industrial use is produced by the steam-reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at 800C to give hydrogen and carbon monoxide: CH4(g) 1 H2O(g) CO(g) 1 3H2(g) H 5 260 kJ/mol The secondary stage is carried out at about 1000C, in the presence of air, to convert the remaining methane to hydrogen: CH4(g) 1 1 2O2(g) CO(g) 1 2H2(g) H 5 35.7 kJ/mol (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stage? (b) The equilibrium constant Kc for the primary stage is 18 at 800C. (i) Calculate KP for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

Photosynthesis can be represented by 6CO2(g) 1 6H2O(l) C6H12O6(s) 1 6O2(g) H 5 2801 kJ/mol Explain how the equilibrium would be affected by the following changes: (a) partial pressure of CO2 is increased, (b) O2 is removed from the mixture, (c) C6H12O6 (glucose) is removed from the mixture, (d) more water is added, (e) a catalyst is added, (f) temperature is decreased.

Consider the decomposition of ammonium chloride at a certain temperature: NH4Cl(s) NH3(g) 1 HCl(g) Calculate the equilibrium constant KP if the total pressure is 2.2 atm at that temperature.

At 25C, the equilibrium partial pressures of NO2 and N2O4 are 0.15 atm and 0.20 atm, respectively. If the volume is doubled at constant temperature, calculate the partial pressures of the gases when a new equilibrium is established

In 1899 the German chemist Ludwig Mond developed a process for purifying nickel by converting it to the volatile nickel tetracarbonyl [Ni(CO)4] (b.p. 5 42.2C): Ni(s) 1 4CO(g) Ni(CO)4(g) (a) Describe how you can separate nickel and its solid impurities. (b) How would you recover nickel? [Hf for Ni(CO)4 is 2602.9 kJ/mol.]

Consider the equilibrium reaction described in Problem 14.23. A quantity of 2.50 g of PCl5 is placed in an evacuated 0.500-L flask and heated to 250C. (a) Calculate the pressure of PCl5, assuming it does not dissociate. (b) Calculate the partial pressure of PCl5 at equilibrium. (c) What is the total pressure at equilibrium? (d) What is the degree of dissociation of PCl5? (The degree of dissociation is given by the fraction of PCl5 that has undergone dissociation.)

Consider the equilibrium system 3A B. Sketch the changes in the concentrations of A and B over time for the following situations: (a) initially only A is present; (b) initially only B is present; (c) initially both A and B are present (with A in higher concentration). In each case, assume that the concentration of B is higher than that of A at equilibrium.

The vapor pressure of mercury is 0.0020 mmHg at 26C. (a) Calculate Kc and KP for the process Hg(l) Hg(g). (b) A chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring 6.1 m long, 5.3 m wide, and 3.1 m high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor in mg/m3 . Does this concentration exceed the safety limit of 0.05 mg/m3 ? (Ignore the volume of furniture and other objects in the laboratory.)

At 25C, a mixture of NO2 and N2O4 gases are in equilibrium in a cylinder fitted with a movable piston. The concentrations are [NO2] 5 0.0475 M and [N2O4] 5 0.487 M. The volume of the gas mixture is halved by pushing down on the piston at constant temperature. Calculate the concentrations of the gases when equilibrium is reestablished. Will the color become darker or lighter after the change? [Hint: Kc for the dissociation of N2O4 to NO2 is 4.63 3 1023 . N2O4(g) is colorless and NO2(g) has a brown color.]

A student placed a few ice cubes in a drinking glass with water. A few minutes later she noticed that some of the ice cubes were fused together. Explain what happened.

Consider the potential energy diagrams for two types of reactions A B. In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture. Reaction progress A A B B Potential energy Reaction progress Potential energy

The equilibrium constant Kc for the reaction 2NH3(g) N2(g) 1 3H2(g) is 0.83 at 375C. A 14.6-g sample of ammonia is placed in a 4.00-L flask and heated to 375C. Calculate the concentrations of all the gases when equilibrium is reached.

A quantity of 1.0 mole of N2O4 was introduced into an evacuated vessel and allowed to attain equilibrium at a certain temperature N2O4(g) 2NO2(g) The average molar mass of the reacting mixture was 70.6 g/mol. (a) Calculate the mole fractions of the gases. (b) Calculate KP for the reaction if the total pressure was 1.2 atm. (c) What would be the mole fractions if the pressure were increased to 4.0 atm by reducing the volume at the same temperature?

The equilibrium constant (KP) for the reaction C(s) 1 CO2(g) 2CO(g) is 1.9 at 727C. What total pressure must be applied to the reacting system to obtain 0.012 mole of CO2 and 0.025 mole of CO?

The forward and reverse rate constants for the reaction A(g) 1 B(g) C(g) are 3.6 3 1023 /M ? s and 8.7 3 1024 s21 , respectively, at 323 K. Calculate the equilibrium pressures of all the species starting at PA 5 1.6 atm and PB 5 0.44 atm.

The equilibrium constant (KP) for the reaction PCl3(g) 1 Cl2(g) PCl5(g) is 2.93 at 127C. Initially there were 2.00 moles of PCl3 and 1.00 mole of Cl2 present. Calculate the partial pressures of the gases at equilibrium if the total pressure is 2.00 atm.

Consider the reaction between NO2 and N2O4 in a closed container: N2O4(g) 2NO2(g) Initially, 1 mole of N2O4 is present. At equilibrium, mole of N2O4 has dissociated to form NO2. (a) Derive an expression for KP in terms of and P, the total pressure. (b) How does the expression in (a) help you predict the shift in equilibrium due to an increase in P? Does your prediction agree with Le Chteliers principle?

The dependence of the equilibrium constant of a reaction on temperature is given by the vant Hoff equation: ln K 5 2H RT 1 C where C is a constant. The following table gives the equilibrium constant (KP) for the reaction at various temperatures 2NO(g) 1 O2(g) 2NO2(g) KP 138 5.12 0.436 0.0626 0.0130 T(K) 600 700 800 900 1000 Determine graphically the H for the reaction.

(a) Use the vant Hoff equation in Problem 14.118 to derive the following expression, which relates the equilibrium constants at two different temperatures ln K1 K2 5 H R a 1 T2 2 1 T1 b How does this equation support the prediction based on Le Chteliers principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are 31.82 mmHg at 30C and 92.51 mmHg at 50C. Calculate the molar heat of vaporization of water

The KP for the reaction SO2Cl2(g) SO2(g) 1 Cl2(g) is 2.05 at 648 K. A sample of SO2Cl2 is placed in a container and heated to 648 K while the total pressure is kept constant at 9.00 atm. Calculate the partial pressures of the gases at equilibrium.

The boat form and chair form of cyclohexane (C6H12) interconverts as shown here: k1 Boat Chair k1 In this representation, the H atoms are omitted and a C atom is assumed to be at each intersection of two lines (bonds). The conversion is first order in each direction. The activation energy for the chair S boat conversion is 41 kJ/mol. If the frequency factor is 1.0 3 1012 s21 , what is k1 at 298 K? The equilibrium constant Kc for the reaction is 9.83 3 103 at 298 K.

Consider the following reaction at a certain temperature A2 1 B2 2AB The mixing of 1 mole of A2 with 3 moles of B2 gives rise to x mole of AB at equilibrium. The addition of 2 more moles of A2 produces another x mole of AB. What is the equilibrium constant for the reaction?

Iodine is sparingly soluble in water but much more so in carbon tetrachloride (CCl4). The equilibrium constant, also called the partition coefficient, for the distribution of I2 between these two phases I2(aq) I2(CCl4) is 83 at 20C. (a) A student adds 0.030 L of CCl4 to 0.200 L of an aqueous solution containing 0.032 g I2. The mixture is shaken and the two phases are then allowed to separate. Calculate the fraction of I2 remaining in the aqueous phase. (b) The student now repeats the extraction of I2 with another 0.030 L of CCl4. Calculate the fraction of the I2 from the original solution that remains in the aqueous phase. (c) Compare the result in (b) with a single extraction using 0.060 L of CCl4. Comment on the difference.

Consider the following equilibrium system: N2O4(g) 2NO2(g) H 5 58.0 kJ/mol (a) If the volume of the reacting system is changed at constant temperature, describe what a plot of P versus 1/V would look like for the system. (Hint: See Figure 5.7.) (b) If the temperatures of the reacting system is changed at constant pressure, describe what a plot of V versus T would look like for the system. (Hint: See Figure 5.9.)

At 1200C, the equilibrium constant (Kc) for the reaction I2(g) 2I(g) is 2.59 3 1023 . Calculate the concentrations of I2 and I after the stopcock is opened and the system reestablishes equilibrium at the same temperature. 0.100 mol I2 0.0161 mol I 1 L 2 L

Estimate the vapor pressure of water at 60C (see Problem 14.119).

A compound XY2(s) decomposes to form X(g) and Y(g) according to the following chemical equation: XY2(s) X(g) 1 2Y(g) A 0.01-mol sample of XY2(s) was placed in a 1-L vessel, which was sealed and heated to 500C. The reaction was allowed to reach equilibrium, at which point some XY2(s) remained in the vessel. The experiment was repeated, this time using a 2-L vessel, and again some XY2(s) remained in the vessel after equilibrium was established. This process was repeated, each time doubling the volume of the vessel, until finally a 16-L vessel was used, at which point heating the vessel and its contents to 500C resulted in decomposition of the entire 0.01 mole of XY2(s) according to the above reaction. Estimate Kc and KP for the reaction at 500C

Using the simplified chemical equilibrium given in the Chemistry in Action essay on p. 651, by how much would the concentration of hemoglobin, Hb, in a persons blood need to increase if she moved to an altitude of 2 km above sea level, in order to give the same concentration of HbO2 as when she was living at sea level?

The equilibrium constant (KP) for the reaction I2(g) 2I(g) is 1.8 3 104 at 872 K and 0.048 at 1173 K. From these data, estimate the bond enthalpy of I2. (Hint: See vant Hoffs equation in Problem 14.119.)