The equilibrium constant for the H2 1 1 2 O2m H2O reaction

Problem 1P Write three different KP relations for reacting ideal. gas mixtures, and state when each relation should be used.

Problem 5P Which element is more likely to dissociate into its ' monatomic form at 3000 K, H2 or N2? Why?

Problem 2P A reaction chamber contains a mixture of CO2, CO, and O2 in equilibrium at a specified temperature and pressure. How will (a) increasing the temperature at constant pressure and (b) increasing the pressure at consent temperature affect the number of moles of CO2?

Problem 4P A reaction chamber contains a mixture of CO2, CO, and O2 in equilibrium at a specified temperature and pressure. Now some N2 is added to the mixture while the mixture temperature and pressure are kept constant. Will this affect the number of moles of O2? How?

Problem 117P The value of Henry’s constant for CO2 gas dissolved in water at 290 K is 12.8 MPa. Consider water exposed to atmospheric air at 100 kPa that contains 3 percent CO2 by volume. Under phase equilibrium conditions, the mole fraction of CO2 gas dissolved in water at 290 K is (a) 2.3 × 10-4 ________________ (b) 3.0 × 10-4 ________________ (c) 0.80 × 10-4 ________________ (d) 2.2 × 10-4 ________________ (e) 5.6 × 10-4

The equilibrium constant of the dissociation reaction \(\mathrm{H}_{2} \rightarrow 2 \mathrm{H}\) at \(3000 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is \(K_{P}\). Express the equilibrium constants of the following reactions at \(3000 \mathrm{~K}\)in terms of \(K_{P_{1}}\) : (a) \(\mathrm{H}_{2} \rightleftharpoons 2 \mathrm{H}\) at \(2 \mathrm{~atm}\) (b) \(\quad 2 \mathrm{H} \rightleftharpoons \mathrm{H}_{2}\) at \(1 \mathrm{~atm}\) (c) \(\quad 2 \mathrm{H}_{2} \rightleftharpoons 4 \mathrm{H}\) (d) \(\mathrm{H}_{2}+2 \mathrm{~N}_{2} \rightleftharpoons 2 \mathrm{H}+2 \mathrm{~N}_{2} \quad\) at \(2 \mathrm{~atm}\) (e) \(\quad 6 \mathrm{H} \rightleftharpoons 3 \mathrm{H}_{2} \quad\)at \(4 \mathrm{~atm}\) Equation Transcription: ? ? ? ? ? Text Transcription: H_2 rightarrow 2H s 3000 K 1 atm K_P_1 3000 K K_P_1 H_2 leftrightharpoons 2H 2 atm 2H leftrightharpoons H_2 1 atm 2H_2 leftrightharpoon 4H 1 atm H_2+2N_2 leftrightharpoons 2H+2N_2 2 atm 6H leftrightharpoons 3H_2 4 atm

Problem 3P A reaction chamber contains a mixture of N2 and N in equilibrium at a specified temperature and pressure. How will (a) increasing the temperature at constant pressure and (b) increasing the pressure at constant temperature affect the number of moles of N2?

The equilibrium constant for the \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons\) \(\mathrm{H}_{2} \mathrm{O}\) reaction at \(1 \mathrm{~atm}\) and \(1200 \mathrm{~K}\) is \(K_{P}\). Use this information to determine the equilibrium constant for the following reactions: (a) at \(1 \mathrm{~atm} \quad \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) (b) at \(7 \mathrm{~atm} \quad \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) (c) at \(1 \mathrm{~atm} \quad 3 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 3 \mathrm{H}_{2}+\frac{3}{2} \mathrm{O}_{2}\) (d) at \(12 \mathrm{~atm} \quad 3 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 3 \mathrm{H}_{2}+\frac{3}{2} \mathrm{O}_{2}\) Equation Transcription: ? ? ? ? ? Text Transcription: H_2+1/2O_2 leftrightharpoons H_2O 1 atm 1200 K K_P 1 atm H_2+1/2O_2 leftrightharpoonsH_2O 7 atm H_2+1/2O_2 leftrightharpoonsH_2O 1 atm 3H_2O leftrightharpoons 3H_2+3/2O_2 12 atm 3H_2O leftrightharpoons+3H_2+3/2O_2

The equilibrium constant of the reaction \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}\) \(\rightarrow \mathrm{CO}_{2}\) at \(1000 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is \(K_{P_{1}}\). Express the equilibrium constant of the following reactions at \(1000 \mathrm{~K}\) in terms of \(K_{P_{1}}\) : (a) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) at \(3 \mathrm{~atm}$\) (b) \(\mathrm{CO}_{2} \rightleftharpoons \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}\) at \(1 \mathrm{~atm}\)$ (c) \(\quad \mathrm{CO}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+\frac{1}{2} \mathrm{O}_{2}$ at \(1 \mathrm{~atm}$ (d) \(\mathrm{CO}+2 \mathrm{O}_{2}+5 \mathrm{~N}_{2} \rightleftharpoons \mathrm{CO}_{2}+1.5 \mathrm{O}_{2}+5 \mathrm{~N}_{2}$ at \(4 \mathrm{~atm}$ (e) \(\quad 2 \mathrm{CO}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{CO}_{2}$ at \(1 \mathrm{~atm}$ Equation Transcription: ? ? ? ? ? Text Transcription: CO+1/2O_2CO_2 1000 K 1 atm K_P_1 1000 K K_P_1 CO+1/2O_2 leftrightharpoons CO_2 3 atm CO_2 leftrightharpoons CO+1/2O_2 1 atm CO+O_2 leftrightharpoons CO_2+1/2O_2 1 atm CO+2O_2+5N_2 leftrightharpoons CO_2+1.5O_2+5N_24 atm 2CO+O_2 leftrightharpoons 2CO_2 1 atm

Problem 11P At temperature will nitrogen be 0.2 percent disassociated at (a) 1 kPa and (b) 10 kPa?

A mixture of ideal gases is made up of 30 percent \(\mathrm{N}_{2}, 30\) percent \(\mathrm{O}_{2}\), and 40 percent \(\mathrm{H}_{2} \mathrm{O}\) by mole fraction. Determine the Gibbs function of the \(\mathrm{N}_{2}\) when the mixture pressure is \(5 \mathrm{~atm}\), and its temperature is \(600 \mathrm{~K}\). Equation Transcription: Text Transcription: N_2 O_2 H_2O N_2 5 atm 600 K

Problem 13P Repeat Prob. 16–12 for a pressure of 6 atm. Problem 16–12 Determine the temperature at which 5 percent of diatomic oxygen (O2) dissociates into monatomic oxygen (O) at a pressure of 3 atm.

Using the Gibbs function data, determine the equilibrium constant \(K_{P}\) for the reaction \(\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}+\mathrm{OH}\) at \(25^{\circ} \mathrm{C}\). Compare your result with the \(K_{P}\) value listed in Table A-28. Equation Transcription: ? Text Transcription: K_P H_2O leftrightharpoons 1/2 H_2+OH 25^circC K_P

Problem 9P Consider a mixture of CO2, CO, and O2 in equilibrium at a specified temperature and pressure. Now the pressure is doubled. (a) Will the equilibrium constant KP change? ________________ (b) Will the number of moles of CO2, CO, and O2 change? How?

Problem 12P Determine the temperature at which 5 percent of diatomic oxygen (O2) dissociates into monatomic oxygen (O) at a pressure of 3 atm.

A gaseous mixture of 30 percent (by mole fraction) methane and 70 percent carbon dioxide is heated at \(1 \mathrm{~atm}\) pressure to \(1200 \mathrm{~K}\). What is the equilibrium composition (by mole fraction) of the resulting mixture? The natural logarithm of the equilibrium constant for the reaction \(\mathrm{C}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{4}\) at \(1200 \mathrm{~K}\) is 4.147. Equation Transcription: ? Text Transcription: 1 atm 1200 K C+2H_2 leftrightharpoons CH_4 1200 K

Carbon dioxide is commonly produced through the reaction \(\mathrm{C}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\). Determine the yield of carbon dioxide (mole fraction) when this is done in a reactor maintained at \(1 \mathrm{~atm}\) and \(3800 \mathrm{~K}\). The natural logarithm of the equilibrium constant for the reaction \(\mathrm{C}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) at \(3800 \mathrm{~K}\) is -0.461. Equation Transcription: ? ? Text Transcription: C+O_2 leftrightharpoons CO_2 1 atm 3800 K C+O_2 leftrightharpoons CO_2 3800 K

Determine the composition of the products of the disassociation reaction \(\mathrm{CO}_{2} \rightleftharpoons \mathrm{CO}+\mathrm{O}\) when the products are at \(1 \mathrm{~atm}\) and \(2500 \mathrm{~K}\). Note: First evaluate the \(K_{P}\) of this reaction using the \(K_{P}\) values of the reactions \(\mathrm{CO}_{2} \rightleftharpoons\) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}\) and \(0.5 \mathrm{O}_{2} \rightleftharpoons \mathrm{O}\). Equation Transcription: ? ? ? Text Transcription: CO_2 leftrightharpoons CO+O 1 atm 2500 K K_P K_P CO_2 leftrightharpoons CO+1/2O_2 0.5O_2 leftrightharpoons O

Using Gibbs function data, determine the equilibrium constant \(K_{P}\) for the reaction \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) at (a) \(537 \mathrm{R}\) and (b) \(3240 \mathrm{R}\). Compare your results with the \(K_{P}\)values listed in Table A-28. Equation Transcription: ? Text Transcription: K_P H_2+1/2O_2 leftrightharpoons H_2O 537 R 3240 R K_P ________________

Using the Gibbs function data, determine the equilibrium constant \(K_{P}\) for the dissociation process \(\mathrm{CO}_{2} \rightleftharpoons\) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}\) at \((a) 298 \mathrm{~K}\) and \((b) 1800 \mathrm{~K}\). Compare your results with the \(K_{P}\) values listed in Table A-28. Equation Transcription: ? Text Transcription: K_P CO_2 leftrightharpoons CO+1/2O_2 298 K 1800 K K_P

Determine the equilibrium constant \(K_{P}\) for the process \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}=\mathrm{CO}_{2}\) at (a) \(298 \mathrm{~K}\) and \((b) 2000 \mathrm{~K}\). Compare your results with the values for \(K_{P}\) listed in Table A-28. Equation Transcription: Text Transcription: K_P CO+1/2O_2=CO_2 298 K 2000 K K_P

Determine the equilibrium constant \(K_{P}\) for the reaction \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C}\). Equation Transcription: ? Text Transcription: K_P CH_4+2O_2 leftrightharpoons CO_2+2H_2O 25^circ C

Problem 19P The reaction N2 + O2 ? 2NO occurs in internal combustion engines. Determine the equilibrium mole fraction of NO when the pressure is 101 kPa and the temperature is 1800 K.

Problem 25P Carbon monoxide is burned with 100 percent excess air during a steady-flow process at a pressure of 1 atm. At what temperature will 97 percent of CO burn to CO2? Assume the equilibrium mixture consists of CO2, CO, O2, and N2.

Problem 28P Air (79 percent N2 and 21 percent O2) is heated to 2000 K at a constant pressure of 2 atm. Assuming the equilibrium mixture consists of N2,O2, and NO, determine the equilibrium composition at this state. Is it realistic to assume that no monatomic oxygen or nitrogen will be present in the equilibrium mixture? Will the equilibrium composition change if the pressure is doubled at constant temperature?

Problem 27P Repeat Prob. 16–25 using data in English units. Problem 16–25 Carbon monoxide is burned with 100 percent excess air during a steady-flow process at a pressure of 1 atm. At what temperature will 97 percent of CO burn to CO2? Assume the equilibrium mixture consists of CO2, CO, O2, and N2.

Problem 29P Hydrogen (H2) is heated to 3800 Kata constant pressure of 5 atm. Determine the percentage of H2 that will dissociate into H during this process.

Problem 31P A mixture of 1 mol of CO and 3 mol of O2 is heated to 2200 K at a pressure of 2 atm. Determine the equilibrium composition, assuming the mixture consists of CO2, CO, and O2.

Use the Gibbs function to determine the equilibrium constant of the \(\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}\) reaction at (a) \(1000 \mathrm{~K}\) and \((b) 2000 \mathrm{~K}\). How do these compare to the equilibrium constants of Table A-28? Equation Transcription: ? Text Transcription: H_2O leftrightharpoons H_2+1/2O_2 1000 K 2000 K

Problem 30P Carbon dioxide (CO2) is heated to 2400 K at a constant pressure of 3 atm. Determine the percentage of CO2 that will dissociate into CO and O2 during this process.

Problem 32P A mixture of 3 mol of N2,1 mol of O2, and 0.1 mol of Ar is heated to 2400 K at a constant pressure of 10 atm. Assuming the equilibrium mixture consists of N2, O2, Ar, and NO, determine the equilibrium composition.

Liquid propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) enters a combustion chamber at \(25^{\circ} \mathrm{C}\) at a rate of \(1.2 \mathrm{~kg} / \mathrm{min}\) where it is mixed and burned with 150 percent excess air that enters the combustion chamber at \(12^{\circ} \mathrm{C}\). If the combustion gases consist of \(\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{O}_{2}\), and \(\mathrm{N}_{2}\) that exit at \(1200 \mathrm{~K}\) and \(2 \mathrm{~atm}\), determine (a) the equilibrium composition of the product gases and (b) the rate of heat transfer from the combustion chamber. Is it realistic to disregard the presence of \(\mathrm{NO}\) in the product gases? Equation Transcription: Text Transcription: (C_3H_8) 25^circC 1.2 kg/min 12C CO_2,H_2O,CO,O_2,N_2 1200 K 2 atm NO

Determine the mole fraction of sodium that ionizes according to the reaction \(\mathrm{Na} \rightleftharpoons \mathrm{Na}^{+}+e^{-}\) at \(2000 \mathrm{~K}\) and \(0.8 \operatorname{atm}\left(K_{P}=0.668\) for this reaction). Equation Transcription: ? Text Transcription: Na leftrightharpoon Na^++e^- 2000 K 0.8 atm(K_P=0.668

Problem 34P A steady-flow combustion chamber is supplied with CO gas at 560 R and 16 psia at a rate of 12.5 ft3/min and with oxygen (O2) at 537 R and 16 psia at a rate of 0.7 lbm/min. The combustion products leave the combustion chamber at 3600 R and 16 psia. If the combustion gases consist of CO2, CO, and O2, determine (a) the equilibrium composition of the product gases and (b) the rate of heat transfer from the combustion chamber.

Problem 39P A constant-volume tank contains a mixture of 1 kmol H2 and 1 kmol O2 at 25°C and 1 atm. The contents are ignited. Determine the final temperature and pressure in the tank when the combustion gases are H2O, H2, and O2.

Problem 38P Estimate KP for the following equilibrium reaction at 2500 K: CO + H2O = CO2 + H2 At 2000 K it is known that the enthalpy of reaction is –26,176 kJ/kmol and KP is 0.2209. Compare your result with the value obtained from the definition of the equilibrium constant.

Oxygen \(\left(\mathrm{O}_{2}\right)\) is heated during a steady-flow process at 1 atm from 298 to \(3000 \mathrm{~K}\) at a rate of \(0.5 \mathrm{~kg} / \mathrm{min}\). Determine the rate of heat supply needed during this process, assuming (a) some \(\mathrm{O}_{2}\) dissociates into \(\mathrm{O}$ and (b) no dissociation takes place. Equation Transcription: Text Transcription: O_2 1 atm 3000 K 0.5 kg/min O_2 O

Show that as long as the extent of the reaction, \(\alpha\), for the disassociation reaction \(\mathrm{X}_{2} \rightleftharpoons 2 \mathrm{X}\) is smaller than one, \(\alpha\) is given by \(\alpha=\sqrt{\frac{K_{P}}{4+K_{P}}}\) Equation Transcription: ? Text Transcription: alpha X_2 leftrightharpons 2x alpha alpha=sqrt K_P/4+K_P

Problem 42P When determining the equilibrium composition of a mixture involving simultaneous reactions, how would you determine the number of KP relations needed?

Problem 43P One mole of H2O is heated to 3400 K at a pressure of 1 atm. Determine the equilibrium composition, assuming that only H2O, OH, O2, and H2 are present.

Problem 41P What is the equilibrium criterion for systems that involve two or more simultaneous chemical reactions?

Problem 44P A mixture of 2 mol of CO2 and 1 mol of O2 is heated to 3200 K at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only CO2, CO, O2, and O are present.

Air ( 21 percent \(\mathrm{O}_{2}, 79\) percent \(\mathrm{N}_{2}\) ) is heated to \(5400 \mathrm{R}\) at a pressure of \(1 \mathrm{~atm}\). Determine the equilibrium composition, assuming that only \(\mathrm{O}_{2}, \mathrm{~N}_{2}, \mathrm{O}\), and \(\mathrm{NO}\) are present. Is it realistic to assume that no \(\mathrm{N}\) will be present in the final equilibrium mixture? Equation Transcription: Text Transcription: O_2 N_2 5400 R 1 atm O_2,N_2,O,NO N

Air ( 21 percent \(\mathrm{O}_{2}\), 79 percent \(\mathrm{N}_{2}\) ) is heated to \(3000 \mathrm{~K}\) at a pressure of \(2 \mathrm{~atm}\). Determine the equilibrium composition, assuming that only \(\mathrm{O}_{2}, \mathrm{~N}_{2}, \mathrm{O}\), and \(\mathrm{NO}\) are present. Is it realistic to assume that no \(N\) will be present in the final equilibrium mixture? Equation Transcription: Text Transcription: O_2 N_2 3000 K 2 atm O_2,N_2,O,NO N

Problem 51P What is the importance of the van’t Hoff equation?

Problem 48P Water vapor (H2O) is heated during a steady-flow process at 1 atm from 298 to 3000 K at a rate of 0.2 kg/min. Determine the rate of heat supply needed during this process, assuming (a) some H2O dissociates into H2, O2, and OH and (b) no dissociation takes place.

Estimate the enthalpy of reaction \(\bar{h}_{R}\) for the dissociation process \(\mathrm{O}_{2} \rightleftarrows 2 \mathrm{O}\) at \(3100 \mathrm{~K}\), using (a) enthalpy data and (b) \(K_{p}\) data. Equation Transcription: ? Text Transcription: Bar h_R O_2 leftrightharpoons 2O 3100 K K_P

Estimate the enthalpy of reaction \(\bar{h}_{R}\) for the combustion process of carbon monoxide at \(1800 K\), using (a) enthalpy data and (b) \(K_{p}\) data. Equation Transcription: Text Transcription: Bar h_R 1800 K K_P

Problem 52P Will a fuel bum more completely at 2000 or 2500 K?

Estimate the enthalpy of reaction \(\bar{h}_{R}\) for the dissociation process \(\mathrm{CO}_{2} \rightleftharpoons \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}\) at \(2200 \mathrm{~K}\), using (a) enthalpy data and \((b) K_{P}\) data. Equation Transcription: ? Text Transcription: Bar h_R CO_2 leftrightharpoons CO+1/2O_2 2200 K K_P

Using the enthalpy of reaction \(\bar{h}_{R}\) data and the \(K_{P}\) value at \(2400 \mathrm{~K}\), estimate the \(K_{P}\) value of the combustion process \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) at \(2600 \mathrm{~K}\). Equation Transcription: ? Text Transcription: Bar h_R K_P 2400 K K_P H_2+1/ 2O_2 leftrightharpoons H_2O 2600 K

Problem 59P Consider a tank that contains a saturated liquid-vapor mixture of water in equilibrium. Some vapor is now allowed to escape the tank at constant temperature and pressure. Will this disturb the phase equilibrium and cause some of the liquid to evaporate?

Estimate the enthalpy of reaction \(\bar{h}_{R}\) for the combustion process of carbon monoxide at 3960 \(R\), using (a) enthalpy data and (b) \(K_{p}\) data. Equation Transcription: Text Transcription: Bar h_R 3960 R K_P

Problem 60P Consider a two-phase mixture of ammonia and water in equilibrium. Can this mixture exist in two phases at the same temperature but at a different pressure?

Problem 62P Using solubility data of a gas in a solid, explain how you would determine the molar concentration of the gas in the solid at the solid-gas interface at a specified temperature.

Problem 61P Using the solubility data of a solid in a specified liquid, explain how you would determine the mole fraction of the solid in the liquid at the interface at a specified temperature.

Problem 66P Show that a saturated liquid-vapor mixture of refrig-erant-134a at –10°C satisfies the criterion for phase equilibrium.

Problem 63P Using the Henry’s constant data for a gas dissolved in a liquid, explain how you would determine the ' mole fraction of the gas dissolved in the liquid at the interface at a specified temperature.

Problem 64P Air at 70°F and 100 psia is blown through a porous media which is saturated with liquid water at 70°F. Determine the maximum partial pressure of the water evaporated into the air as it emerges from the porous media.

Problem 65P Water is sprayed into air at 80°F and 14.3 psia, and the falling water droplets are collected in a container on the floor. Determine the mass and mole fractions of air dissolved in the water.

Problem 67P Show that a mixture of saturated liquid water and saturated water vapor at 300 kPa satisfies the criterion for phase equilibrium.

A liquid-vapor mixture of refrigerant-134a is at \(280 \mathrm{kPa}\) with a quality of 70 percent. Determine the value of the Gibbs function, in \(\mathrm{kJ} / \mathrm{kg}\), when the two phases are in equilibrium. Equation Transcription: Text Transcription:

Problem 70P An ammonia-water mixture is at 10°C. Determine the pressure of the ammonia vapor when the mole fraction of the ammonia in the liquid is (a) 20 percent and (b)80 percent. The saturation pressure of ammonia at 10°C is 615.3 kPa.

Problem 72P Using the liquid-vapor equilibrium diagram of an oxygen-nitrogen mixture at 100 kPa, determine the temperature at which the composition of the vapor phase is 79 percent N2 and 21 percent O2.

Problem 73P An oxygen-nitrogen mixture consists Of 30 kg of oxygen and 40 kg of nitrogen. This mixture is cooled to 84 K at 0.1 MPa pressure. Determine the mass of the oxygen in the liquid and gaseous phase.

Problem 77P In absorption refrigeration systems, a two-phase equilibrium mixture of liquid ammonia (NH3) and water (H2O) is frequently used. Consider a liquid–vapor mixture of ammonia and water in equilibrium at 30°C. If the composition of the liquid phase is 60 percent NH3 and 40 percent H2O by mole numbers, determine the composition of the vapor phase of this mixture. Saturation pressure of NH3 at 30°C is 1167.4 kPa.

Problem 74P What is the total mass of the liquid phase of Prob. 16-76.

Problem 69P Calculate the value of the Gibbs function for saturated steam at 500°F as a saturated liquid, saturated vapor, and a mixture of liquid and vapor with a quality of 40 percent. Demonstrate that phase equilibrium exists.

Problem 75P A wall made of natural rubber separates O2 and N2 gases at 25°C and 500 kPa. Determine the molar concentrations of O2 and N2 in the wall.

Problem 71P Using the liquid–vapor equilibrium diagram of an oxygen–nitrogen mixture, determine the composition of each phase at 84 K and 100 kPa.

Problem 76P Consider a rubber plate that is in contact with nitrogen gas at 298 K and 250 kPa. Determine the molar and mass density of nitrogen in the rubber at the interface.

Problem 81P Consider a glass of water in a room at 27°C and 97 kPa. If the relative humidity in the room is 100 percent and the water and the air are in thermal and phase equilibrium, determine (a) the mole fraction of the water vapor in the air and (b) the mole fraction of air in the water.

An ammonia-water absorption refrigeration unit operates its absorber at \(0^{\circ} \mathrm{C}\) and its generator at \(46^{\circ} \mathrm{C}\). The vapor mixture in the generator and absorber is to have an ammonia mole fraction of 96 percent. Assuming ideal behavior, determine the operating pressure in the (a) generator and (b) absorber. Also determine the mole fraction of the ammonia in the (c) strong liquid mixture being pumped from the absorber and the (d) weak liquid solution being drained from the generator. The saturation pressure of ammonia at \(0^{\circ} \mathrm{C}\) is \(430.6 \mathrm{kPa}\), and at \(46^{\circ} \mathrm{C}\) it is \\(1830.2 \mathrm{kPa}\). Equation Transcription: Text Transcription: 0^circC 46^circC 0^circC 430.6 kPa 46^circC 1830.2 kPa

Problem 79P Rework Prob. 16-81 when the temperature in the absorber is increased to 6°C and the temperature in the generator is reduced to 40°C. The saturation pressure of ammonia at-6°C is 534.8 kPa, and at 40°C it is 1556.7 kPa.

Problem 80P Foam products such as shaving cream are made by liquid mixtures whose ingredients are primarily water and a refrigerant such as refrigerant-134a. Consider a liquid mixture of water and refrigerant-134a with a water mass fraction of 90 percent that is at 20°C. What is the mole fraction of the water and refrigerant-134a vapor in the gas which fdls the bubbles that form the foam?

Problem 82P Consider a carbonated drink in a bottle at 27°C and 115 kPa. Assuming the gas space above the liquid consists of a saturated mixture of CO2 and water vapor and treating the drink as water, determine (a) the mole fraction of the water vapor in the CO2 gas and (b) the mass of dissolved CO2 in a 300-ml drink.

Problem 83P Determine the mole fraction of argon that ionizes according to the reaction Ar ? Ar+ + e– at 10,000 K and 0.35 atm (KP = 0.00042 for this reaction).

Using the Gibbs function data, determine the equilibrium constant \(K_{P}\) for the dissociation process \(\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{O}\) at \(2000 \mathrm{~K}\). Compare your result with the \(K_{p}\) value listed in Table A-28. Equation Transcription: ? Text Transcription: K_P O_2 leftrightharpoons 2O 2000 K K_P

Problem 85P Determine the equilibrium constant for the reaction CH4 + 2O2 ? CO2 + 2H2O when the reaction occurs at 100 kPa and 2000 K. The natural logarithms of the equilibrium constant for the reaction C + 2H2 ? CH4 and C + O2 ? CO2 at 2000 K are 7.847 and 23.839, respectively.

Problem 86P Consider a glass of water in a room at 25°C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are in thermal equilibrium, determine (a) the mole fraction of the water vapor in the room air, (b) the mole fraction of the water vapor in the air adjacent to the water surface, and (c) the mole fraction of air in the water near the surface.

Problem 87P Repeat Prob. 16–86 for a relative humidity of 25 percent. Problem 16–86 Consider a glass of water in a room at 25°C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are in thermal equilibrium, determine (a) the mole fraction of the water vapor in the room air, (b) the mole fraction of the water vapor in the air adjacent to the water surface, and (c) the mole fraction of air in the water near the surface.

Problem 90P Consider the reaction CH4 + 2O2 ? CO2 + 2H2O when the reaction occurs at 450 kPa and 3000 K. Determine the equilibrium partial pressure of the carbon dioxide. The natural logarithms of the equilibrium constant for the reactions C + 2H2 ? CH4 and C + O2 ? CO2 at 3000 K are 9.685 and 15.869, respectively.

Problem 92P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

\(10 \mathrm{kmol}\) of methane gas are heated from \(1 \mathrm{~atm}\) and \(298 \mathrm{~K}\) to \(1 \mathrm{~atm}\) and \(1000 \mathrm{~K}\). Calculate the total amount of heat transfer required when (a) disassociation is neglected and (b) when disassociation is considered. The natural logarithm of the equilibrium constant for the reaction \(\mathrm{C}+2 \mathrm{H}_{2}\) \(\rightleftharpoons \mathrm{CH}_{4}\) at \(1000 \mathrm{~K}\) is 2.328. For the solution of part (a) use empirical coefficients of Table \(A-2c\). For the solution of part (b) use constant specific heats and take the constant volume specific heats of methane, hydrogen and carbon at \(1000 \mathrm{~K}\) to be 63.3,21.7, and \(0.711 \mathrm{~kJ} / \mathrm{kmol} \cdot \mathrm{K}\), respectively. The constant-volume specific heat of methane at \(298 \mathrm{~K}\) is \(27.8 \mathrm{~kJ} / \mathrm{kmol} \cdot \mathrm{K}\). Equation Transcription: ? Text Transcription: 10 kmol 1 atm 298 K 1 atm 1000 K C+2H_2 leftrightharpoons CH_4 1000 K A-2c 1000 K 0.711 kJ/kmol cdot K 298 K 27.8 kJ/kmol cdot K

Reconsider Prob. 16–88. Using EES (or other) software, study the effect of excess air on the equilibrium composition and the exit temperature by varying the percent excess air from 0 to 200 percent. Plot the exit temperature against the percent excess air, and discuss the results.

Problem 93P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

Methane gas \(\left(\mathrm{CH}_{4}\right)\) at \(25^{\circ} \mathrm{C}\) is burned with the stoichiometric amount of air at \(5^{\circ} \mathrm{C}\) during an adiabatic steady-flow combustion process at \(1 \mathrm{~atm}\). Assuming the product gases consist of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{N}_{2}\), and \(\mathrm{O}_{2}\), determine (a) the equilibrium composition of the product gases and (b) the exit temperature. Equation Transcription: Text Transcription: (CH_4) 25^circC 25^circC CO_2,H_2O,CO,N_2,O_2

Problem 94P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

Problem 96P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

Problem 95P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

Problem 97P Solid carbon at 25°C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25°C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727°C.

Estimate the enthalpy of reaction \(\bar{h}_{R}\) for the combustion process of hydrogen at \(2400 \mathrm{~K}\), using (a) enthalpy data and (b) \(K_{p}\) data. Equation Transcription: Text Transcription: Bar h_R 2400 K K_P

Problem 98P A mixture of 2 mol of H2O and 3 mol of O2 is heated to 3600 K at a pressure of 8 atm. Determine the equilibrium composition of the mixture, assuming that only H2O, OH, O2, and H2 are present.

Problem 99P A mixture of 3 mol of CO2 and 3 mol of O2 is heated to 3400 Kata pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only CO2, CO, O2, and O are present.

Reconsider Prob. 16-101. Using EES (or other) software, investigate the effect of temperature on the enthalpy of reaction using both methods by varying the temperature from 2000 to 3000 \(\mathrm{K}\). Equation Transcription: Text Transcription: 3000 K

Problem 104P A carbonated drink is fully charged with C02 gas at 17°C and 600 kPa such that the entire bulk of the drink is in thermodynamic equilibrium with the CO2-water vapor mixture. Now consider a 2-L soda bottle. If the CO2 gas in that bottle were to be released and stored in a container at 20°C and 100 kPa, determine the volume of the container.

Problem 107P Show that when the three phases of a pure substance are in equilibrium, the specific Gibbs function of each phase is the same.

Using the enthalpy of reaction \(\bar{h}_{R}\) data and the \(K_{P}\) value at \(2200 \mathrm{~K}\), estimate the \(K_{P}\) value of the dissociation process \(\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{O}\) at \(2400 \mathrm{~K}\). Equation Transcription: ? Text Transcription: Bar h_R K_P 2200 K K_P O_2 leftrightharpoons 2O 2400 K

Problem 108P Show that when the two phases of a two-component system are in equilibrium, the specific Gibbs function of each phase of each component is the same.

If the equilibrium constant for the reaction \(\mathrm{CO}+\) \(\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) is \(K\), the equilibrium constant for the reaction \(\mathrm{CO}_{2}+3 \mathrm{~N}_{2} \rightleftharpoons \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}+3 \mathrm{~N}_{2}\) at the same temperature is (a) \(1 / K\) (b) \(1 /(K+3)$ (c) \(4 K$ (d) \(K$ (e) \(1 / K^{2}$ Equation Transcription: ? ? Text Transcription: CO+1/2O_2 leftrightharpoonsCO_2 K CO_2+3N_2 leftrightharpoonsCO+1/2O_2+3N_2 1/K 1/(K+3) 4K K

If the equilibrium constant for the reaction \(\mathrm{H}_{2}+\) \(\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) is \(K\), the equilibrium constant for the reaction \(2 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 2 \mathrm{H}_{2}+\mathrm{O}_{2}\) at the same temperature is (a) \(1 / K\) (b) \(1 /(2 K)\) (c) \(2 K\) (d) \(K^{2}\) (e) \(1 / K^{2}\) Equation Transcription: ? ? Text Transcription: H_2+1/2O_2 leftrightharpoons H_2O 2H_2O+ leftrightharpoons 2H_2+O_2 1/K 1/2(K) 2K K^2 1/K^2

The equilibrium constant for the reaction \(\mathrm{H}_{2}+\) \(\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) at \(1 \mathrm{~atm}\) and \(1500^{\circ} \mathrm{C}\) is given to be \(K\). Of the reactions given below, all at $1500^{\circ} \mathrm{C}$, the reaction that has a different equilibrium constant is (a) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) at \(5 \mathrm{~atm}\) (b) \(2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}\) at \(1 \mathrm{~atm}\) (c) \(\mathrm{H}_{2}+\mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\frac{1}{2} \mathrm{O}_{2}\) at \(2 \mathrm{~atm}\) (d) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}+3 \mathrm{~N}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+3 \mathrm{~N}_{2}\) at \(5 \mathrm{~atm}\) (e) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}+3 \mathrm{~N}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+3 \mathrm{~N}_{2}\) at \(1 \mathrm{~atm}\) Equation Transcription: ? ? ? ? ?? ?? Text Transcription: H_2+1/2O_2 leftrightharpoons H2O 1 atm 1500^circC K 1500^circC H_2+1/2O_2 leftrightharpoons H_2O 5 atm 2H_2+O_2 leftrightharpoons 2H_2O 1 atm H_2+O_2 leftrightharpoons H_2O+1/2 2 atm H_2+1/2O_2 leftrightharpoons 3N_2 leftrightharpoons H_2O+3N_2 5 atm H_2+1/2O_2 leftrightharpoons 3N_2 leftrightharpoons H_2O+3N_2 1 atm

Of the reactions given below, the reaction whose equilibrium composition at a specified temperature is not affected by pressure is (a) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) (c) \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\) (d) \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{~N}\) (e) all of the above Equation Transcription: ? ? ? ? Text Transcription: H_2+1/2O_2 leftrightharpoons H_2O CO+1/2O_2 leftrightharpoons CO_2 N_2+O_2 leftrightharpoons 2NO N_2 leftrightharpoons 2N

Of the reactions given below, the reaction whose number of moles of products increases by the addition of inert gases into the reaction chamber at constant pressure and temperature is (a) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) (c)\(\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\) (d) \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{~N}\) (e) all of the above Equation Transcription: ? ? ? ? Text Transcription: H_2+1/2O_2 leftrightharpoons H_2O CO+1/2O_2 leftrightharpoons CO_2 N_2+O_2 leftrightharpoons 2NO N_2 leftrightharpoons 2N

Problem 115P Propane C3H8 is burned with air, and the combustion products consist of CO2, CO, H2O,O2, N2, OH, H2, and NO. The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) 1 ________________ (b) 2 ________________ (c) 3 ________________ (d) 4 ________________ (e) 5

Problem 114P Moist air is heated to a very high temperature. If the equilibrium composition consists of H2O, O2, N2, OH, H2, and NO, the number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) l ________________ (b) 2 ________________ (c) 3 ________________ (d) 4 ________________ (e) 5

Problem 116P Consider a gas mixture that consists of three components. The number of independent variables that need to be specified to fix the state of the mixture is (a) 1 ________________ (b) 2 ________________ (c) 3 ________________ (d) 4 ________________ (e) 5

Write three different relations for reacting ideal-gas mixtures, and state when each relation should be used.

A reaction chamber contains a mixture of , , and in equilibrium at a specified temperature and pressure. How will (a) increasing the temperature at constant pressure and (b) increasing the pressure at constant temperature affect the number of moles of ?

A reaction chamber contains a mixture of and N in equilibrium at a specified temperature and pressure. How will (a) increasing the temperature at constant pressure and (b) increasing the pressure at constant temperature affect the number of moles of ?

A reaction chamber contains a mixture of , , and in equilibrium at a specified temperature and pressure. Now some is added to the mixture while the mixture temperature and pressure are kept constant. Will this affect the number of moles of ? How?

Which element is more likely to dissociate into its monatomic form at , or ? Why?

The equilibrium constant for the reaction at and is . Use this information to determine the equilibrium constant for the following reactions: (a) at 1 atm (b) at 7 atm (c) at 1 atm (d) at 12 atm

The equilibrium constant of the dissociation reaction and is . Express the equilibrium constants of the following reactions at in terms of : (a) (b) (c) (d) (e) at

The equilibrium constant of the reaction at and is , Express the equilibrium constant of the following reactions at in terms of : (a) (b) (c) (d) (e)

Consider a mixture of , , and in equilibrium at a specified temperature and pressure. Now the pressure is doubled. (a) Will the equilibrium constant change? (b) Will the number of moles of , , and change? How?

A mixture of ideal gases is made up of 30 percent , 30 percent , and 40 percent by mole fraction. Determine the Gibbs function of the when the mixture pressure is , and its temperature is .

At what temperature will nitrogen be 0.2 percent disassociated at (a) and (b) ?

Determine the temperature at which 5 percent of diatomic oxygen dissociates into monatomic oxygen at a pressure of .

Repeat Prob. 16-12 for a pressure of .

Using the Gibbs function data, determine the equilibrium constant for the reaction at . Compare your result with the value listed in Table A-28.

Use the Gibbs function to determine the equilibrium constant of the reaction at (a) 1000 K and (b) 2000 K. How do these compare to the equilibrium constants of Table A28?

Carbon dioxide is commonly produced through the reaction . Determine the yield of carbon dioxide (mole fraction) when this is done in a reactor maintained at 1 atm and 3800 k. The natural logarithm of the equilibrium constant for the reaction at 3800 K is

A gaseous mixture of 30 percent (by mole fraction) methane and 70 percent carbon dioxide is heated at 1 atm pressure to 1200 K. What is the equilibrium composition (by mole fraction) of the resulting mixture? The natural logarithm of the equilibrium constant for the reaction at is 4.147.

Determine the composition of the products of the dissociation reaction when the products are at and . Note: First evaluate the of this reaction using the values of the reactions and

The reaction occurs in internal combustion engines. Determine the equilibrium mole fraction of NO when the pressure is and the temperature is 1800 K.

Using Gibbs function data, determine the equilibrium constant for the reaction at (a) 537 R and (b) 3240 R. Compare your results with the values listed in Table A-28.

Determine the equilibrium constant for the process at (a) 298 K and (b) 2000 K. Compare your results with the values for listed in Table A-28.

Study the effect of varying the percent excess air during the steady-flow combustion of hydrogen at a pressure of 1 atm. At what temperature will 97 percent of H2 burn into H2O? Assume the equilibrium mixture consists of H2O, H2, O2, and N2.

Determine the equilibrium constant KP for the reaction CH4 + 2O2 m CO2 + 2H2O at 25C.

Using the Gibbs function data, determine the equilibrium constant KP for the dissociation process CO2m CO 1 1 2O2 at (a) 298 K and (b) 1800 K. Compare your results with the KP values listed in Table A28.

Carbon monoxide is burned with 100 percent excess air during a steady-flow process at a pressure of 1 atm. At what temperature will 97 percent of CO burn to CO2? Assume the equilibrium mixture consists of CO2, CO, O2, and N2.

Reconsider Prob. 1625. Using EES (or other) software, study the effect of varying the percent excess air during the steady-flow process from 0 to 200 percent on the temperature at which 97 percent of CO burns into CO2. Plot the temperature against the percent excess air, and discuss the results.

Repeat Prob. 1625 using data in English units.

Air (79 percent N2 and 21 percent O2) is heated to 2000 K at a constant pressure of 2 atm. Assuming the equilibrium mixture consists of N2, O2, and NO, determine the equilibrium composition at this state. Is it realistic to assume that no monatomic oxygen or nitrogen will be present in the equilibrium mixture? Will the equilibrium composition change if the pressure is doubled at constant temperature?

Hydrogen (H2) is heated to 3800 K at a constant pressure of 5 atm. Determine the percentage of H2 that will dissociate into H during this process.

Carbon dioxide (CO2) is heated to 2400 K at a constant pressure of 3 atm. Determine the percentage of CO2 that will dissociate into CO and O2 during this process.

A mixture of 1 mol of CO and 3 mol of O2 is heated to 2200 K at a pressure of 2 atm. Determine the equilibrium composition, assuming the mixture consists of CO2, CO, and O2.

A mixture of 3 mol of N2, 1 mol of O2, and 0.1 mol of Ar is heated to 2400 K at a constant pressure of 10 atm. Assuming the equilibrium mixture consists of N2, O2, Ar, and NO, determine the equilibrium composition.

Determine the mole fraction of sodium that ionizes according to the reaction Na m Na+ 1 e2 at 2000 K and 0.8 atm (KP 5 0.668 for this reaction).

A steady-flow combustion chamber is supplied with CO gas at 560 R and 16 psia at a rate of 12.5 ft3 /min and with oxygen (O2) at 537 R and 16 psia at a rate of 0.7 lbm/ min. The combustion products leave the combustion chamber at 3600 R and 16 psia. If the combustion gases consist of CO2, CO, and O2, determine (a) the equilibrium composition of the product gases and (b) the rate of heat transfer from the combustion chamber.

Liquid propane (C3H8) enters a combustion chamber at 25C at a rate of 1.2 kg/min where it is mixed and burned with 150 percent excess air that enters the combustion chamber at 12C. If the combustion gases consist of CO2, H2O, CO, O2, and N2 that exit at 1200 K and 2 atm, determine (a) the equilibrium composition of the product gases and (b) the rate of heat transfer from the combustion chamber. Is it realistic to disregard the presence of NO in the product gases?

Reconsider Prob. 1635. Using EES (or other) software, investigate if it is realistic to disregard the presence of NO in the product gases?

Oxygen (O2) is heated during a steady-flow process at 1 atm from 298 to 3000 K at a rate of 0.5 kg/min. Determine the rate of heat supply needed during this process, assuming (a) some O2 dissociates into O and (b) no dissociation takes place.

Estimate KP for the following equilibrium reaction at 2500 K: CO 1 H2O 5 CO2 1 H2 At 2000 K it is known that the enthalpy of reaction is 226,176 kJ/kmol and KP is 0.2209. Compare your result with the value obtained from the definition of the equilibrium constant.

A constant-volume tank contains a mixture of 1 kmol H2 and 1 kmol O2 at 25C and 1 atm. The contents are ignited. Determine the final temperature and pressure in the tank when the combustion gases are H2O, H2, and O2.

Show that as long as the extent of the reaction, a, for the disassociation reaction X2m2X is smaller than one, a is given by a 5 KP 4 1 KP

What is the equilibrium criterion for systems that involve two or more simultaneous chemical reactions?

When determining the equilibrium composition of a mixture involving simultaneous reactions, how would you determine the number of KP relations needed?

One mole of H2O is heated to 3400 K at a pressure of 1 atm. Determine the equilibrium composition, assuming that only H2O, OH, O2, and H2 are present.

A mixture of 2 mol of CO2 and 1 mol of O2 is heated to 3200 K at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only CO2, CO, O2, and O are present.

Air (21 percent O2, 79 percent N2) is heated to 3000 K at a pressure of 2 atm. Determine the equilibrium composition, assuming that only O2, N2, O, and NO are present. Is it realistic to assume that no N will be present in the final equilibrium mixture?

Air (21 percent O2, 79 percent N2) is heated to 5400 R at a pressure of 1 atm. Determine the equilibrium composition, assuming that only O2, N2, O, and NO are present. Is it realistic to assume that no N will be present in the final equilibrium mixture?

Reconsider Prob. 1646E. Use EES (or other) software to obtain the equilibrium solution. Compare your solution technique with that used in Prob. 1646E.

Water vapor (H2O) is heated during a steady-flow process at 1 atm from 298 to 3000 K at a rate of 0.2 kg/min. Determine the rate of heat supply needed during this process, assuming (a) some H2O dissociates into H2, O2, and OH and (b) no dissociation takes place.

Reconsider Prob. 1648. Using EES (or other) software, study the effect of the pressure on the rate of heat supplied for the two cases. Let the pressure vary from 1 to 10 atm. For each of the two cases, plot the rate of heat supplied as a function of pressure

Ethyl alcohol (C2H5OH(g)) at 25C is burned in a steady-flow adiabatic combustion chamber with 40 percent excess air that also enters at 25C. Determine the adiabatic flame temperature of the products at 1 atm assuming the significant equilibrium reactions are CO2 5 CO 1 1 2O2 and 1 2N2 1 1 2O2 5 NO. Plot the adiabatic flame temperature and kmoles of CO2, CO, and NO at equilibrium for values of percent excess air between 10 and 100 percent.

What is the importance of the vant Hoff equation?

Will a fuel burn more completely at 2000 or 2500 K?

Estimate the enthalpy of reaction h R for the dissociation process O2 m 2O at 3100 K, using (a) enthalpy data and (b) KP data. A

Estimate the enthalpy of reaction h R for the combustion process of carbon monoxide at 1800 K, using (a) enthalpy data and (b) KP data.

Estimate the enthalpy of reaction h R for the combustion process of carbon monoxide at 3960 R, using (a) enthalpy data and (b) KP data.

Using the enthalpy of reaction h R data and the KP value at 2400 K, estimate the KP value of the combustion process H2 1 1 2O2mH2O at 2600 K.

Estimate the enthalpy of reaction h R for the dissociation process CO2mCO 1 1 2O2 at 2200 K, using (a) enthalpy data and (b) KP data.

Estimate the enthalpy of reaction for the equilibrium reaction CH4 1 2O2mCO2 1 2H2O at 2500 K, using (a) enthalpy data and (b) KP data. Obtain enthalpy and entropy properties from EES.

Consider a tank that contains a saturated liquid vapor mixture of water in equilibrium. Some vapor is now allowed to escape the tank at constant temperature and pressure. Will this disturb the phase equilibrium and cause some of the liquid to evaporate?

Consider a two-phase mixture of ammonia and water in equilibrium. Can this mixture exist in two phases at the same temperature but at a different pressure?

Using the solubility data of a solid in a specified liquid, explain how you would determine the mole fraction of the solid in the liquid at the interface at a specified temperature.

Using solubility data of a gas in a solid, explain how you would determine the molar concentration of the gas in the solid at the solidgas interface at a specified temperature

Using the Henrys constant data for a gas dissolved in a liquid, explain how you would determine the mole fraction of the gas dissolved in the liquid at the interface at a specified temperature

Air at 70F and 100 psia is blown through a porous media which is saturated with liquid water at 70F. Determine the maximum partial pressure of the water evaporated into the air as it emerges from the porous media.

Water is sprayed into air at 80F and 14.3 psia, and the falling water droplets are collected in a container on the floor. Determine the mass and mole fractions of air dissolved in the water.

Show that a saturated liquidvapor mixture of refrigerant-134a at 210C satisfies the criterion for phase equilibrium.

Show that a mixture of saturated liquid water and saturated water vapor at 300 kPa satisfies the criterion for phase equilibrium.

A liquid-vapor mixture of refrigerant-134a is at 280 kPa with a quality of 70 percent. Determine the value of the Gibbs function, in kJ/kg, when the two phases are in equilibrium.

Calculate the value of the Gibbs function for saturated steam at 500F as a saturated liquid, saturated vapor, and a mixture of liquid and vapor with a quality of 40 percent. Demonstrate that phase equilibrium exists.

An ammonia-water mixture is at 10C. Determine the pressure of the ammonia vapor when the mole fraction of the ammonia in the liquid is (a) 20 percent and (b) 80 percent. The saturation pressure of ammonia at 10C is 615.3 kPa.

Using the liquidvapor equilibrium diagram of an oxygennitrogen mixture, determine the composition of each phase at 84 K and 100 kPa.

Using the liquidvapor equilibrium diagram of an oxygennitrogen mixture at 100 kPa, determine the temperature at which the composition of the vapor phase is 79 percent N2 and 21 percent O2.

An oxygen-nitrogen mixture consists of 30 kg of oxygen and 40 kg of nitrogen. This mixture is cooled to 84 K at 0.1 MPa pressure. Determine the mass of the oxygen in the liquid and gaseous phase.

What is the total mass of the liquid phase of Prob. 1673.

A wall made of natural rubber separates O2 and N2 gases at 25C and 500 kPa. Determine the molar concentrations of O2 and N2 in the wall.

Consider a rubber plate that is in contact with nitrogen gas at 298 K and 250 kPa. Determine the molar and mass density of nitrogen in the rubber at the interface.

In absorption refrigeration systems, a two-phase equilibrium mixture of liquid ammonia (NH3) and water (H2O) is frequently used. Consider a liquidvapor mixture of ammonia and water in equilibrium at 30C. If the composition of the liquid phase is 60 percent NH3 and 40 percent H2O by mole numbers, determine the composition of the vapor phase of this mixture. Saturation pressure of NH3 at 30C is 1167.4 kPa.

An ammonia-water absorption refrigeration unit operates its absorber at 0C and its generator at 46C. The vapor mixture in the generator and absorber is to have an ammonia mole fraction of 96 percent. Assuming ideal behavior, determine the operating pressure in the (a) generator and (b) absorber. Also determine the mole fraction of the ammonia in the (c) strong liquid mixture being pumped from the absorber and the (d) weak liquid solution being drained from the generator. The saturation pressure of ammonia at 0C is 430.6 kPa, and at 46C it is 1830.2 kPa.

Rework Prob. 1678 when the temperature in the absorber is increased to 6C and the temperature in the generator is reduced to 40C. The saturation pressure of ammonia at 6C is 534.8 kPa, and at 40C it is 1556.7 kPa.

Foam products such as shaving cream are made by liquid mixtures whose ingredients are primarily water and a refrigerant such as refrigerant-134a. Consider a liquid mixture of water and refrigerant-134a with a water mass fraction of 90 percent that is at 20C. What is the mole fraction of the water and refrigerant-134a vapor in the gas which fills the bubbles that form the foam?

Consider a glass of water in a room at 27C and 97 kPa. If the relative humidity in the room is 100 percent and the water and the air are in thermal and phase equilibrium, determine (a) the mole fraction of the water vapor in the air and (b) the mole fraction of air in the water.

Consider a carbonated drink in a bottle at 27C and 115 kPa. Assuming the gas space above the liquid consists of a saturated mixture of CO2 and water vapor and treating the drink as water, determine (a) the mole fraction of the water vapor in the CO2 gas and (b) the mass of dissolved CO2 in a 300-ml drink.

Determine the mole fraction of argon that ionizes according to the reaction Ar m Ar1 1 e2 at 10,000 K and 0.35 atm (KP 5 0.00042 for this reaction).

Using the Gibbs function data, determine the equilibrium constant KP for the dissociation process O2 m 2O at 2000 K. Compare your result with the KP value listed in Table A28.

Determine the equilibrium constant for the reaction CH4 1 2O2 m CO2 1 2H2O when the reaction occurs at 100 kPa and 2000 K. The natural logarithms of the equilibrium constant for the reaction C 1 2H2 m CH4 and C 1 O2 m CO2 at 2000 K are 7.847 and 23.839, respectively.

Consider a glass of water in a room at 25C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are in thermal equilibrium, determine (a) the mole fraction of the water vapor in the room air, (b) the mole fraction of the water vapor in the air adjacent to the water surface, and (c) the mole fraction of air in the water near the surface.

Repeat Prob. 1686 for a relative humidity of 25 percent.

Methane gas (CH4) at 25C is burned with the stoichiometric amount of air at 25C during an adiabatic steady-flow combustion process at 1 atm. Assuming the product gases consist of CO2, H2O, CO, N2, and O2, determine (a) the equilibrium composition of the product gases and (b) the exit temperature.

Reconsider Prob. 1688. Using EES (or other) software, study the effect of excess air on the equilibrium composition and the exit temperature by varying the percent excess air from 0 to 200 percent. Plot the exit temperature against the percent excess air, and discuss the results.

Consider the reaction CH4 1 2O2 m CO2 1 2H2O when the reaction occurs at 450 kPa and 3000 K. Determine the equilibrium partial pressure of the carbon dioxide. The natural logarithms of the equilibrium constant for the reactions C 1 2H2 m CH4 and C 1 O2 m CO2 at 3000 K are 9.685 and 15.869, respectively.

10 kmol of methane gas are heated from 1 atm and 298 K to 1 atm and 1000 K. Calculate the total amount of heat transfer required when (a) disassociation is neglected and (b) when disassociation is considered. The natural logarithm of the equilibrium constant for the reaction C m 1 2H2 CH4 at 1000 K is 2.328. For the solution of part (a) use empirical coefficients of Table A2c. For the solution of part (b) use constant specific heats and take the constantvolume specific heats of methane, hydrogen and carbon at 1000 K to be 63.3, 21.7, and 0.711 kJ/kmolK, respectively. The constant-volume specific heat of methane at 298 K is 27.8 kJ/kmolK.

Solid carbon at 25C is burned with a stoichiometric amount of air which is at 1 atm pressure and 25C. Determine the number of moles of CO2 formed per kmol of carbon when only CO2, CO, O2, and N2 are present in the products and the products are at 1 atm and 727C.

Determine the amount of heat released per kilogram of carbon by the combustion of the Prob. 1692.

Methane gas is burned with 30 percent excess air. This fuel enters a steady flow combustor at 101 kPa and 25C, and is mixed with the air. The products of combustion leave this reactor at 101 kPa and 1600 K. Determine the equilibrium composition of the products of combustion, and the amount of heat released by this combustion, in kJ/kmol methane.

Gaseous octane is burned with 40 percent excess air in an automobile engine. During combustion, the pressure is 600 psia and the temperature reaches 3600 R. Determine the equilibrium composition of the products of combustion.

Propane gas is burned steadily at 1 atm pressure with a 10 percent excess oxygen supplied by atmospheric air. The reactants enter a steady flow combustor at 25C. Determine the final temperature of the products if the combustion is done without any heat transfer, and the equilibrium composition.

A constant-volume tank contains a mixture of 1 mol of H2 and 0.5 mol of O2 at 25C and 1 atm. The contents of the tank are ignited, and the final temperature and pressure in the tank are 2800 K and 5 atm, respectively. If the combustion gases consist of H2O, H2, and O2, determine (a) the equilibrium composition of the product gases and (b) the amount of heat transfer from the combustion chamber. Is it realistic to assume that no OH will be present in the equilibrium mixture?

A mixture of 2 mol of H2O and 3 mol of O2 is heated to 3600 K at a pressure of 8 atm. Determine the equilibrium composition of the mixture, assuming that only H2O, OH, O2, and H2 are present.

A mixture of 3 mol of CO2 and 3 mol of O2 is heated to 3400 K at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only CO2, CO, O2, and O are present.

Reconsider Prob. 1699. Using EES (or other) software, study the effect of pressure on the equilibrium composition by varying pressure from 1 atm to 10 atm. Plot the amount of CO present at equilibrium as a function of pressure.

Estimate the enthalpy of reaction hR for the combustion process of hydrogen at 2400 K, using (a) enthalpy data and (b) KP data.

Reconsider Prob. 16101. Using EES (or other) software, investigate the effect of temperature on the enthalpy of reaction using both methods by varying the temperature from 2000 to 3000 K.

Using the enthalpy of reaction hR data and the KP value at 2200 K, estimate the KP value of the dissociation process O2 m 2O at 2400 K.

A carbonated drink is fully charged with CO2 gas at 17C and 600 kPa such that the entire bulk of the drink is in thermodynamic equilibrium with the CO2water vapor mixture. Now consider a 2-L soda bottle. If the CO2 gas in that bottle were to be released and stored in a container at 20C and 100 kPa, determine the volume of the container.

Tabulate the natural log of the equilibrium constant as a function of temperature between 298 to 3000 K for the equilibrium reaction CO 1 H2O 5 CO2 1 H2. Compare your results to those obtained by combining the ln KP values for the two equilibrium reactions CO2 5 CO 1 1 2O2 and H2O 5 H2 1 1 2O2 given in Table A28.

Ethyl alcohol (C2H5OH(g)) at 25C is burned in a steady-flow adiabatic combustion chamber with 90 percent excess air that also enters at 25C. Determine the adiabatic flame temperature of the products at 1 atm assuming the only significant equilibrium reaction is CO2 5 CO 1 1 2O2. Plot the adiabatic flame temperature as the percent excess air varies from 10 to 100 percent.

Show that when the three phases of a pure substance are in equilibrium, the specific Gibbs function of each phase is the same.

Show that when the two phases of a two-component system are in equilibrium, the specific Gibbs function of each phase of each component is the same.

If the equilibrium constant for the reaction H2 1 1 2O2mH2O is K, the equilibrium constant for the reaction 2H2O m 2H2 1 O2 at the same temperature is (a) 1/K (b) 1/(2K) (c) 2K (d ) K2 (e) 1/K2

If the equilibrium constant for the reaction CO 1 1 2O2mCO2 is K, the equilibrium constant for the reaction CO2 1 3N2mCO 1 1 2O2 1 3N2 at the same temperature is (a) 1/K (b) 1/(K 1 3) (c) 4K (d ) K (e) 1/K2

The equilibrium constant for the reaction H2 1 1 2O2mH2O at 1 atm and 1500C is given to be K. Of the reactions given below, all at 1500C, the reaction that has a different equilibrium constant is (a) H2 1 1 2O2mH2O at 5 atm (b) 2H2 1 O2 m 2H2O at 1 atm (c) H2 1 O2mH2O 1 1 2O2 at 2 atm (d) H2 1 1 2O2 1 3N2mH2O 1 3N2 at 5 atm (e) H2 1 1 2O2 1 3N2mH2O 1 3N2 at 1 atm

Of the reactions given below, the reaction whose equilibrium composition at a specified temperature is not affected by pressure is (a) H2 1 1 2O2mH2O (b) CO 1 1 2O2mCO2 (c) N2 1 O2 m 2NO (d ) N2 m 2N (e) all of the above

Of the reactions given below, the reaction whose number of moles of products increases by the addition of inert gases into the reaction chamber at constant pressure and temperature is (a) H2 1 1 2O2mH2O (b) CO 1 1 2O2mCO2 (c) N2 1 O2 m 2NO (d ) N2 m 2N (e) all of the above

Moist air is heated to a very high temperature. If the equilibrium composition consists of H2O, O2, N2, OH, H2, and NO, the number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5

Propane C3H8 is burned with air, and the combustion products consist of CO2, CO, H2O, O2, N2, OH, H2, and NO. The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5

Consider a gas mixture that consists of three components. The number of independent variables that need to be specified to fix the state of the mixture is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5

The value of Henrys constant for CO2 gas dissolved in water at 290 K is 12.8 MPa. Consider water exposed to atmospheric air at 100 kPa that contains 3 percent CO2 by volume. Under phase equilibrium conditions, the mole fraction of CO2 gas dissolved in water at 290 K is (a) 2.3 3 1024 (b) 3.0 3 1024 (c) 0.80 3 1024 (d ) 2.2 3 1024 (e) 5.6 3 1024

The solubility of nitrogen gas in rubber at 25C is 0.00156 kmol/m3 bar. When phase equilibrium is established, the density of nitrogen in a rubber piece placed in a nitrogen gas chamber at 300 kPa is (a) 0.005 kg/m3 (b) 0.018 kg/m3 (c) 0.047 kg/m3 (d) 0.13 kg/m3 (e) 0.28 kg/m3

An engineer suggested that high-temperature disassociation of water be used to produce a hydrogen fuel. A reactor-separator has been designed that can accommodate temperatures as high as 4000 K and pressures as much as 5 atm. Water enters this reactor-separator at 25C. The separator separates the various constituents in the mixture into individual streams whose temperature and pressure match those of the reactor-separator. These streams are then cooled to 25C and stored in atmospheric pressure tanks with the exception of any remaining water, which is returned to the reactor to repeat the process again. Hydrogen gas from these tanks is later burned with a stoichiometric amount of air to provide heat for an electrical power plant. The parameter that characterizes this system is the ratio of the heat released by burning the hydrogen to the amount of heat used to generate the hydrogen gas. Select the operating pressure and temperature for the reactor-separator that maximizes this ratio. Can this ratio ever be bigger than unity?

An article that appeared in the Reno GazetteJournal on May 18, 1992, quotes an inventor as saying that he has turned water into motor vehicle fuel in a breakthrough that would increase engine efficiency, save gasoline, and reduce smog. There is also a picture of a car that the inventor has modified to run on half water and half gasoline. The inventor claims that sparks from catalytic poles in the converted engine break down the water into oxygen and hydrogen, which is burned with the gasoline. He adds that hydrogen has a higher energy density than carbon and the high-energy density enables one to get more power. The inventor states that the fuel efficiency of his car increased from 20 mpg (miles per gallon) to more than 50 mpg of gasoline as a result of conversion and notes that the conversion has sharply reduced emissions of hydrocarbons, carbon monoxide, and other exhaust pollutants. Evaluate the claims made by the inventor, and write a report that is to be submitted to a group of investors who are considering financing this invention.

One means of producing liquid oxygen from atmospheric air is to take advantage of the phase-equilibrium properties of oxygen-nitrogen mixtures. This system is illustrated in Fig. P16121. In this cascaded-reactors system, dry atmospheric air is cooled in the first reactor until liquid is formed. According to the phase-equilibrium properties, this liquid will be richer in oxygen than in the vapor phase. The vapor in the first reactor is discarded while the oxygen enriched liquid leaves the first reactor and is heated in a heat exchanger until it is again a vapor. The vapor mixture enters the second reactor where it is again cooled until a liquid that is further enriched in oxygen is formed. The vapor from the second reactor is routed back to the first reactor while the liquid is routed to another heat exchanger and another reactor to repeat the process once again. The liquid formed in the third reactor is very rich in oxygen. If all three reactors are operated at 1 atm pressure, select the three temperatures that produce the greatest amount of 99 percent pure oxygen.

Automobiles are major emitters of air pollutants such as NOx, CO, and hydrocarbons HC. Find out the legal limits of these pollutants in your area, and estimate the total amount of each pollutant, in kg, that would be produced in your town if all the cars were emitting pollutants at the legal limit. State your assumptions.