Thermodynamics: An Engineering Approach

Yunus A. Çengel, Michael A. Boles

Chapter 16

Chemical and Phase Equilibrium - all with Video Answers

Educators

Chapter Questions

Problem 1

Write three different $K_{P}$ relations for reacting ideal gas mixtures, and state when each relation should be used.

Rory Naguib

Rory Naguib

Numerade Educator

Problem 2

A reaction chamber contains a mixture of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2}$ 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 $\mathrm{CO}_{2} ?$

Rory Naguib

Numerade Educator

Problem 3

A reaction chamber contains a mixture of $\mathrm{N}_{2}$ and $\mathrm{N}$ 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 $\mathrm{N}_{2} ?$

Rory Naguib

Numerade Educator

Problem 4

A reaction chamber contains a mixture of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2}$ in equilibrium at a specified temperature and pressure. Now some $\mathrm{N}_{2}$ is added to the mixture while the mixture temperature and pressure are kept constant. Will this affect the number of moles of $\mathrm{O}_{2} ?$ How?

Rory Naguib

Numerade Educator

Problem 5

Which element is more likely to dissociate into its monatomic form at $3000 \mathrm{K}, \mathrm{H}_{2}$ or $\mathrm{N}_{2} ?$ Why?

Rory Naguib

Numerade Educator

Problem 6

The equilibrium constant for the $\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons$ $\mathrm{H}_{2} \mathrm{O}$ reaction at 1 atm and $1200 \mathrm{K}$ is $K_{P \cdot}$ Use this information to determine the equilibrium constant for the following reactions:
$(a)$ at 1 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 atm $\quad 3 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 3 \mathrm{H}_{2}+\frac{3}{2} \mathrm{O}_{2}$

Rory Naguib

Numerade Educator

Problem 7

The equilibrium constant of the dissociation reaction $\mathrm{H}_{2} \rightarrow 2 \mathrm{H}$ at $3000 \mathrm{K}$ and 1 atm is $K_{P_{1}} .$ Express the equilibrium constants of the following reactions at $3000 \mathrm{K}$ in terms of $K_{P_{1}}$:
$(a) \quad \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{H} \quad$ at $2 \mathrm{atm}$
$(b) \quad 2 \mathrm{H} \rightleftharpoons \mathrm{H}_{2} \quad$ at 1 atm
$(c) \quad 2 \mathrm{H}_{2} \rightleftharpoons 4 \mathrm{H} \quad$ at $1 \mathrm{atm}$
$(d) \quad \mathrm{H}_{2}+2 \mathrm{N}_{2} \rightleftharpoons 2 \mathrm{H}+2 \mathrm{N}_{2}$ at 2 atm
$(e) \quad 6 \mathrm{H} \rightleftharpoons 3 \mathrm{H}_{2} \quad$ at $4 \mathrm{atm}$

Rory Naguib

Numerade Educator

Problem 8

The equilibrium constant of the reaction $\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}$ $\rightarrow \mathrm{CO}_{2}$ at $1000 \mathrm{K}$ and 1 atm is $K_{P_{1}} .$ Express the equilibrium constant of the following reactions at $1000 \mathrm{K}$ in terms of $K_{P_{1}}$:
$(a) \quad \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2} \quad$ at $3 \mathrm{atm}$
$(b)$ $\mathrm{CO}_{2} \rightleftharpoons \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \quad$ at $1 \mathrm{atm}$
$(c) 2 \mathrm{H}_{2} \rightleftharpoons 4 \mathrm{H}$at 1 atm
$(d) \quad \mathrm{H}_{2}+2 \mathrm{N}_{2} \rightleftharpoons 2 \mathrm{H}+2 \mathrm{N}_{2}$ at 2 atm
$(e)$ $6 \mathrm{H} \rightleftharpoons 3 \mathrm{H}_{2} $ at $4 \mathrm{atm}$

Rory Naguib

Numerade Educator

Problem 9

Consider a mixture of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2}$ in equilibrium at a specified temperature and pressure. Now the pressure is doubled.
(a) Will the equilibrium constant $K_{P}$ change?
(b) Will the number of moles of $\mathrm{CO}_{2}$, $\mathrm{CO}$, and $\mathrm{O}_{2}$ change? How?

Rory Naguib

Numerade Educator

Problem 10

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 atm, and its temperature is $600 \mathrm{K}$.

Jincy M Saji

Numerade Educator

Problem 11

At what temperature will nitrogen be 0.2 percent disassociated at $(a) 1 \mathrm{kPa}$ and $(b) 10 \mathrm{kPa} ?$

Jincy M Saji

Numerade Educator

Problem 12

Determine the temperature at which 5 percent of diatomic oxygen $\left(\mathrm{O}_{2}\right)$ dissociates into monatomic oxygen (O) at a pressure of 3 atm.

Jincy M Saji

Numerade Educator

Problem 13

Repeat Prob. $16-12$ for a pressure of 6 atm.

Jincy M Saji

Numerade Educator

Problem 14

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 $A-28$.

Jincy M Saji

Numerade Educator

Problem 15

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 $\mathrm{A}-28 ?$

Jincy M Saji

Numerade Educator

Problem 16

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 atm and 3800 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 $-0.461 .$

Rory Naguib

Numerade Educator

Problem 17

A gaseous mixture of 30 percent (by mole fraction) methane and 70 percent carbon dioxide is heated at 1 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.

Jincy M Saji

Numerade Educator

Problem 18

Determine the composition of the products of the disassociation reaction $\mathrm{CO}_{2} \rightleftharpoons \mathrm{CO}+\mathrm{O}$ when the products are at 1 atm and 2500 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 $0.5 \mathrm{O}_{2} \rightleftharpoons \mathrm{O}$.

Jincy M Saji

Numerade Educator

Problem 19

The reaction $\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}$ occurs in internal combustion engines. Determine the equilibrium mole fraction of NO when the pressure is $101 \mathrm{kPa}$ and the temperature is $1800 \mathrm{K}$.

Penny Riley

Numerade Educator

Problem 20

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 $A-28$.

Jincy M Saji

Numerade Educator

Problem 21

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 $\mathrm{A}-28$.

Rory Naguib

Numerade Educator

Problem 22

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 $\mathrm{H}_{2}$ burn into $\mathrm{H}_{2} \mathrm{O}$ ? Assume the equilibrium mixture consists of $\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2}, \mathrm{O}_{2},$ and $\mathrm{N}_{2}$.

Jincy M Saji

Numerade Educator

Problem 23

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 $25^{\circ} \mathrm{C}$.

Rory Naguib

Numerade Educator

Problem 24

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 $\mathrm{A}-28$.

Rory Naguib

Numerade Educator

Problem 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 $\mathrm{CO}$ burn to $\mathrm{CO}_{2}$ ? Assume the equilibrium mixture consists of $\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{O}_{2},$ and $\mathrm{N}_{2}$.

Rory Naguib

Numerade Educator

Problem 26

Reconsider Prob. $16-25 .$ 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 $\mathrm{CO}$ burns into $\mathrm{CO}_{2}$. Plot the temperature against the percent excess air, and discuss the results.

Jincy M Saji

Numerade Educator

Problem 27

Repeat Prob. $16-25$ using data in English units.

Rory Naguib

Numerade Educator

Problem 28

Air (79 percent $\mathrm{N}_{2}$ and 21 percent $\mathrm{O}_{2}$ ) is heated to $2000 \mathrm{K}$ at a constant pressure of 2 atm. Assuming the equilibrium mixture consists of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{NO},$ 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?

Rory Naguib

Numerade Educator

Problem 29

Hydrogen $\left(\mathrm{H}_{2}\right)$ is heated to $3800 \mathrm{K}$ at a constant pressure of 5 atm. Determine the percentage of $\mathrm{H}_{2}$ that will dissociate into H during this process.

Jincy M Saji

Numerade Educator

Problem 30

Carbon dioxide $\left(\mathrm{CO}_{2}\right)$ is heated to $2400 \mathrm{K}$ at a constant pressure of 3 atm. Determine the percentage of $\mathrm{CO}_{2}$ that will dissociate into $\mathrm{CO}$ and $\mathrm{O}_{2}$ during this process.

Rory Naguib

Numerade Educator

Problem 31

A mixture of 1 mol of $C O$ and 3 mol of $O_{2}$ is heated to $2200 \mathrm{K}$ at a pressure of 2 atm. Determine the equilibrium composition, assuming the mixture consists of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2}$.

Jincy M Saji

Numerade Educator

Problem 32

A mixture of $3 \mathrm{mol}$ of $\mathrm{N}_{2}, 1 \mathrm{mol}$ of $\mathrm{O}_{2},$ and $0.1 \mathrm{mol}$ of Ar is heated to $2400 \mathrm{K}$ at a constant pressure of $10 \mathrm{atm}$ Assuming the equilibrium mixture consists of $\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{Ar}$, and $\mathrm{NO},$ determine the equilibrium composition.

Jincy M Saji

Numerade Educator

Problem 33

Determine the mole fraction of sodium that ionizes according to the reaction $\mathrm{Na} \rightleftharpoons \mathrm{Na}^{+}+e^{-}$ at $2000 \mathrm{K}$ and $0.8 \operatorname{atm}\left(K_{P}=0.668 \text { for this reaction }\right)$.

Rory Naguib

Numerade Educator

Problem 34

A steady-flow combustion chamber is supplied with $\mathrm{CO}$ gas at $560 \mathrm{R}$ and 16 psia at a rate of $12.5 \mathrm{ft}^{3} / \mathrm{min}$ and with oxygen $\left(\mathrm{O}_{2}\right)$ at $537 \mathrm{R}$ and 16 psia at a rate of $0.7 \mathrm{lbm} /$ min. The combustion products leave the combustion chamber at $3600 \mathrm{R}$ and 16 psia. If the combustion gases consist of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2},$ determine $(a)$ the equilibrium composition of the product gases and ( $b$ ) the rate of heat transfer from the combustion chamber.

Rory Naguib

Numerade Educator

Problem 35

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 NO in the product gases?

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 36

Reconsider Prob. $16-35 .$ Using EES (or other) software, investigate if it is realistic to disregard the presence of $\mathrm{NO}$ in the product gases?

Jincy M Saji

Numerade Educator

Problem 37

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.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 38

Estimate $K_{P}$ for the following equilibrium reaction at 2500 \mathrm{K}: $\mathrm{CO}+\mathrm{H}_{2} \mathrm{O}=\mathrm{CO}_{2}+\mathrm{H}_{2}$ At $2000 \mathrm{K}$ it is known that the enthalpy of reaction is $-26,176 \mathrm{kJ} / \mathrm{kmol}$ and $K_{P}$ is $0.2209 .$ Compare your result with the value obtained from the definition of the equilibrium constant.

Rory Naguib

Numerade Educator

Problem 39

A constant-volume tank contains a mixture of $1 \mathrm{kmol} \mathrm{H}_{2}$ and $1 \mathrm{kmol} \mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm. The contents are ignited. Determine the final temperature and pressure in the tank when the combustion gases are $\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2},$ and $\mathrm{O}_{2}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 40

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 $\alpha=\sqrt{\frac{K_{P}}{4+K_{P}}}$

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 41

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

Rory Naguib

Numerade Educator

Problem 42

When determining the equilibrium composition of a mixture involving simultaneous reactions, how would you determine the number of $K_{P}$ relations needed?

Rory Naguib

Numerade Educator

Problem 43

One mole of $\mathrm{H}_{2} \mathrm{O}$ is heated to $3400 \mathrm{K}$ at a pressure of 1 atm. Determine the equilibrium composition, assuming that only $\mathrm{H}_{2} \mathrm{O}, \mathrm{OH}, \mathrm{O}_{2},$ and $\mathrm{H}_{2}$ are present.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 44

A mixture of 2 mol of $\mathrm{CO}_{2}$ and $1 \mathrm{mol}$ of $\mathrm{O}_{2}$ is heated to $3200 \mathrm{K}$ at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only $\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{O}_{2}$,and $\mathrm{O}$ are present.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 45

Air $\left(21 \text { percent } \mathrm{O}_{2}, 79 \text { percent } \mathrm{N}_{2}\right)$ is heated to $3000 \mathrm{K}$ at a pressure of 2 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?

Narayan Hari

Numerade Educator

Problem 46

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

Narayan Hari

Numerade Educator

Problem 47

Reconsider Prob. 16-46E. Use EES (or other) software to obtain the equilibrium solution. Compare your solution technique with that used in Prob. $16-46 \mathrm{E}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 48

Water vapor $\left(\mathrm{H}_{2} \mathrm{O}\right)$ is heated during a steady-flow process at 1 atm from 298 to $3000 \mathrm{K}$ at a rate of $0.2 \mathrm{kg} / \mathrm{min}$. Determine the rate of heat supply needed during this process, assuming $(a)$ some $\mathrm{H}_{2} \mathrm{O}$ dissociates into $\mathrm{H}_{2}, \mathrm{O}_{2},$ and $\mathrm{OH}$ and $(b)$ no dissociation takes place.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 49

Reconsider Prob. $16-48 .$ 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.

Jincy M Saji

Numerade Educator

Problem 50

Ethyl alcohol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\right)$ at $25^{\circ} \mathrm{C}$ is burned in a steady-flow adiabatic combustion chamber with 40 percent excess air that also enters at $25^{\circ} \mathrm{C}$. Determine the adiabatic flame temperature of the products at 1 atm assuming the significant equilibrium reactions are $\mathrm{CO}_{2}=$ $\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}$ and $\frac{1}{2} \mathrm{N}_{2}+\frac{1}{2} \mathrm{O}_{2}=$ NO. Plot the adiabatic flame temperature and kmoles of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{NO}$ at equilibrium for values of percent excess air between 10 and 100 percent.

Jincy M Saji

Numerade Educator

Problem 51

What is the importance of the van't Hoff equation?

Rory Naguib

Numerade Educator

Problem 52

Will a fuel burn more completely at 2000 or $2500 \mathrm{K} ?$

Rory Naguib

Numerade Educator

Problem 53

Estimate the enthalpy of reaction $\bar{h}_{R}$ for the dissociation process $\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{O}$ at $3100 \mathrm{K},$ using $(a)$ enthalpy data and $(b) \quad K_{P} $ data.

Rory Naguib

Numerade Educator

Problem 54

Estimate the enthalpy of reaction $\bar{h}_{R}$ for the combustion process of carbon monoxide at $1800 \mathrm{K},$ using
(a) enthalpy data and (b) $K_{P}$ data.

Rory Naguib

Numerade Educator

Problem 55

Estimate the enthalpy of reaction $\bar{h}_{R}$ for the combustion process of carbon monoxide at $3960 \mathrm{R}$, using (a) enthalpy data and (b) $K_{p}$ data.

Rory Naguib

Numerade Educator

Problem 56

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 $2600 \mathrm{K}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 57

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.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 58

Estimate the enthalpy of reaction for the equilibrium reaction $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ at $2500 \mathrm{K}$, using $(a)$ enthalpy data and $(b) K_{P}$ data. Obtain enthalpy and entropy properties from EES.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 59

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?

Rory Naguib

Numerade Educator

Problem 60

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?

Rory Naguib

Numerade Educator

Problem 61

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.

Rory Naguib

Numerade Educator

Problem 62

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.

Rory Naguib

Numerade Educator

Problem 63

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.

Rory Naguib

Numerade Educator

Problem 64

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

Rory Naguib

Numerade Educator

Problem 65

Water is sprayed into air at $80^{\circ} \mathrm{F}$ 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.

Rory Naguib

Numerade Educator

Problem 66

Show that a saturated liquid-vapor mixture of refrigerant-134a at $-10^{\circ} \mathrm{C}$ satisfies the criterion for phase equilibrium.

Jincy M Saji

Numerade Educator

Problem 67

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

Rory Naguib

Numerade Educator

Problem 68

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.

Rory Naguib

Numerade Educator

Problem 69

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

Jincy M Saji

Numerade Educator

Problem 70

An ammonia-water mixture is at $10^{\circ} \mathrm{C} .$ 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 $10^{\circ} \mathrm{C}$ is $615.3 \mathrm{kPa}$.

Rory Naguib

Numerade Educator

Problem 71

Using the liquid-vapor equilibrium diagram of an oxygen-nitrogen mixture, determine the composition of each phase at $84 \mathrm{K}$ and $100 \mathrm{kPa}$.

Rory Naguib

Numerade Educator

Problem 72

Using the liquid-vapor equilibrium diagram of an oxygen-nitrogen mixture at $100 \mathrm{kPa}$, determine the temperature at which the composition of the vapor phase is 79 percent $\mathrm{N}_{2}$ and 21 percent $\mathrm{O}_{2}$.

Rory Naguib

Numerade Educator

Problem 73

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

Rory Naguib

Numerade Educator

Problem 74

What is the total mass of the liquid phase of Prob. $16-73$.

Rory Naguib

Numerade Educator

Problem 75

A wall made of natural rubber separates $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ gases at $25^{\circ} \mathrm{C}$ and 500 kPa. Determine the molar concentrations of $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ in the wall.

Rory Naguib

Numerade Educator

Problem 76

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

Rory Naguib

Numerade Educator

Problem 77

In absorption refrigeration systems, a two-phase equilibrium mixture of liquid ammonia $\left(\mathrm{NH}_{3}\right)$ and water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ is frequently used. Consider a liquid-vapor mixture of ammonia and water in equilibrium at $30^{\circ} \mathrm{C}$. If the composition of the liquid phase is 60 percent $\mathrm{NH}_{3}$ and 40 percent $\mathrm{H}_{2} \mathrm{O}$ by mole numbers, determine the composition of the vapor phase of this mixture. Saturation pressure of $\mathrm{NH}_{3}$ at $30^{\circ} \mathrm{C}$ is $1167.4 \mathrm{kPa}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 78

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 $1830.2 \mathrm{kPa}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 79

Rework Prob. $16-78$ when the temperature in the absorber is increased to $6^{\circ} \mathrm{C}$ and the temperature in the generator is reduced to $40^{\circ} \mathrm{C}$. The saturation pressure of ammonia at $6^{\circ} \mathrm{C}$ is $534.8 \mathrm{kPa}$, and at $40^{\circ} \mathrm{C}$ it is $1556.7 \mathrm{kPa}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 80

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 $20^{\circ} \mathrm{C}$. What is the mole fraction of the water and refrigerant-134a vapor in the gas which fills the bubbles that form the foam?

Aashna Calidas

Numerade Educator

Problem 81

Consider a glass of water in a room at $27^{\circ} \mathrm{C}$ and $97 \mathrm{kPa} .$ 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.

Rory Naguib

Numerade Educator

Problem 82

Consider a carbonated drink in a bottle at $27^{\circ} \mathrm{C}$ and 115 kPa. Assuming the gas space above the liquid consists of a saturated mixture of $\mathrm{CO}_{2}$ and water vapor and treating the drink as water, determine ( $a$ ) the mole fraction of the water vapor in the $\mathrm{CO}_{2}$ gas and $(b)$ the mass of dissolved $\mathrm{CO}_{2}$ in a $300-m 1$ drink.

Rory Naguib

Numerade Educator

Problem 83

Determine the mole fraction of argon that ionizes according to the reaction $\mathrm{Ar} \rightleftharpoons \mathrm{Ar}^{+}+e^{-}$ at $10,000 \mathrm{K}$ and 0.35 atm $\left(K_{P}=0.00042 \text { for this reaction }\right)$.

Rory Naguib

Numerade Educator

Problem 84

Using the Gibbs function data, determine the equilibrium constant $K_{P}$ for the dissociation process $\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{O}$ at 2000 K. Compare your result with the $K_{P}$ value listed in Table $A-28$.

Rory Naguib

Numerade Educator

Problem 85

Determine the equilibrium constant for the reaction $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ when the reaction occurs at $100 \mathrm{kPa}$ and $2000 \mathrm{K} .$ The natural logarithms of the equilibrium constant for the reaction $\mathrm{C}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{4}$ and $\mathrm{C}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}$ at $2000 \mathrm{K}$ are 7.847 and 23.839, respectively.

Rory Naguib

Numerade Educator

Problem 86

Consider a glass of water in a room at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa} .$ 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.

Mahnoor Amin

Numerade Educator

Problem 87

Repeat Prob. $16-86$ for a relative humidity of 25 percent.

Mahnoor Amin

Numerade Educator

Problem 88

Methane gas $\left(\mathrm{CH}_{4}\right)$ at $25^{\circ} \mathrm{C}$ is burned with the stoichiometric amount of air at $25^{\circ} \mathrm{C}$ during an adiabatic steady-flow combustion process at 1 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.

Hast Aggarwal

Numerade Educator

Problem 89

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.

Jincy M Saji

Numerade Educator

Problem 90

Consider the reaction $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+$ $2 \mathrm{H}_{2} \mathrm{O}$ when the reaction occurs at $450 \mathrm{kPa}$ and $3000 \mathrm{K} .$ Determine the equilibrium partial pressure of the carbon dioxide. The natural logarithms of the equilibrium constant for the reactions $\mathrm{C}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{4}$ and $\mathrm{C}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}$ at $3000 \mathrm{K}$ are 9.685 and $15.869,$ respectively

Rory Naguib

Numerade Educator

Problem 91

$10 \mathrm{kmol}$ of methane gas are heated from 1 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 $A-2 c$. For the solution of part ( $b$ ) use constant specific heats and take the constantvolume 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 $27.8 \mathrm{kJ} / \mathrm{kmol} \cdot \mathrm{K}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 92

Solid carbon at $25^{\circ} \mathrm{C}$ is burned with a stoichiometric amount of air which is at 1 atm pressure and $25^{\circ} \mathrm{C}$. Determine the number of moles of $\mathrm{CO}_{2}$ formed per $\mathrm{kmol}$ of carbon when only $\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{O}_{2},$ and $\mathrm{N}_{2}$ are present in the products and the products are at 1 atm and $727^{\circ} \mathrm{C}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 93

Determine the amount of heat released per kilogram of carbon by the combustion of the Prob. 16-92 .

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 94

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

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 95

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.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 96

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 $25^{\circ} \mathrm{C}$. Determine the final temperature of the products if the combustion is done without any heat transfer, and the equilibrium composition.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 97

A constant-volume tank contains a mixture of 1 mol of $\mathrm{H}_{2}$ and $0.5 \mathrm{mol}$ of $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm. The contents of the tank are ignited, and the final temperature and pressure in the tank are $2800 \mathrm{K}$ and 5 atm, respectively. If the combustion gases consist of $\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2},$ and $\mathrm{O}_{2},$ 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 $\mathrm{OH}$ will be present in the equilibrium mixture?

Rory Naguib

Numerade Educator

Problem 98

A mixture of 2 mol of $\mathrm{H}_{2} \mathrm{O}$ and $3 \mathrm{mol}$ of $\mathrm{O}_{2}$ is heated to $3600 \mathrm{K}$ at a pressure of 8 atm. Determine the equilibrium composition of the mixture, assuming that only $\mathrm{H}_{2} \mathrm{O}, \mathrm{OH}, \mathrm{O}_{2}$, and $\mathrm{H}_{2}$ are present.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 99

A mixture of 3 mol of $\mathrm{CO}_{2}$ and 3 mol of $\mathrm{O}_{2}$ is heated to $3400 \mathrm{K}$ at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only $\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{O}_{2},$ and $\mathrm{O}$ are present.

Jincy M Saji

Numerade Educator

Problem 100

Reconsider Prob. $16-99 . \text { Using EES (or other })$ software, study the effect of pressure on the equilibrium composition by varying pressure from 1 atm to 10 atm. Plot the amount of $\mathrm{CO}$ present at equilibrium as a function of pressure.

Manik Pulyani

Numerade Educator

Problem 101

Estimate the enthalpy of reaction $\bar{h}_{R}$ for the combustion process of hydrogen at $2400 \mathrm{K},$ using $(a)$ enthalpy data and $(b) \quad K_{P} $ data.

Rory Naguib

Numerade Educator

Problem 102

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 $3000 \mathrm{K}$.

Akshaya Rs

Numerade Educator

Problem 103

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 $2400 \mathrm{K}$.

Jincy M Saji

Numerade Educator

Problem 104

A carbonated drink is fully charged with $\mathrm{CO}_{2}$ gas at $17^{\circ} \mathrm{C}$ and $600 \mathrm{kPa}$ such that the entire bulk of the drink is in thermodynamic equilibrium with the $\mathrm{CO}_{2}$ -water vapor mixture. Now consider a 2 -L soda bottle. If the $\mathrm{CO}_{2}$ gas in that bottle were to be released and stored in a container at $20^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine the volume of the container.

Rory Naguib

Numerade Educator

Problem 105

Tabulate the natural log of the equilibrium constant as a function of temperature between 298 to $3000 \mathrm{K}$ for the equilibrium reaction $\mathrm{CO}+\mathrm{H}_{2} \mathrm{O}=$ $\mathrm{CO}_{2}+\mathrm{H}_{2} .$ Compare your results to those obtained by combining the $\ln K_{P}$ values for the two equilibrium reactions $\mathrm{CO}_{2}=$ $\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}$ and $\mathrm{H}_{2} \mathrm{O}=\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}$ given in Table $\mathrm{A}-28$.

Jincy M Saji

Numerade Educator

Problem 106

Ethyl alcohol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\right)$ at $25^{\circ} \mathrm{C}$ is burned in a steady-flow adiabatic combustion chamber with 90 percent excess air that also enters at $25^{\circ} \mathrm{C}$. Determine the adiabatic flame temperature of the products at 1 atm assuming the only significant equilibrium reaction is $\mathrm{CO}_{2}=$ $\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} .$ Plot the adiabatic flame temperature as the percent excess air varies from 10 to 100 percent.

Jincy M Saji

Numerade Educator

Problem 107

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

Rory Naguib

Numerade Educator

Problem 108

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.

Rory Naguib

Numerade Educator

Problem 109

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
$(a) 1 / K$
$(b) 1 /(2 K)$
$(c) 2 K$
$(d) K^{2}$
$(e) 1 / K^{2}$

Rory Naguib

Numerade Educator

Problem 110

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
$(a) 1 / K$
$(b) 1 /(K+3)$
$(c) 4 K$
$(d) K$
$(e) 1 / K^{2}$

Rory Naguib

Numerade Educator

Problem 111

The equilibrium constant for the reaction $\mathrm{H}_{2}+$ $\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}$ at 1 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 atm
$(b) 2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}$ at 1 atm
$(c) \mathrm{H}_{2}+\mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\frac{1}{2} \mathrm{O}_{2}$ at 2 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 $5 \mathrm{atm}$
$(e) \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}+3 \mathrm{N}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+3 \mathrm{N}_{2} \quad$ at 1 atm

Rory Naguib

Numerade Educator

Problem 112

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

Rory Naguib

Numerade Educator

Problem 113

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

Rory Naguib

Numerade Educator

Problem 114

Moist air is heated to a very high temperature. If the equilibrium composition consists of $\mathrm{H}_{2} \mathrm{O}, \mathrm{O}_{2}, \mathrm{N}_{2}, \mathrm{OH}$, $\mathrm{H}_{2},$ and $\mathrm{NO} .$ The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is
$(a) 1$
$(b) 2$
$(c) 3$
$(d) 4$
$(e) 5$

Rory Naguib

Numerade Educator

Problem 115

Propane $\mathrm{C}_{3} \mathrm{H}_{8}$ is burned with air, and the combustion products consist of $\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{H}_{2} \mathrm{O}, \mathrm{O}_{2}, \mathrm{N}_{2}, \mathrm{OH}$, $\mathrm{H}_{2},$ and $\mathrm{NO}$. The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is
$(a) 1$
$(b) 2$
$(c) 3$
$(d) 4$
$(e) 5$

Rory Naguib

Numerade Educator

Problem 116

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
$(a) 1$
$(b) 2$
$(c) 3$
$(d) 4$
$(e) 5$

Rory Naguib

Numerade Educator

Problem 117

The value of Henry's constant for $\mathrm{CO}_{2}$ gas dissolved in water at $290 \mathrm{K}$ is $12.8 \mathrm{MPa}$. Consider water exposed to atmospheric air at 100 kPa that contains 3 percent $\mathrm{CO}_{2}$ by volume. Under phase equilibrium conditions, the mole fraction of $\mathrm{CO}_{2}$ gas dissolved in water at $290 \mathrm{K}$ is
$(a) 2.3 \times 10^{-4}$
$(b) 3.0 \times 10^{-4}$
$(c) 0.80 \times 10^{-4}$
$(d) 2.2 \times 10^{-4}$
$(e) 5.6 \times 10^{-4}$

Rory Naguib

Numerade Educator

Problem 118

The solubility of nitrogen gas in rubber at $25^{\circ} \mathrm{C}$ is $0.00156 \mathrm{kmol} / \mathrm{m}^{3} \cdot$ bar. When phase equilibrium is established the density of nitrogen in a rubber piece placed in a nitrogen gas chamber at $300 \mathrm{kPa}$ is
$(a) 0.005 \mathrm{kg} / \mathrm{m}^{3}$
$(b) 0.018 \mathrm{kg} / \mathrm{m}^{3}$
$(c) 0.047 \mathrm{kg} / \mathrm{m}^{3}$
$(d) 0.13 \mathrm{kg} / \mathrm{m}^{3}$
$(e) 0.28 \mathrm{kg} / \mathrm{m}^{3}$

Rory Naguib

Numerade Educator

Problem 119

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 $4000 \mathrm{K}$ and pressures as much as 5 atm. Water enters this reactor-separator at $25^{\circ} \mathrm{C}$. 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 $25^{\circ} \mathrm{C}$ 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?

Ajay Singhal

Numerade Educator

Problem 120

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 $50 \mathrm{mpg}$ 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.

David Collins

Numerade Educator

Problem 121

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. $\mathrm{P} 16-121 .$ 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.

Lottie Adams

Numerade Educator

Problem 122

Automobiles are major emitters of air pollutants such as $\mathrm{NO}_{x}, \mathrm{CO},$ and hydrocarbons HC. Find out the legal limits of these pollutants in your area, and estimate the total amount of each pollutant, in $\mathrm{kg},$ that would be produced in your town if all the cars were emitting pollutants at the legal limit. State your assumptions.

Noah Boudrie

Numerade Educator