Chapter 8, Problem 8.41E

Write an equilibrium expression for each of the following gaseous reactions:

a. ${\text{3O}}_2\rightleftarrows 2{\text{O}}_3$

b. ${\text{COCl}}_{\text{2}}\rightleftarrows \text{CO}+{\text{Cl}}_2$

c. ${\text{CS}}_2+4{\text{H}}_2\rightleftarrows {\text{CH}}_4+2{\text{H}}_2\text{S}$

d. ${\text{2SO}}_2+{\text{O}}_2\rightleftarrows 2{\text{SO}}_3$

e. $\text{CO}+{\text{H}}_2\text{O}\rightleftarrows {\text{CO}}_2+{\text{H}}_2$

Interpretation Introduction

(a)

Interpretation:

The equilibrium expression for the given gaseous reaction is to be stated.

Concept Introduction:

The equilibrium constant of a reaction is expressed as the ratio of concentration of products and reactants each raised to the power of their stoichiometric coefficients. A general equilibrium reaction is represented as,$a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

The equilibrium constant for the above chemical reaction is expressed as,$K=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Where,

• $\left[\text{A}\right]$ represents the equilibrium concentration of reactant $\text{A}$.

• $\left[\text{B}\right]$ represents the equilibrium concentration of reactant $\text{B}$.

• $\left[\text{C}\right]$ represents the equilibrium concentration of product $\text{C}$.

• $\left[\text{D}\right]$ represents the equilibrium concentration of product $\text{D}$.

• $a$ represents the stoichiometric coefficient of reactant $\text{A}$.

• $b$ represents the stoichiometric coefficient of reactant $\text{B}$.

• $c$ represents the stoichiometric coefficient of product $\text{C}$.

• $d$ represents the stoichiometric coefficient of product $\text{D}$.

Answer to Problem 8.41E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{{\left[{\text{O}}_3\right]}^2}{{\left[{\text{O}}_2\right]}^3}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{3O}}_2\rightleftarrows 2{\text{O}}_3$

The concentration of the product ${\text{O}}_3$ will be in the numerator and is raised to the power $2$. The concentration of reactant ${\text{O}}_2$ will be in the denominator and is raised to the power $3$.

Therefore, the equilibrium constant for the above gaseous reaction is expressed as,$K=\frac{{\left[{\text{O}}_3\right]}^2}{{\left[{\text{O}}_2\right]}^3}$

Conclusion

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{{\left[{\text{O}}_3\right]}^2}{{\left[{\text{O}}_2\right]}^3}$

Interpretation Introduction

(b)

Interpretation:

The equilibrium expression for the given gaseous reaction is to be stated.

Concept Introduction:

The equilibrium constant of a reaction is expressed as the ratio of concentration of products and reactants each raised to the power of their stoichiometric coefficients. A general equilibrium reaction is represented as,$a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

The equilibrium constant for the above chemical reaction is expressed as,$K=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Where,

• $\left[\text{A}\right]$ represents the equilibrium concentration of reactant $\text{A}$.

• $\left[\text{B}\right]$ represents the equilibrium concentration of reactant $\text{B}$.

• $\left[\text{C}\right]$ represents the equilibrium concentration of product $\text{C}$.

• $\left[\text{D}\right]$ represents the equilibrium concentration of product $\text{D}$.

• $a$ represents the stoichiometric coefficient of reactant $\text{A}$.

• $b$ represents the stoichiometric coefficient of reactant $\text{B}$.

• $c$ represents the stoichiometric coefficient of product $\text{C}$.

• $d$ represents the stoichiometric coefficient of product $\text{D}$.

Answer to Problem 8.41E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[\text{CO}\right]\left[{\text{Cl}}_2\right]}{\left[{\text{COCl}}_{\text{2}}\right]}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{COCl}}_{\text{2}}\rightleftarrows \text{CO}+{\text{Cl}}_2$

The concentration of the product $\text{CO}$ and ${\text{Cl}}_2$ will be in the numerator. The concentration of the reactant ${\text{COCl}}_{\text{2}}$ will be in the denominator. All concentrations are raised to the power $1$.

Therefore, the equilibrium constant for the above gaseous reaction is expressed as,$K=\frac{\left[\text{CO}\right]\left[{\text{Cl}}_2\right]}{\left[{\text{COCl}}_{\text{2}}\right]}$

Conclusion

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[\text{CO}\right]\left[{\text{Cl}}_2\right]}{\left[{\text{COCl}}_{\text{2}}\right]}$

Interpretation Introduction

(c)

Interpretation:

The equilibrium expression for the given gaseous reaction is to be stated.

Concept Introduction:

The equilibrium constant of a reaction is expressed as the ratio of concentration of products and reactants each raised to the power of their stoichiometric coefficients. A general equilibrium reaction is represented as,$a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

The equilibrium constant for the above chemical reaction is expressed as,$K=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Where,

• $\left[\text{A}\right]$ represents the equilibrium concentration of reactant $\text{A}$.

• $\left[\text{B}\right]$ represents the equilibrium concentration of reactant $\text{B}$.

• $\left[\text{C}\right]$ represents the equilibrium concentration of product $\text{C}$.

• $\left[\text{D}\right]$ represents the equilibrium concentration of product $\text{D}$.

• $a$ represents the stoichiometric coefficient of reactant $\text{A}$.

• $b$ represents the stoichiometric coefficient of reactant $\text{B}$.

• $c$ represents the stoichiometric coefficient of product $\text{C}$.

• $d$ represents the stoichiometric coefficient of product $\text{D}$.

Answer to Problem 8.41E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[{\text{CH}}_4\right]{\left[{\text{H}}_2\text{S}\right]}^2}{\left[{\text{CS}}_2\right]{\left[{\text{H}}_2\right]}^4}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{CS}}_2+4{\text{H}}_2\rightleftarrows {\text{CH}}_4+2{\text{H}}_2\text{S}$

The concentration of the product ${\text{CH}}_4$ and ${\text{H}}_2\text{S}$ will be in the numerator. The concentration of the product ${\text{CH}}_4$ is raised to the power $1$ and ${\text{H}}_2\text{S}$ is raised to the power $2$. The concentration of reactant ${\text{CS}}_2$ and ${\text{H}}_2$ will be in the denominator. The concentration of reactant ${\text{CS}}_2$ is raised to the power $1$ and ${\text{H}}_2$ is raised to the power $4$.

Therefore, the equilibrium constant for the above gaseous reaction is expressed as,$K=\frac{\left[{\text{CH}}_4\right]{\left[{\text{H}}_2\text{S}\right]}^2}{\left[{\text{CS}}_2\right]{\left[{\text{H}}_2\right]}^4}$

Conclusion

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[{\text{CH}}_4\right]{\left[{\text{H}}_2\text{S}\right]}^2}{\left[{\text{CS}}_2\right]{\left[{\text{H}}_2\right]}^4}$

Interpretation Introduction

(d)

Interpretation:

The equilibrium expression for the given gaseous reaction is to be stated.

Concept Introduction:

The equilibrium constant of a reaction is expressed as the ratio of concentration of products and reactants each raised to the power of their stoichiometric coefficients. A general equilibrium reaction is represented as,$a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

The equilibrium constant for the above chemical reaction is expressed as,$K=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Where,

• $\left[\text{A}\right]$ represents the equilibrium concentration of reactant $\text{A}$.

• $\left[\text{B}\right]$ represents the equilibrium concentration of reactant $\text{B}$.

• $\left[\text{C}\right]$ represents the equilibrium concentration of product $\text{C}$.

• $\left[\text{D}\right]$ represents the equilibrium concentration of product $\text{D}$.

• $a$ represents the stoichiometric coefficient of reactant $\text{A}$.

• $b$ represents the stoichiometric coefficient of reactant $\text{B}$.

• $c$ represents the stoichiometric coefficient of product $\text{C}$.

• $d$ represents the stoichiometric coefficient of product $\text{D}$.

Answer to Problem 8.41E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{{\left[{\text{SO}}_3\right]}^2}{\left[{\text{O}}_2\right]{\left[{\text{SO}}_2\right]}^2}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{2SO}}_2+{\text{O}}_2\rightleftarrows 2{\text{SO}}_3$

The concentration of the product ${\text{SO}}_3$ will be in the numerator and is raised to the power $2$. The concentration of reactant ${\text{SO}}_2$ and ${\text{O}}_2$ will be in the denominator. The concentration of reactant ${\text{O}}_2$ is raised to the power $1$ and ${\text{SO}}_2$ is raised to the power $2$.

Therefore, the equilibrium constant for the above gaseous reaction is expressed as,$K=\frac{{\left[{\text{SO}}_3\right]}^2}{\left[{\text{O}}_2\right]{\left[{\text{SO}}_2\right]}^2}$

Conclusion

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{{\left[{\text{SO}}_3\right]}^2}{\left[{\text{O}}_2\right]{\left[{\text{SO}}_2\right]}^2}$

Interpretation Introduction

(e)

Interpretation:

The equilibrium expression for the given gaseous reaction is to be stated.

Concept Introduction:

The equilibrium constant of a reaction is expressed as the ratio of concentration of products and reactants each raised to the power of their stoichiometric coefficients. A general equilibrium reaction is represented as,$a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

The equilibrium constant for the above chemical reaction is expressed as,$K=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Where,

• $\left[\text{A}\right]$ represents the equilibrium concentration of reactant $\text{A}$.

• $\left[\text{B}\right]$ represents the equilibrium concentration of reactant $\text{B}$.

• $\left[\text{C}\right]$ represents the equilibrium concentration of product $\text{C}$.

• $\left[\text{D}\right]$ represents the equilibrium concentration of product $\text{D}$.

• $a$ represents the stoichiometric coefficient of reactant $\text{A}$.

• $b$ represents the stoichiometric coefficient of reactant $\text{B}$.

• $c$ represents the stoichiometric coefficient of product $\text{C}$.

• $d$ represents the stoichiometric coefficient of product $\text{D}$.

Answer to Problem 8.41E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[{\text{CO}}_2\right]\left[{\text{H}}_2\right]}{\left[\text{CO}\right]\left[{\text{H}}_2\text{O}\right]}$

Explanation of Solution

The given gaseous reaction is represented as,$\text{CO}+{\text{H}}_2\text{O}\rightleftarrows {\text{CO}}_2+{\text{H}}_2$

The concentration of the product ${\text{CO}}_2$ and ${\text{H}}_2$ will be in the numerator. The concentration of reactant $\text{CO}$ and ${\text{H}}_2\text{O}$ will be in the denominator. All the concentrations are raised to the power $1$.

Therefore, the equilibrium constant for the above gaseous reaction is expressed as,$K=\frac{\left[{\text{CO}}_2\right]\left[{\text{H}}_2\right]}{\left[\text{CO}\right]\left[{\text{H}}_2\text{O}\right]}$

Conclusion

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[{\text{CO}}_2\right]\left[{\text{H}}_2\right]}{\left[\text{CO}\right]\left[{\text{H}}_2\text{O}\right]}$