Chapter 8, Problem 8.42E

Interpretation Introduction

(a)

Interpretation:

The equilibrium expression for the given 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 8.42E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[\text{Fe}{\left(\text{CN}\right)}_6{}^{3-}\right]}{\left[{\text{Fe}}^{\text{3+}}\right]{\left[{\text{CN}}^{-}\right]}^6}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{Fe}}^{\text{3+}}+6{\text{CN}}^{-}\rightleftarrows \text{Fe}{\left(\text{CN}\right)}_6{}^{3-}$

The concentration of the product $\text{Fe}{\left(\text{CN}\right)}_6{}^{3-}$ will be in the numerator and is raised to the power $1$. The concentration of reactant ${\text{Fe}}^{\text{3+}}$ and ${\text{CN}}^{-}$ will be in the denominator. The concentration of reactant ${\text{Fe}}^{\text{3+}}$ is raised to the power $1$ and ${\text{CN}}^{-}$ is raised to the power $6$. Therefore, the equilibrium constant for the above reaction is expressed as,$K=\frac{\left[\text{Fe}{\left(\text{CN}\right)}_6{}^{3-}\right]}{\left[{\text{Fe}}^{\text{3+}}\right]{\left[{\text{CN}}^{-}\right]}^6}$

Conclusion

The equilibrium constant for the given reaction is expressed as,$K=\frac{\left[\text{Fe}{\left(\text{CN}\right)}_6{}^{3-}\right]}{\left[{\text{Fe}}^{\text{3+}}\right]{\left[{\text{CN}}^{-}\right]}^6}$

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 8.42E

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

Explanation of Solution

The given gaseous reaction is represented as,${\text{Ag}}^{+}+2{\text{NH}}_3\rightleftarrows \text{Ag}{\left({\text{NH}}_3\right)}_2{}^{+}$

The concentration of the product $\text{Ag}{\left({\text{NH}}_3\right)}_2{}^{+}$ will be in the numerator and is raised to the power $1$. The concentration of reactant ${\text{NH}}_3$ and ${\text{Ag}}^{+}$ will be in the denominator. The concentration of reactant ${\text{Ag}}^{+}$ is raised to the power $1$ and ${\text{NH}}_3$ is raised to the power $2$. Therefore, the equilibrium constant for the above reaction is expressed as,$K=\frac{\left[\text{Ag}{\left({\text{NH}}_3\right)}_2{}^{+}\right]}{\left[{\text{Ag}}^{+}\right]{\left[{\text{NH}}_3\right]}^2}$

Conclusion

The equilibrium constant for the given reaction is expressed as,$K=\frac{\left[\text{Ag}{\left({\text{NH}}_3\right)}_2{}^{+}\right]}{\left[{\text{Ag}}^{+}\right]{\left[{\text{NH}}_3\right]}^2}$

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 8.42E

The equilibrium constant for the given gaseous reaction is expressed as,$K=\frac{\left[{\text{AuCl}}_4{}^{-}\right]}{\left[{\text{Au}}^{3+}\right]{\left[{\text{Cl}}^{-}\right]}^4}$

Explanation of Solution

The given gaseous reaction is represented as,${\text{Au}}^{3+}+4{\text{Cl}}^{-}\rightleftarrows {\text{AuCl}}_4{}^{-}$

The concentration of the product ${\text{AuCl}}_4{}^{-}$ will be in the numerator and is raised to the power $1$. The concentration of reactant ${\text{Au}}^{3+}$ and ${\text{Cl}}^{-}$ will be in the denominator. The concentration of reactant ${\text{Au}}^{3+}$ is raised to the power $1$ and ${\text{Cl}}^{-}$ is raised to the power $4$. Therefore, the equilibrium constant for the above reaction is expressed as,$K=\frac{\left[{\text{AuCl}}_4{}^{-}\right]}{\left[{\text{Au}}^{3+}\right]{\left[{\text{Cl}}^{-}\right]}^4}$

Conclusion

The equilibrium constant for the given reaction is expressed as,$K=\frac{\left[{\text{AuCl}}_4{}^{-}\right]}{\left[{\text{Au}}^{3+}\right]{\left[{\text{Cl}}^{-}\right]}^4}$