Chapter 13, Problem 53UTC

Write the equilibrium expression for each of the following reactions: $(13.3)$
a. ${\text{CH}}_4(\text{g})+2{\text{O}}_2(\text{g})\rightleftarrows {\text{CO}}_2(\text{g})+2{\text{H}}_2\text{O}(\text{g})$
b. $4{\text{NH}}_3(g)+3{\text{O}}_2(g)\rightleftarrows 2{\text{N}}_2(g)+6{\text{H}}_2\text{O}(g)$
c. $\text{C}(s)+2{\text{H}}_2(g)\rightleftarrows {\text{CH}}_4(g)$ a

Interpretation Introduction

Interpretation:

Equilibrium constant expression for the given reactionshould be identified.

Concept introduction:

Equilibrium is the condition at which the rate of formation of product is equal to rate of disappearance of reactant.

Equilibrium constant is the concentration of product raise to its stochiometric coefficient divided to the concentration of reactant raise to its stochiometric coefficient, pure solids and liquids are not included in the equilibrium constant expression.

Answer to Problem 53UTC

Solution:

$\text{K}=\frac{\left[{\text{CO}}_2\right]{[{\text{H}}_2\text{O}]}^2}{\left[{\text{CH}}_4\right]{[{\text{O}}_2]}^2}$

Given:

  ${\mathrm{CH}}_4\left(g\right)+2O_2\left(g\right) \rightleftharpoons C{O}_2\left(g\right) +2H_{2}O\left(g\right)$

Explanation of Solution

Water having stochiometric coefficient as 2 and oxygen having stochiometriccoefficient as 2.

$\text{K}=\frac{\left[{\text{CO}}_2\right]{[{\text{H}}_2\text{O}]}^2}{\left[{\text{CH}}_4\right]{[{\text{O}}_2]}^2}$

Interpretation Introduction

Interpretation:

Equilibrium constant expression for each given reactionshould be identified.

Concept introduction:

Equilibrium is the condition at which the rate of formation of product is equal to rate of disappearance of reactant.

Equilibrium constant is the concentration of product raise to its stochiometric coefficient divided to the concentration of reactant raise to its stochiometric coefficient, pure solids and liquids are not included in the equilibrium constant expression.

Answer to Problem 53UTC

Solution:

$\text{K}=\frac{{\left[{\text{N}}_2\right]}^2{[{\text{H}}_2\text{O}]}^6}{{[{\text{NH}}_3]}^4{[{\text{O}}_2]}^3}$

Given:

  ${\text{4NH}}_{\text{3}}\left(\text{g}\right){\text{ + 3O}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons {\text{ 2N}}_{\text{2}}\left(\text{g}\right){\text{ + 6H}}_{\text{2}}\text{O}\left(\text{g}\right)$

Explanation of Solution

Nitrogen having stochiometric coefficient as 2, water having stochiometric coefficient as 6, ammonia having stochiometric coefficient as 4 and oxygen having stochiometric coefficient as 3.

$\text{K}=\frac{{\left[{\text{N}}_2\right]}^2{[{\text{H}}_2\text{O}]}^6}{{[{\text{NH}}_3]}^4{[{\text{O}}_2]}^3}$

Interpretation Introduction

Interpretation:

Equilibrium constant expression for each given reactionshould be identified.

Concept introduction:

Equilibrium is the condition at which the rate of formation of product is equal to rate of disappearance of reactant.

Equilibrium constant is the concentration of product raise to its stochiometric coefficient divided to the concentration of reactant raise to its stochiometric coefficient, pure solids and liquids are not included in the equilibrium constant expression.

Answer to Problem 53UTC

Solution:

$\text{K}=\frac{\left[{\text{CH}}_4\right]}{{[{\text{H}}_2]}^2}$

Given:

  $\text{C}\left(\text{s}\right){\text{ + 2H}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons {\text{ CH}}_{\text{4}}\left(\text{g}\right)$

Explanation of Solution

Hydrogen having stochiometric coefficient as 2, pure solids are not included in the equilibrium constant expression. 

$\text{K}=\frac{\left[{\text{CH}}_4\right]}{{[{\text{H}}_2]}^2}$