Chapter 15, Problem 1PS

Write equilibrium constant expressions for the following reactions. For gases, use either pressures or concentrations.

1. (a) 2 H₂O₂(g) ⇄ 2 H₂O(g) + O₂(g)
2. (b) CO(g) + ½ O₂g ⇄ CO₂(g)
3. (c) C(s) + CO₂(g) ⇄ 2 CO(g)
4. (d) NiO(s) + CO(g) ⇄ Ni(s) + CO₂(g)

Interpretation Introduction

Interpretation: The equilibrium constant for the given reaction has to be identified.

Concept Introduction: At equilibrium the concentration of the reaction and the product is equated to a constant $\text{K}$, where $\text{K}$ is known as the equilibrium

If a reaction is as $\text{aA}\text{+}\text{bB}\to \text{cC}\text{+}\text{dD}$ ,

The equilibrium constant $\text{K}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Answer to Problem 1PS

The equilibrium constant for the reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{{\text{[H}}_{\text{2}}\text{O]}}^{\text{2}}{\text{[O}}_{\text{2}}\text{]}}{{{\text{[H}}_{\text{2}}{\text{O}}_{\text{2}}\text{]}}^{\text{2}}}{\text{K}}_{\text{p}}\text{=}\frac{{{\text{(H}}_{\text{2}}\text{O)}}^{\text{2}}{\text{(O}}_{\text{2}}\text{)}}{{{\text{(H}}_{\text{2}}{\text{O}}_{\text{2}}\text{)}}^{\text{2}}}$

Explanation of Solution

The equilibrium constant for the reaction can be calculated as,

$2{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}(g)\rightleftarrows 2{\text{H}}_{\text{2}}\text{O}(g)+{\text{O}}_{\text{2}}(g)$

The product concentrations appear in the numerator and reactant concentrations appear in the denominator. Each concentration should be raised to a power equal to the stoichiometric coefficient in the balanced equation.

The equilibrium constant for the above reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{{\text{[H}}_{\text{2}}\text{O]}}^{\text{2}}{\text{[O}}_{\text{2}}\text{]}}{{{\text{[H}}_{\text{2}}{\text{O}}_{\text{2}}\text{]}}^{\text{2}}}{\text{K}}_{\text{p}}\text{=}\frac{{{\text{(H}}_{\text{2}}\text{O)}}^{\text{2}}{\text{(O}}_{\text{2}}\text{)}}{{{\text{(H}}_{\text{2}}{\text{O}}_{\text{2}}\text{)}}^{\text{2}}}$

Interpretation Introduction

Interpretation: The equilibrium constant for the given reaction has to be identified.

Concept Introduction: At equilibrium the concentration of the reaction and the product is equated to a constant $\text{K}$, where $\text{K}$ is known as the equilibrium

If a reaction is as $\text{aA}\text{+}\text{bB}\to \text{cC}\text{+}\text{dD}$ ,

The equilibrium constant $\text{K}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Answer to Problem 1PS

The equilibrium constant for the reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[CO}}_{\text{2}}\text{]}}{{\text{[CO][O}}_{\text{2}}{\text{]}}^{\text{1/2}}}{\text{K}}_{\text{p}}\text{=}\frac{{\text{(CO}}_{\text{2}}\text{)}}{{\text{(CO)(O}}_{\text{2}}{\text{)}}^{\text{1/2}}}$

Explanation of Solution

The equilibrium constant for the reaction can be calculated as,

$\text{CO}(g)+1/2{\text{O}}_{\text{2}}(g)\rightleftarrows C{O}_{\text{2}}(g)$

The product concentrations appear in the numerator and reactant concentrations appear in the denominator. Each concentration should be raised to a power equal to the stoichiometric coefficient in the balanced equation.

The equilibrium constant for the above reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{{\text{[H}}_{\text{2}}\text{O]}}^{\text{2}}{\text{[O}}_{\text{2}}\text{]}}{{{\text{[H}}_{\text{2}}{\text{O}}_{\text{2}}\text{]}}^{\text{2}}}{\text{K}}_{\text{p}}\text{=}\frac{{{\text{(H}}_{\text{2}}\text{O)}}^{\text{2}}{\text{(O}}_{\text{2}}\text{)}}{{{\text{(H}}_{\text{2}}{\text{O}}_{\text{2}}\text{)}}^{\text{2}}}$

Interpretation Introduction

Interpretation: The equilibrium constant for the given reaction has to be identified.

Concept Introduction: At equilibrium the concentration of the reaction and the product is equated to a constant $\text{K}$, where $\text{K}$ is known as the equilibrium

If a reaction is as $\text{aA}\text{+}\text{bB}\to \text{cC}\text{+}\text{dD}$ ,

The equilibrium constant $\text{K}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Answer to Problem 1PS

The equilibrium constant for the reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[CO]}}^{\text{2}}}{{\text{[C][CO}}_{\text{2}}\text{]}}{\text{K}}_{\text{p}}\text{=}\frac{{\text{(CO)}}^{\text{2}}}{{\text{(C)(CO}}_{\text{2}}\text{)}}$

Explanation of Solution

The equilibrium constant for the reaction can be calculated as,

$\text{C}(s)+C{\text{O}}_{\text{2}}(g)\rightleftarrows 2CO(g)$

The product concentrations appear in the numerator and reactant concentrations appear in the denominator. Each concentration should be raised to a power equal to the stoichiometric coefficient in the balanced equation.

The equilibrium constant for the above reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[CO]}}^{\text{2}}}{{\text{[C][CO}}_{\text{2}}\text{]}}{\text{K}}_{\text{p}}\text{=}\frac{{\text{(CO)}}^{\text{2}}}{{\text{(C)(CO}}_{\text{2}}\text{)}}$

Interpretation Introduction

Interpretation: The equilibrium constant for the given reaction has to be identified.

Concept Introduction: At equilibrium the concentration of the reaction and the product is equated to a constant $\text{K}$, where $\text{K}$ is known as the equilibrium

If a reaction is as $\text{aA}\text{+}\text{bB}\to \text{cC}\text{+}\text{dD}$ ,

The equilibrium constant $\text{K}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Answer to Problem 1PS

The equilibrium constant for the reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[Ni][CO}}_{\text{2}}\text{]}}{\text{[NiO]}\text{[CO]}}{\text{K}}_{\text{p}}\text{=}\frac{{\text{(Ni)(CO}}_{\text{2}}\text{)}}{\text{(NiO)(CO)}}$

Explanation of Solution

The equilibrium constant for the reaction can be calculated as,

$NiC(s)+C\text{O}(g)\rightleftarrows Ni(s)+C{O}_2(g)$

The product concentrations appear in the numerator and reactant concentrations appear in the denominator. Each concentration should be raised to a power equal to the stoichiometric coefficient in the balanced equation.

The equilibrium constant for the above reaction is given below,

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[Ni][CO}}_{\text{2}}\text{]}}{\text{[NiO]}\text{[CO]}}{\text{K}}_{\text{p}}\text{=}\frac{{\text{(Ni)(CO}}_{\text{2}}\text{)}}{\text{(NiO)(CO)}}$