Chapter 17.6, Problem 17.14AFP

(a)

Interpretation Introduction

Interpretation:

Value of ${\text{K}}_{\text{p}}$ has to be calculated.

Concept Introduction:

Equilibrium constant (K) is the equilibrium ratio of concentration/partial pressure of product to reactant in which the stoichiometric term raised to the power of each component’s concentration or partial pressure. It has a particular value at a particular temperature.

Consider a reaction, a moles of A gives b moles of B as follows,

$\text{a A }\rightleftharpoons \text{ b B}$

The equilibrium constant for this reaction can be written as follows,

$\text{K = }\frac{{\text{[B]}}_{\text{eq}}^{\text{b}}}{{\text{[A]}}_{\text{eq}}^{\text{a}}}$

Where,

    $\begin{array}{l}{\text{[A]}}_{\text{eq}}^{}\text{= equilibrium concentration of A}\\ {\text{[B]}}_{\text{eq}}^{}\text{ = equilibrium concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

Relationship between ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$: ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$ are related by the following equation,

The equilibrium constant in terms of concentration ${\text{K}}_{\text{c}}$ and in terms of partial pressure ${\text{K}}_{\text{p}}$ are related by an equation given below.

${\text{K}}_{\text{p}}{\text{ = K}}_{\text{c}}{\left(\text{RT}\right)}^{{\text{Δn}}_{\text{gas}}}$

Where,

    $\begin{array}{l}{\text{K}}_{\text{p}}\text{= equilibrium constant in terms of pressure}\\ {\text{K}}_{\text{c}}\text{= equilibrium constant in terms of concentration}\\ {\text{Δn}}_{\text{gas}}\text{= number of moles gaseous products - number of moles gaseous reactants}\\ \text{R = universal gas constant}\end{array}$

Reaction quotient (Q) is the ratio of concentration/partial pressure of product to reactant in which the stoichiometric term raised to the power of each component’s concentration or partial pressure.

The direction of chemical reaction can be predicted by comparing the reaction quotient and equilibrium constant.

The reaction quotient for above reaction can be written as follows,

$\text{Q = }\frac{{\text{[B]}}_{}^{\text{b}}}{{\text{[A]}}_{}^{\text{a}}}$

Where,

    $\begin{array}{l}{\text{[A]}}_{}^{}\text{= concentration of A}\\ {\text{[B]}}_{}^{}\text{ = concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

If $\text{Q>K}$, reaction proceed in the backward direction and if $\text{Q<K}$, reaction proceed in the forward direction.

Pressure can be expressed as $\text{P = }\frac{\text{nRT}}{\text{V}}.$

Where,

    $\begin{array}{l}\text{P = Pressure of the gas}\\ \text{n = number of moles}\\ \text{R = universal gas constant}\\ \text{T = temperature}\\ \text{V = volume of gas}\end{array}$

(b)

Interpretation Introduction

Interpretation:

For the mixtures that are not in equilibrium, the direction in which the reaction proceeds has to be mentioned.

Concept Introduction:

Equilibrium constant (K) is the equilibrium ratio of concentration/partial pressure of product to reactant in which the stoichiometric term raised to the power of each component’s concentration or partial pressure. It has a particular value at a particular temperature.

Consider a reaction, a moles of A gives b moles of B as follows,

$\text{a A }\rightleftharpoons \text{ b B}$

The equilibrium constant for this reaction can be written as follows,

$\text{K = }\frac{{\text{[B]}}_{\text{eq}}^{\text{b}}}{{\text{[A]}}_{\text{eq}}^{\text{a}}}$

Where,

    $\begin{array}{l}{\text{[A]}}_{\text{eq}}^{}\text{= equilibrium concentration of A}\\ {\text{[B]}}_{\text{eq}}^{}\text{ = equilibrium concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

Relationship between ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$: ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$ are related by the following equation,

The equilibrium constant in terms of concentration ${\text{K}}_{\text{c}}$ and in terms of partial pressure ${\text{K}}_{\text{p}}$ are related by an equation given below.

${\text{K}}_{\text{p}}{\text{ = K}}_{\text{c}}{\left(\text{RT}\right)}^{{\text{Δn}}_{\text{gas}}}$

Where,

    $\begin{array}{l}{\text{K}}_{\text{p}}\text{= equilibrium constant in terms of pressure}\\ {\text{K}}_{\text{c}}\text{= equilibrium constant in terms of concentration}\\ {\text{Δn}}_{\text{gas}}\text{= number of moles gaseous products - number of moles gaseous reactants}\\ \text{R = universal gas constant}\end{array}$

Reaction quotient (Q) is the ratio of concentration/partial pressure of product to reactant in which the stoichiometric term raised to the power of each component’s concentration or partial pressure.

The direction of chemical reaction can be predicted by comparing the reaction quotient and equilibrium constant.

The reaction quotient for above reaction can be written as follows,

$\text{Q = }\frac{{\text{[B]}}_{}^{\text{b}}}{{\text{[A]}}_{}^{\text{a}}}$

Where,

    $\begin{array}{l}{\text{[A]}}_{}^{}\text{= concentration of A}\\ {\text{[B]}}_{}^{}\text{ = concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

If $\text{Q>K}$, reaction proceed in the backward direction and if $\text{Q<K}$, reaction proceed in the forward direction.

Pressure can be expressed as $\text{P = }\frac{\text{nRT}}{\text{V}}.$

Where,

    $\begin{array}{l}\text{P = Pressure of the gas}\\ \text{n = number of moles}\\ \text{R = universal gas constant}\\ \text{T = temperature}\\ \text{V = volume of gas}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The effect of temperature on the given reaction at equilibrium has to be explained.

Concept Introduction:

In exothermic reaction $\left(\Delta \text{H<0}\right)$ heat is liberated. So heat is considered as product in these reactions. Therefore the increase in temperature leads to backward reaction and decrease in temperature leads to forward reaction.