Chapter 17, Problem 17.61P

(a)

Interpretation Introduction

Interpretation:

The reason has to be given for the equilibrium constant (K) remaining constant even though equilibrium shifts towards right when reactant concentration increases.

Concept Introduction:

Le Chatelier principle states that, whenever a system at equilibrium is disturbed, the system will undergo reactions and try to cancel that effect and retain equilibrium. Here the disturbance means change in concentration of any of the component, change in temperature, pressure or volume.

At equilibrium rate of forward reaction is equal to the rate of backward reaction. So concentration of reactant and products are constant at equilibrium.

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

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

At equilibrium, rate of formation of B will be equal to rate of decomposition of A. So, rate can be written as follows,

${\text{k}}_{\text{fwd}}{\text{[A]}}_{\text{eq}}^{\text{a}}{\text{ = k}}_{\text{rev}}{\text{[B]}}_{\text{eq}}^{\text{b}}$

Where,

    $\begin{array}{l}{\text{k}}_{\text{fwd}}\text{ = rate of forward reaction}\\ {\text{k}}_{\text{rev}}\text{ = rate of backward reaction}\\ {\text{[A]}}_{\text{eq}}^{}\text{= equilibrium concentration of A}\\ {\text{[B]}}_{\text{eq}}^{}\text{ = equilibrium concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

On rearranging the ratio of rate constant becomes equal to ratio of concentration which is equal to a constant called equilibrium constant K.

Equilibrium constant K can be written as follows,

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

So equilibrium constant K can be defined as the ratio of equilibrium concentration of products to reactants at a particular temperature.

(b)

Interpretation Introduction

Interpretation:

The reason has to be given for the equilibrium constant (K) remaining constant even though equilibrium shifts towards fewer moles of gas when volume is decreased.

Concept Introduction:

Le Chatelier principle states that, whenever a system at equilibrium is disturbed, the system will undergo reactions and try to cancel that effect and retain equilibrium. Here the disturbance means change in concentration of any of the component, change in temperature, pressure or volume.

At equilibrium rate of forward reaction is equal to the rate of backward reaction. So concentration of reactant and products are constant at equilibrium.

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

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

At equilibrium, rate of formation of B will be equal to rate of decomposition of A. So, rate can be written as follows,

${\text{k}}_{\text{fwd}}{\text{[A]}}_{\text{eq}}^{\text{a}}{\text{ = k}}_{\text{rev}}{\text{[B]}}_{\text{eq}}^{\text{b}}$

Where,

    $\begin{array}{l}{\text{k}}_{\text{fwd}}\text{ = rate of forward reaction}\\ {\text{k}}_{\text{rev}}\text{ = rate of backward reaction}\\ {\text{[A]}}_{\text{eq}}^{}\text{= equilibrium concentration of A}\\ {\text{[B]}}_{\text{eq}}^{}\text{ = equilibrium concentration of B}\\ \text{ a = stoichiometric co-efficient of A}\\ \text{ b = stoichiometric co-efficient of A}\end{array}$

On rearranging the ratio of rate constant becomes equal to ratio of concentration which is equal to a constant called equilibrium constant K.

Equilibrium constant K can be written as follows,

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

So equilibrium constant K can be defined as the ratio of equilibrium concentration of product to reactant at a particular temperature.

(c)

Interpretation Introduction

Interpretation:

The reason has to be given for the shift of equilibrium towards backward direction during exothermic reaction and change in equilibrium constant (K) in this reaction.

Concept Introduction:

Le Chatelier principle states that, whenever a system at equilibrium is disturbed, the system will undergo reactions and try to cancel that effect and retain equilibrium. Here the disturbance means change in concentration of any of the component, change in temperature, pressure or volume.

During exothermic reaction energy is released. That is $\text{ΔH}$ value will be negative. Decrease in temperature favors forward reaction for exothermic processes.

Equilibrium constant K can be written as follows,

$\text{K = }\frac{{\text{k}}_{\text{fwd}}}{{\text{k}}_{\text{rev}}}$

Where,

    $\begin{array}{l}{\text{k}}_{\text{fwd}}\text{ = rate of forward reaction}\\ {\text{k}}_{\text{rev}}\text{ = rate of backward reaction}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The reason has to be given for the increase in equilibrium constant when temperature is increased in an endothermic reaction.

Concept Introduction:

Le Chatelier principle states that, whenever a system at equilibrium is disturbed, the system will undergo reactions and try to cancel that effect and retain equilibrium. Here the disturbance means change in concentration of any of the component, change in temperature, pressure or volume.

During endothermic reaction heat energy is absorbed. That is $\text{ΔH}$ value will be positive. Increase in temperature favors forward reaction for endothermic processes.

The equilibrium constant can be written as follows,

$K=\frac{\left[product\right]}{\left[reac\tan t\right]}$