Chapter 13, Problem 13.114CHP

(a)

Interpretation Introduction

Interpretation:

The equilibrium pressure of ${\text{WBr}}_{\text{4}}$ near the walls of the bulb (for the given reaction)has to be calculated.

Concept introduction:

Equilibrium constant$\left({\text{K}}_{\text{p}}\right)$:

In gas phase reactions, partial pressure is used to write equilibrium equation than molar concentration. Equilibrium constant $\left({\text{K}}_{\text{p}}\right)$ is defined as ratio of partial pressure of products to partial pressure of reactants. Each partial pressure term is raised to a power, which is same as the coefficients in the chemical reaction

Consider the reaction where A reacts to give B.

$\text{aA}\rightleftharpoons \text{bB}$

$\begin{array}{l}\text{Rate of forward reaction = Rate of reverse reaction}\\ {\text{k}}_{\text{f}}{\text{P}}_{\text{A}}{}^{\text{a}}{\text{=k}}_{\text{r}}{\text{P}}_{\text{B}}{}^{\text{a}}\end{array}$

On rearranging,

$\frac{{\text{P}}_{\text{B}}{}^{\text{b}}}{{\text{P}}_{\text{A}}{}^{\text{a}}}\text{=}\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}{\text{=K}}_{\text{p}}$

Where,

${\text{k}}_{\text{f}}$ is the rate constant of the forward reaction.

${\text{k}}_{\text{r}}$ is the rate constant of the reverse reaction.

${\text{K}}_{\text{p}}$ is the equilibrium constant.

The pressure of each species of ideal gas and its molar concentration are directly proportional to each other.

$\begin{array}{l}{\text{P}}_{\text{A}}{\text{V = n}}_{\text{A}}\text{RT}\\ \\ {\text{P}}_{\text{A}}\text{ = }\frac{{\text{n}}_{\text{A}}}{\text{V}}\text{RT}\text{=}\text{[A]RT}\end{array}$

In same way ${\text{P}}_{\text{B}}\text{ =}\text{[B]RT}$. Thus, equilibrium constant ${\text{K}}_{\text{p}}$ is given as

$\begin{array}{l}{\text{K}}_{\text{p}}\text{=}\frac{{\text{[B]}}^{\text{b}}}{{\text{[A]}}^{\text{a}}}\text{×}{\text{(RT)}}^{\text{b-a}}\\ \\ {\text{K}}_{\text{p}}{\text{ = K}}_{\text{c}}{\text{(RT)}}^{\text{Δn}}\end{array}$

Where,

R is gas constant

T is absolute temperature

$\text{Δn}$ is difference in moles of products to reactants in gas phase.

(b)

Interpretation Introduction

Interpretation:

The given reaction is endothermic or exothermic has to be identified.

Concept introduction:

Le Chatelier's principle states that if a system in equilibrium gets disturbed due to modification of concentration, temperature, volume, and pressure, then it reset to counteract the effect of disturbance.

Effect of change in temperature:

Endothermic reaction: In this reaction increase in temperature which is absorbed in reactant side, the reaction occurs in a way to relieve the stress in reactant side. The reaction occurs along the direction of product side and increases equilibrium constant.

Exothermic reaction: In this reaction increase in temperature which is released in product side, the reaction occurs in a way to relieve the stress in product side. The reaction occurs along the direction of reactant side and decreases equilibrium constant.

(c)

Interpretation Introduction

Interpretation:

The calculated pressure of ${\text{WBr}}_{\text{4}}$ makes reaction to reverse at $\text{2800K}$ has to be shown.

Concept introduction:

Reaction quotient (Q):

Reaction quotient (Q) is the ratio of product of concentration of products to that of product of concentration of reactants, raised to the power of coefficients.

Consider a reaction

$\text{aA + bB}\stackrel{}{\rightleftharpoons }\text{cC + dD}$

$\text{Reaction}\text{quotient}{\text{Q}}_{\text{c}}\text{=}\frac{{\text{[C]}}_{\text{t}}{}^{\text{c}}{\text{[D]}}_{\text{t}}{}^{\text{d}}}{{\text{[A]}}_{\text{t}}{}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Where,

a, b, c and d are coefficients of each species.

t is arbitrary time for measuring concentration .

Figure 1