Chapter 17.5, Problem 17.10AFP

(a)

Interpretation Introduction

Interpretation:

For the reaction, ${\text{PCl}}_{\text{5(g)}}\stackrel{}{\rightleftharpoons }{\text{ PCl}}_{\text{3(g)}}{\text{ + Cl}}_{\text{2(g)}}$ and the given reaction condition, the direction to which the reaction will proceed has to be given.

Concept Introduction:

Comparison of ${\text{Q}}_{\text{c}}{\text{ and K}}_{\text{c}}$ :

When ${\text{Q}}_{\text{c}}{\text{ < K}}_{\text{c}}$, the reaction will proceed in right direction, $\text{reactants}\stackrel{}{\to }\text{products}$

When ${\text{Q}}_{\text{c}}{\text{ > K}}_{\text{c}}$, the reaction will proceed in left direction, $\text{reactants}\stackrel{}{\leftarrow }\text{products}$

When ${\text{Q}}_{\text{c}}{\text{ = K}}_{\text{c}}$, the reaction will remain unchanged, $\text{reactants}\stackrel{}{\rightleftharpoons }\text{products}$

(b)

Interpretation Introduction

Interpretation:

For the reaction, ${\text{PCl}}_{\text{5(g)}}\stackrel{}{\rightleftharpoons }{\text{ PCl}}_{\text{3(g)}}{\text{ + Cl}}_{\text{2(g)}}$ at equilibrium, the concentration of ${\text{[PCl}}_{\text{5}}\text{] = 0}\text{.2065}$. The equilibrium concentration of all other components has to be calculated.

Concept Introduction:

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

Equilibrium constant $\left({\text{K}}_{\text{c}}\right)$ is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration 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.

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

    $\begin{array}{l}\text{Rate of forward reaction = Rate of reverse reaction}\\ {\text{k}}_{\text{f}}{\left[\text{A}\right]}^{\text{a}}{\text{=k}}_{\text{r}}{\left[\text{B}\right]}^{\text{b}}\end{array}$

On rearranging,

    $\frac{{\left[\text{B}\right]}^{\text{b}}}{{\left[\text{A}\right]}^{\text{a}}}\text{=}\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}{\text{=K}}_{\text{c}}$

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.

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