Chapter 12, Problem 100QRT

Interpretation Introduction

Interpretation:

The value of ${\text{K}}_{\text{C}}$ has to be calculated for the decomposition reaction of ${\text{SO}}_{\text{3}}$.

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.

Relation between ${\text{K}}_{\text{p}}$ and ${\text{K}}_{\text{c}}$:

The relation between and ${\text{K}}_{\text{p}}$ and ${\text{K}}_{\text{c}}$ is given by the following equation.

  ${\text{K}}_{\text{p}}{\text{ = K}}_{\text{c}}{\text{(RT)}}^{\Delta \text{ngas}}$

Where,

${\text{K}}_{\text{p}}$ is the equilibrium constant in terms of partial pressure

${\text{K}}_{\text{c}}$ is the equilibrium constant in terms of concentration

$\Delta \text{ngas = moles of gaseous product - moles of gaseous reactant}$

Only moles of gaseous products and reactants is used to calculate $\Delta \text{ngas}$

Ideal gas equation:

The ideal gas equation is given by,

  $\text{P}\text{V}\text{=}\text{n}\text{R}\text{T}$

Where,

  $\text{P}$ is the pressure,

  $\text{V}$ is the volume,

  $\text{T}$ is the temperature,

  $\text{R}$ is molar gas constant,

  $n$ is the number of moles.