Chapter 12, Problem 122QRT

(a)

Interpretation Introduction

Interpretation:

The value of ${\text{K}}_{\text{p}}$ and ${\text{K}}_{\text{C}}$ has to be calculated for water at ${\text{25}}^{\text{o}}\text{C}$ and the vapor pressure of water is $\text{0}\text{.03126}\text{atm}$.

  ${\text{H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\stackrel{}{\rightleftharpoons }{\text{H}}_{\text{2}}{\text{O}}_{\left(\text{g}\right)}$

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.

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 value of ${\text{K}}_{\text{p}}$ has to be calculated for water at ${\text{100}}^{\text{o}}\text{C}$ and the vapor pressure of water is $\text{0}\text{.03126}\text{atm}$.

  ${\text{H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\stackrel{}{\rightleftharpoons }{\text{H}}_{\text{2}}{\text{O}}_{\left(\text{g}\right)}$

Concept Introduction:

Refer part (a)

(c)

Interpretation Introduction

Interpretation:

A general rule for calculating the value of ${\text{K}}_{\text{p}}$ for any liquid in equilibrium with its vapor at its normal boiling point has to be suggested.

Concept Introduction:

Refer part (a)