Chapter 14, Problem 14.59QE

Interpretation Introduction

Interpretation:

The concentration of all species after the attainment of equilibrium in the following reaction has to be determined.

  ${\text{2SO}}_3\left(\text{g}\right)\rightleftharpoons {\text{2SO}}_2\left(\text{g}\right)+{\text{O}}_{\text{2}}\left(\text{g}\right)$

Concept Introduction:

The condition of equilibrium is a state of balance of processes that runs in opposite directions. At equilibrium, the formation of product from reactant balanced the formation of reactant from product. Also, the change in concentration of reaction and product seems to be negligible at equilibrium state.

The general equilibrium reaction is as follows:

  $a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

Here,

$\text{A}$ and $\text{B}$ are the reactants.

$\text{C}$ and $\text{D}$ are products.

$a$ and $b$ are the stoichiometric coefficients of reactants.

$c$ and $d$ are the stoichiometric coefficients of products.

The relation of equilibrium constant $K_{\text{p}}$ and $K_{\text{c}}$ is as follows:

  $K_{\text{p}}=K_{\text{c}}{\left(RT\right)}^{\Delta n}$        (1)

Here, $\Delta n$ is change in number of moles of gas.

The formula to calculate the value of $\Delta n$ is as follows:

  $\Delta n=\left(\begin{array}{l}\text{total number of moles of}\\ \text{gas on the product side}\end{array}\right)-\left(\begin{array}{l}\text{total number of moles of}\\ \text{gas on the reactant side}\end{array}\right)$        (2)

The value of $\Delta n$ can be zero, negative and positive.

The expression of the equilibrium constant for the above reaction is as follows:

  $K_{\text{c}}=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$        (3)

Here,

$K_{\text{c}}$ is the equilibrium constant.

$\left[\text{C}\right]$ is the concentration of $\text{C}$.

$\left[\text{D}\right]$ is the concentration of $\text{D}$.

$\left[\text{A}\right]$ is the concentration of $\text{A}$.

$\left[\text{B}\right]$ is the concentration of $\text{B}$.