Chapter 17, Problem 17.89P

(a)

Interpretation Introduction

Interpretation:

The oxidation of ${\text{SO}}_{\text{2}}$ in the manufacture of sulfuric acid determines that ${\text{K}}_{\text{c}}\text{ = 1}{\text{.7×18}}^{\text{8}}\text{ at 600}\text{.K}$:

  ${\text{2SO}}_{\text{2(g)}}{\text{+ O}}_{\text{2(g)}}\rightleftharpoons {\text{2SO}}_{\text{3(g)}}$

At equilibrium, ${\text{P}}_{{\text{SO}}_{\text{3}}}\text{= 300}{\text{.atm and P}}_{{\text{O}}_{\text{2}}}\text{= 100}\text{.atm}$.  ${\text{P}}_{{\text{SO}}_{\text{2}}}$ has to be calculated.

Concept Introduction:

Equilibrium constant using partial pressure:

The equilibrium constant of partial pressure can be defined as the ratio of products and reactants concentration at equilibrium in terms of partial pressure.

For a reaction,

  ${\text{aA}}_{\text{(g)}}{\text{+ bB}}_{\text{(g)}}\rightleftharpoons {\text{cC}}_{\text{(g)}}{\text{+ dD}}_{\text{(g)}}$

The expression of ${\text{K}}_{\text{p}}$ can be given as

  ${\text{K}}_{\text{p}}\text{ = }\frac{{{\text{(P}}_{\text{C}}\text{)}}^{\text{c}}{{\text{(P}}_{\text{D}}\text{)}}^{\text{d}}}{{{\text{(P}}_{\text{A}}\text{)}}^{\text{a}}{{\text{(P}}_{\text{B}}\text{)}}^{\text{b}}}$

(b)

Interpretation Introduction

Interpretation:

An engineer places a mixture of $\text{0}{\text{.0040 mol of SO}}_{\text{2(g)}}$ and $\text{0}{\text{.0028 mol of O}}_{\text{2(g)}}$ in a $\text{1}\text{.0-L}$ container and raises the temperature to $\text{1000 K}$.  At equilibrium, $\text{0}{\text{.0020 mol of SO}}_{\text{3(g)}}$ is present.  For this reaction, at $\text{1000 K}$, ${\text{K}}_{\text{c}}{\text{ and P}}_{{\text{SO}}_{\text{2}}}$ has to be calculated.

Concept Introduction:

Equilibrium constant:

The relationship between the concentration of products and concentration of reactants in a chemical reaction at equilibrium is said to be equilibrium constant.  It is denoted by $\text{K}$.

For a reaction,

  $\text{xX + yY }\rightleftharpoons \text{ zZ}$

The expression of $\text{K}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{c}}\text{ = }\frac{{\text{[Z]}}^{\text{z}}}{{\text{[X]}}^{\text{x}}{\text{[Y]}}^{\text{y}}}\\ \\ \text{where,}\text{[X] = equilibrium concentration of X}\\ \\ \text{[Y] = equilibrium concentration of Y}\\ \\ \text{[Z] = equilibrium concentration of Z}\end{array}$

Pressure can be calculated using ideal gas equation.

  $\begin{array}{l}\text{PV =nRT}\\ \\ \text{P =}\frac{\text{nRT}}{\text{V}}\\ \\ \text{where,}\text{P = Pressure}\\ \\ \text{V = Volume}\\ \\ \text{R = universal gas constant}\\ \\ \text{T = temperature}\\ \\ \text{n = number of moles}\end{array}$