Chapter 17, Problem 41A

Interpretation Introduction

Interpretation: The concentration of ozone in the system has to be calculated.

Concept introduction: For a balanced chemical reaction,

  $aA+bB\rightleftharpoons cC+dD$

The equilibrium expression is ratio of the concentration of the products to the concentration of the reactants. The concentration of each reactant/product is raised to a power corresponding to their coefficient in the balanced equation.

The law of chemical equilibrium is given by the equilibrium expression,

  $K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

The equilibrium constant is represented as $K.$

Answer to Problem 41A

The concentration of ozone in the system is $\text{1}{\text{.8×10}}^{\text{-8}}\text{M}\text{.}$

Explanation of Solution

The given chemical reaction is,

  $3O_2\left(g\right)\rightleftharpoons 2O_3\left(g\right)$

Given data,

The equilibrium concentration of $\left[O_2\right]$ is $\text{0}\text{.0012}\text{M}\text{.}$

The equilibrium constant is $\text{1}{\text{.8×10}}^{\text{-7}}\text{.}$

For a balanced chemical reaction,

  $aA+bB\rightleftharpoons cC+dD$

Where,

• $A,B,C,D$ are chemical species.
• $a,b,c$ and $d$ are coefficients in the balanced equation.

The equilibrium expression is given as,

  $K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Where,

  $K$ is the value of equilibrium constant.

For the given reaction, the expression for equilibrium constant is written as,

  $K=\frac{{\left[O_3\right]}^2}{{\left[O_2\right]}^3}$

Rearrange the above expression to calculate the concentration of ozone.

  $\begin{array}{l}{\left[O_3\right]}^2=K\times {\left[O_2\right]}^3\\ \left[O_3\right]=\sqrt{K\times {\left[O_2\right]}^3}\end{array}$

Substitute the values of equilibrium concentration of oxygen and equilibrium constant in the above expression,

  $\begin{array}{l}\left[O_3\right]=\sqrt{\left(\text{1}{\text{.8×10}}^{\text{-7}}\right){\left(\text{0}\text{.0012}\right)}^{\text{3}}}\\ \left[O_3\right]=\sqrt{\left(\text{1}{\text{.8×10}}^{\text{-7}}\right)\left(\text{1}{\text{.728×10}}^{\text{-9}}\right)}\\ \left[O_3\right]=\sqrt{\text{3}{\text{.1104×10}}^{\text{-16}}}\\ \left[O_3\right]=\text{1}{\text{.76×10}}^{\text{-8}}\\ \left[O_3\right]=\text{1}{\text{.8×10}}^{\text{-8}}\end{array}$

The concentration of ozone in the system is $\text{1}{\text{.8×10}}^{\text{-8}}\text{M}\text{.}$

Conclusion

The concentration of ozone in the system is $\text{1}{\text{.8×10}}^{\text{-8}}\text{M}\text{.}$