Chapter 10.3, Problem 4RQ

Interpretation Introduction

Interpretation: The $\Delta H$ for following reaction needs to be calculated.

  $2{\text{N}}_{\text{2}}(g)+6{\text{H}}_{\text{2}}\text{O}\text{(}l\text{)}\to {\text{3O}}_2(g)+4{\text{NH}}_{\text{3}}(g)$

Concept introduction: Hess's law states that the enthalpy change in moving from a set of reactants to a set of products does not depend on the number of steps in the reaction. So,the enthalpy change for the net reaction can be calculated if the enthalpy change of all the steps is known.

Answer to Problem 4RQ

$\Delta H$ for the reaction is $\text{1268}\text{kJ}$ .

Explanation of Solution

The chemical equation for which $\Delta H$ needs to be calculated is,

  $2{\text{N}}_{\text{2}}(g)+6{\text{H}}_{\text{2}}\text{O}\text{(}l\text{)}\to {\text{3O}}_2(g)+4{\text{NH}}_{\text{3}}(g)$

The given reactions are,

  ${\text{2NH}}_{\text{3}}(g)\to {\text{N}}_{\text{2}}(g)+3{\text{H}}_{\text{2}}(g)\Delta H=92\text{kJ}$ …… (1)

  ${\text{2H}}_2(g)+{\text{O}}_{\text{2}}(g)\to 2{\text{H}}_{\text{2}}\text{O}\text{(}g\text{)}\Delta H=-484\text{kJ}$ ……(2)

Reverse both the equation. This changes the sign of enthalpy. And multiply equation (1) by 2 and equation (2) by 3.

  $2{\text{N}}_{\text{2}}(g)+6{\text{H}}_{\text{2}}(g)\to {\text{4NH}}_{\text{3}}(g)\Delta H=-92\times 2\text{kJ=}-\text{184}\text{kJ}$ …… (3)

  $6{\text{H}}_{\text{2}}\text{O}\text{(}g\text{)}\to {\text{6H}}_2(g)+3{\text{O}}_{\text{2}}(g)\Delta H=484\times 3\text{kJ=1452}\text{kJ}$ …… (4)

Now add equation (3) and (4).

  $\begin{array}{l}2{\text{N}}_{\text{2}}(g)+\cancel{6{\text{H}}_{\text{2}}(g)}+6{\text{H}}_{\text{2}}\text{O(}g\text{)}\to {\text{4NH}}_{\text{3}}(g)+\cancel{{\text{6H}}_2(g)}+3{\text{O}}_{\text{2}}(g)\end{array}$

                      $\begin{array}{l}\left[\Delta H=-\text{184 kJ}\text{+1452 kJ}\right]\end{array}$

  $\begin{array}{l}2{\text{N}}_{\text{2}}(g)+6{\text{H}}_{\text{2}}\text{O(}g\text{) }\to {\text{4NH}}_{\text{3}}(g)+3{\text{O}}_{\text{2}}(g)\left[\Delta H=\text{1268}\text{kJ}\right]\end{array}$

Conclusion

By Hess’s law, the enthalpy change for a reaction can be calculated.