Chapter 10, Problem 65A

Interpretation Introduction

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

  

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, enthalpy change for the net reaction can be calculated if the enthalpy change of all the steps is known.

Answer to Problem 65A

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

Explanation of Solution

The given diagram is as follows:

  

The dark blue coloured ball represents nitrogen atoms, light blue coloured ball represents hydrogen atoms and red colored ball represents oxygen atoms. So, the for which $\Delta H$ needs to be calculated is,

  $2{\text{N}}_{\text{2}}+6{\text{H}}_{\text{2}}\text{O}\to 3{\text{O}}_{\text{2}}+4{\text{NH}}_{\text{3}}$...........(1)

The given diagrams are as follows:

  

The chemical equation for the above reaction is as follows:

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

Second reaction is as follows:

  

The chemical equation for the above reaction is as follows:

  $2{\text{H}}_{\text{2}}\left(g\right)+{\text{O}}_{\text{2}}\left(g\right)\to 2{\text{H}}_{\text{2}}\text{O}\left(g\right)\Delta H=-484\text{kJ}$...........(3)

To get equation (1), reverse both equation (2) and (3) and multiply equation (2) by 2 and equation (3) by 3.

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

  ${\text{6H}}_{\text{2}}\text{O}\left(g\right)\to 6{\text{H}}_{\text{2}}\left(g\right)+3{\text{O}}_{\text{2}}\left(g\right)\Delta H=3\times 484\text{kJ}=1452\text{kJ}$...........(5)

Now add equation (4) and (5).

  $\begin{array}{c}{\text{2N}}_{\text{2}}\left(g\right)+\cancel{6{\text{H}}_{\text{2}}}\left(g\right)+{\text{6H}}_{\text{2}}\text{O}\left(g\right)\to 4{\text{NH}}_{\text{3}}+\cancel{6{\text{H}}_{\text{2}}}\left(g\right)+3{\text{O}}_{\text{2}}\left(g\right)\Delta H=-184\text{kJ}+1452\text{kJ}\\ {\text{2N}}_{\text{2}}\left(g\right)++{\text{6H}}_{\text{2}}\text{O}\left(g\right)\to 4{\text{NH}}_{\text{3}}+3{\text{O}}_{\text{2}}\left(g\right)\Delta H=1268\text{kJ}\end{array}$

Conclusion

Hess’s law enables the calculation of heat for a given reaction from known heat of related reactions.