Chapter 10.6, Problem 9PPB

Interpretation Introduction

Interpretation:

The standard enthalpy of reaction has to be calculated and the missing products have to be identified.

Concept Introduction:

Standard enthalpy of reaction:

The change in enthalpy that is associated with the formation of one mole of a substance from its related elements being in standard state is called standard enthalpy of formation (${\text{ΔH}}_{\text{f}}\text{°}$).  The standard enthalpy of formation is used to determine the standard enthalpies of compound and element.

The standard enthalpy of reaction is the enthalpy of reaction that takes place under standard conditions.

The equation for determining the standard enthalpies of compound and element can be given by,

${\text{ΔH°}}_{\text{reaction}}\text{=}{\displaystyle \sum {\text{nΔH°}}_{\text{f}}\text{(products)}}\text{-}{\displaystyle \sum {\text{mΔH°}}_{\text{f}}\text{(reactants)}}$

To calculate: The standard enthalpy of the reaction

Answer to Problem 9PPB

The enthalpy of change of the reaction is $\text{74}\text{.9 kJ}{\text{mol}}^{\text{-1}}$ .

Explanation of Solution

The thermochemical equation can be given as,

$\begin{array}{l}\frac{\text{1}}{\text{2}}{\text{H}}_{\text{2}}\text{+}\frac{\text{1}}{\text{2}}{\text{Cl}}_{\text{2}}\to \text{HCl}{\text{ΔH°}}_{\text{reaction}}=\text{-92}\text{.3}\text{kJ}{\text{mol}}^{\text{-1}}\\ \\ {\text{N}}_{\text{2(g)}}{\text{+4H}}_{\text{2(g)}}{\text{+Cl}}_{\text{2}}\to {\text{2NH}}_{\text{4}}{\text{Cl}}_{\left(\text{s}\right)}{\text{ΔH°}}_{\text{reaction}}\text{=-630}\text{.78}\text{kJ}{\text{mol}}^{\text{-1}}\mathrm{......}(1)\\ \\ {\text{N}}_{\text{2(g)}}{\text{+3H}}_{\text{2(g)}}\to {\text{2NH}}_{\text{3(g)}}{\text{ΔH°}}_{\text{reaction}}\text{=-296}\text{.4}\text{kJ}{\text{mol}}^{\text{-1}}\mathrm{......}(2)\end{array}$

The first equation is reversed and divided by two.

${\text{NH}}_{\text{4}}{\text{Cl}}_{\left(\text{s}\right)}\to \frac{\text{1}}{\text{2}}{\text{N}}_{\text{2(g)}}{\text{+2H}}_{\text{2(g)}}\text{+}\frac{\text{1}}{\text{2}}{\text{Cl}}_{\text{2}}{\text{ΔH°}}_{\text{reaction}}\text{=+315}\text{.39}\text{kJ}{\text{mol}}^{\text{-1}}$

The second equation remains the same.

${\text{N}}_{\text{2(g)}}{\text{+3H}}_{\text{2(g)}}\to {\text{2NH}}_{\text{3(g)}}{\text{ΔH°}}_{\text{reaction}}\text{=-296}\text{.4}\text{kJ}{\text{mol}}^{\text{-1}}$

The missing product can be identified using the reactions of 1 and 2

${\text{NH}}_{\text{4}}{\text{Cl}}_{\left(\text{s}\right)}\to \frac{\text{1}}{\text{2}}{\text{N}}_{\text{2(g)}}{\text{+2H}}_{\text{2(g)}}\text{+}\frac{\text{1}}{\text{2}}{\text{Cl}}_{\text{2}}{\text{ΔH°}}_{\text{reaction}}\text{=+315}\text{.39}\text{kJ}{\text{mol}}^{\text{-1}}$

The second equation is divided by two, to get one of the products

$\frac{1}{2}{\text{N}}_{\text{2(g)}}\text{+}\frac{3}{2}{\text{H}}_{\text{2(g)}}\to {\text{NH}}_{\text{3(g)}}{\text{ΔH°}}_{\text{reaction}}\text{=-148}\text{.2}\text{kJ}{\text{mol}}^{\text{-1}}$

Upon adding all the three equations,

$\begin{array}{l}\underset{\_}{\begin{array}{l}\frac{\text{1}}{\text{2}}{\text{H}}_{\text{2}}\text{+}\frac{\text{1}}{\text{2}}{\text{Cl}}_{\text{2}}\to \text{HCl}{\text{ΔH°}}_{\text{reaction}}=\text{-92}\text{.3}\text{kJ}{\text{mol}}^{\text{-1}}\\ \\ {\text{NH}}_{\text{4}}{\text{Cl}}_{\left(\text{s}\right)}\to \frac{\text{1}}{\text{2}}{\text{N}}_{\text{2(g)}}{\text{+2H}}_{\text{2(g)}}\text{+}\frac{\text{1}}{\text{2}}{\text{Cl}}_{\text{2}}{\text{ΔH°}}_{\text{reaction}}\text{=+315}\text{.39}\text{kJ}{\text{mol}}^{-1}\\ \\ \frac{1}{2}{\text{N}}_{\text{2(g)}}\text{+}\frac{3}{2}{\text{H}}_{\text{2(g)}}\to {\text{NH}}_{\text{3(g)}}{\text{ΔH°}}_{\text{reaction}}\text{=-148}\text{.2}\text{kJ}{\text{mol}}^{\text{-1}}\end{array}}\\ {\text{NH}}_{\text{4}}\text{Cl}\to {\text{NH}}_{\text{3}}\text{+HCl}{\text{ΔH°}}_{\text{reaction}}\text{=74}\text{.89}\text{kJ}{\text{mol}}^{\text{-1}}\end{array}$

Enthalpy of reaction is $\text{74}\text{.9 kJ}{\text{mol}}^{\text{-1}}$

Products were identified as Ammonia and Hydrogen chloride.

Conclusion

The enthalpy of the reaction and missing products were identified.