Chapter 15, Problem 109A

Apply Phosphorus trichloride is a starting material for the preparation of organic phosphorous compounds.Demonstrate how thermochemical equations a and b can be used to determine the enthalpy change for the reaction $PC{l}_3\left(l\right)+C{l}_2\left(g\right)\to PC{l}_5\left(s\right)$ .

a. $P_4\left(s\right)+6C{l}_2\left(g\right)\to 4PC{l}_3\left(l\right)\Delta H=-1280kJ$

b. $P_4\left(s\right)+10C{l}_2\left(g\right)\to 4PC{l}_5\left(s\right)\Delta H=-1774kJ$

Interpretation Introduction

Interpretation:

Enthalpy change, ${\text{ΔH}}_{\text{rxn}}^{\circ }$ , for the reaction ${\text{PCL}}_{\text{3}}\text{(l)}+{\text{Cl}}_{\text{2}}\text{(g)}\to {\text{PCl}}_{\text{3}}\text{(s)}$ is to be calculated.

Concept introduction:

A thermochemical equation is a balanced chemical equation that includes the physical states of all reactants and products and the energy change, usually expressed as the change in enthalpy, $\text{ΔH}$

Answer to Problem 109A

Enthalpy change, ${\text{ΔH}}^{\circ }=\text{-494kJ}$

Explanation of Solution

Given information,

$\begin{array}{l}\text{a}\text{.}{\text{P}}_{\text{4}}{\text{(s)+6Cl}}_{\text{2}}(g)\to {\text{4PCl}}_{\text{3}}\text{(l)}\text{and}\text{ΔH}=-\text{1280kJ}\\ \text{b}\text{.}{\text{P}}_{\text{4}}{\text{(s)+10Cl}}_{\text{2}}(g)\to {\text{4PCl}}_{\text{5}}\text{(s)and}\text{ΔH}=-\text{1774kJ}\end{array}$

From equation a and equation b,

${\text{PCl}}_{\text{3}}{\text{(l)+Cl}}_{\text{2}}\text{(g)}\to {\text{PCl}}_{\text{5}}\text{(s)}$

Since, equation for enthalpy change ${\text{ΔH}}_{\text{rxn}}^{\circ }$ is

$\begin{array}{l}{\text{ΔH}}_{\text{rxn}}^{\circ }={\displaystyle \sum {\text{ΔH}}_{\text{product}}^{\text{o}}}-{\displaystyle \sum {\text{ΔH}}_{\text{reactant}}^{\circ }}\\ {\text{ΔH}}_{\text{rxn}}^{\circ }=\text{(-1774)}-\text{(-1280)}\\ {\text{ΔH}}_{\text{rxn}}^{\circ }=-\text{494kJ}\end{array}$

Conclusion

${\text{ΔH}}_{\text{rxn}}^{\circ }$ is obtained by subtracting the sum of heats of formation of the reactants from the sum of the heats of formation of the products.