Question

Question : Given the following data:

$$\begin{gathered} {\mathbf{P}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{6}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}\stackrel{}{\mathbf{\to }}\mathbf{}\mathbf{4}{\mathbf{PCl}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{1225}\mathbf{.}\mathbf{6}\mathbf{}\mathbf{kJ} \\ {\mathbf{P}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{5}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\stackrel{}{\mathbf{\to }}\mathbf{}\mathbf{}{\mathbf{P}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{10}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{2967}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{kJ} \\ {\mathbf{PCl}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\stackrel{}{\mathbf{\to }}\mathbf{}\mathbf{}{\mathbf{PCl}}_{\mathbf{5}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{84}\mathbf{.}\mathbf{2}\mathbf{}\mathbf{kJ} \\ {\mathbf{PCl}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\stackrel{}{\mathbf{\to }}\mathbf{}{\mathbf{Cl}}_{\mathbf{3}}\mathbf{PO}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{∆}\mathbf{H}\mathbf{=}\mathbf{-}\mathbf{285}\mathbf{.}\mathbf{7}\mathbf{}\mathbf{kJ} \\ \mathbf{Calculate}\mathbf{}\mathbf{H}\mathbf{}\mathbf{for}\mathbf{}\mathbf{the}\mathbf{}\mathbf{reaction} \\ {\mathbf{P}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{10}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{6}{\mathbf{PCl}}_{\mathbf{5}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{}\stackrel{}{\mathbf{\to }}\mathbf{}\mathbf{}\mathbf{10}{\mathbf{Cl}}_{\mathbf{3}}\mathbf{PO}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \end{gathered}$$

Short answer

∆H for the reaction = 610.1 kJ

Step-by-step solution

Numbering of equations

$$\begin{gathered} {\mathrm{P}}_4\left(\mathrm{s}\right)+6{\mathrm{Cl}}_2\left(\mathrm{g}\right)\stackrel{}{\to }4{\mathrm{PCl}}_3\left(\mathrm{g}\right).eq.1∆\mathrm{H}=-1225.6\mathrm{kJ} \\ {\mathrm{P}}_4\left(\mathrm{s}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{}{\to }{\mathrm{P}}_4{\mathrm{O}}_{10}\left(\mathrm{s}\right).eq.2∆\mathrm{H}=-2967.3\mathrm{kJ} \\ {\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\stackrel{}{\to }{\mathrm{PCl}}_5\left(\mathrm{g}\right).eq.3∆\mathrm{H}=-84.2\mathrm{kJ} \\ {\mathrm{PCl}}_3\left(\mathrm{g}\right)+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{}{\to }{\mathrm{Cl}}_3\mathrm{PO}\left(\mathrm{g}\right).eq.4∆\mathrm{H}=-285.7\mathrm{kJ} \end{gathered}$$

Reverse equation 2

${\mathrm{P}}_4{\mathrm{O}}_{10}\left(\mathrm{s}\right)\stackrel{}{\to }{\mathrm{P}}_4\left(\mathrm{s}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)∆\mathrm{H}=-2967.3\mathrm{kJ}$

Reverse equation 3 and multiply by 6

$6{\mathrm{PCl}}_5\left(\mathrm{g}\right)\stackrel{}{\to }6{\mathrm{PCl}}_3\left(\mathrm{g}\right)+6{\mathrm{Cl}}_2\left(\mathrm{g}\right)∆\mathrm{H}=-84.2\mathrm{kJ}$

Multiply equation 4 by 10

$10{\mathrm{PCl}}_3\left(\mathrm{g}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{}{\to }10{\mathrm{Cl}}_3\mathrm{PO}\left(\mathrm{g}\right)∆\mathrm{H}=-285.7\mathrm{kJ}$

Calculation of ∆H by Hess Law

$$\begin{gathered} {\mathrm{P}}_4\left(\mathrm{s}\right)+6{\mathrm{Cl}}_2\left(\mathrm{g}\right)\stackrel{}{\to }4{\mathrm{PCl}}_3\left(\mathrm{g}\right)∆\mathrm{H}=-1225.6\mathrm{kJ} \\ {\mathrm{P}}_4{\mathrm{O}}_{10}\left(\mathrm{s}\right)\stackrel{}{\to }{\mathrm{P}}_4\left(\mathrm{s}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)∆\mathrm{H}=-2967.3\mathrm{kJ} \\ 6{\mathrm{PCl}}_5\left(\mathrm{g}\right)\stackrel{}{\to }6{\mathrm{PCl}}_3\left(\mathrm{g}\right)+6{\mathrm{Cl}}_2\left(\mathrm{g}\right)∆\mathrm{H}=-84.2\mathrm{kJ} \\ 10{\mathrm{PCl}}_3\left(\mathrm{g}\right)+5{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{}{\to }10{\mathrm{Cl}}_3\mathrm{PO}\left(\mathrm{g}\right)∆\mathrm{H}=-285.7\mathrm{kJ} \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ {\mathrm{P}}_4{\mathrm{O}}_{10}\left(\mathrm{s}\right)+6{\mathrm{PCl}}_5\left(\mathrm{g}\right)\stackrel{}{\to }10{\mathrm{Cl}}_3\mathrm{PO}\left(\mathrm{g}\right)∆H=-610.1kJ \end{gathered}$$