Question

Assume that each reaction is carried out in an open container. Select a reaction for which $\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\,$.
A. ${{\text{H}}_{\text{2}}}\left( {\text{g}} \right)\, + {\text{B}}{{\text{r}}_{\text{2}}}\left( {\text{g}} \right) \to \,2\,{\text{HBr}}\,\left( {\text{g}} \right)$
B. ${\text{C}}\left( {\text{s}} \right)\, + 2\,{{\text{H}}_{\text{2}}}{\text{O}}\left( {\text{g}} \right) \to \,2\,{{\text{H}}_2}\left( {\text{g}} \right) + \,{\text{C}}{{\text{O}}_{\text{2}}}\left( {\text{g}} \right)$
C. ${\text{PC}}{{\text{l}}_5}\left( {\text{g}} \right)\, \to \,{\text{PC}}{{\text{l}}_{\text{3}}}\,\left( {\text{g}} \right) + {\text{C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right)$
D. ${\text{2}}\,{\text{CO}}\left( {\text{g}} \right)\, + {{\text{O}}_{\text{2}}}\left( {\text{g}} \right) \to \,2{\text{C}}{{\text{O}}_2}\left( {\text{g}} \right)$

Answer 1

Hint: We will use the relation of $\Delta {\text{H}}$ and $\Delta {\text{E}}$ with the number of moles. When a chemical reaction takes place in an open container, the number of moles of the species changes. The number of moles of gaseous species affects the $\Delta {\text{H}}$ and $\Delta {\text{E}}$.

Formula used: \[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - \Delta {{\text{n}}_g}{\text{RT}}\]

Complete step by step answer:
The relation between $\Delta {\text{H}}$ and $\Delta {\text{E}}$ is as follows:
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - \Delta {{\text{n}}_g}{\text{RT}}\]
Where,
$\Delta {\text{H}}$ is the change in enthalpy.
$\Delta {\text{E}}$ is the change in internal energy.
\[\Delta {{\text{n}}_g}\] is the change in the number of moles of gaseous species.
\[{\text{R}}\] is the gas constant.
\[{\text{T}}\] is temperature.
The change in the number of moles of gaseous species \[\Delta {{\text{n}}_g}\] is calculated as follows:
\[\Delta {{\text{n}}_g} = \,\sum {n_p} - \sum {n_R}\]
Where,
\[\sum {n_p}\] is the sum of the number of moles of all gaseous species present on the product side.
\[\sum {n_R}\] is the sum of the number of moles of all gaseous species present on the reactant side.
Determine the \[\Delta {{\text{n}}_g}\] for each reaction as follows:
For-${{\text{H}}_{\text{2}}}\left( {\text{g}} \right)\, + {\text{B}}{{\text{r}}_{\text{2}}}\left( {\text{g}} \right) \to \,2\,{\text{HBr}}\,\left( {\text{g}} \right)$
$\Delta {{\text{n}}_g} = \,2 - 2$
$\Delta {{\text{n}}_g} = 0$
So, on substituting $\Delta {{\text{n}}_g} = 0$ in $\Delta {\text{H}}$ and $\Delta {\text{E}}$ relation we get,
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - 0\, \times {\text{RT}}\]
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\]
So, for ${{\text{H}}_{\text{2}}}\left( {\text{g}} \right)\, + {\text{B}}{{\text{r}}_{\text{2}}}\left( {\text{g}} \right) \to \,2\,{\text{HBr}}\,\left( {\text{g}} \right)$ reaction,$\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\,$. So, option (A) is correct.
For-${\text{C}}\left( {\text{s}} \right)\, + 2\,{{\text{H}}_{\text{2}}}{\text{O}}\left( {\text{g}} \right) \to \,2\,{{\text{H}}_2}\left( {\text{g}} \right) + \,{\text{C}}{{\text{O}}_{\text{2}}}\left( {\text{g}} \right)$
$\Delta {{\text{n}}_g} = \,3 - 2$
$\Delta {{\text{n}}_g} = 1$
So, on substituting $\Delta {{\text{n}}_g} = 1$ in $\Delta {\text{H}}$ and $\Delta {\text{E}}$ relation we get,
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - 1 \times {\text{RT}}\]
\[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]
So, for ${\text{C}}\left( {\text{s}} \right)\, + 2\,{{\text{H}}_{\text{2}}}{\text{O}}\left( {\text{g}} \right) \to \,2\,{{\text{H}}_2}\left( {\text{g}} \right) + \,{\text{C}}{{\text{O}}_{\text{2}}}\left( {\text{g}} \right)$ reaction, \[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]. So, option (B) is incorrect.
For-${\text{PC}}{{\text{l}}_5}\left( {\text{g}} \right)\, \to \,{\text{PC}}{{\text{l}}_{\text{3}}}\,\left( {\text{g}} \right) + {\text{C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right)$
$\Delta {{\text{n}}_g} = \,2 - 1$
$\Delta {{\text{n}}_g} = 1$
So, on substituting $\Delta {{\text{n}}_g} = 1$ in $\Delta {\text{H}}$ and $\Delta {\text{E}}$ relation we get,
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - 1 \times {\text{RT}}\]
\[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]
So, for ${\text{PC}}{{\text{l}}_5}\left( {\text{g}} \right)\, \to \,{\text{PC}}{{\text{l}}_{\text{3}}}\,\left( {\text{g}} \right) + {\text{C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right)$ reaction, \[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]. So, option (C) is incorrect.
For-${\text{2}}\,{\text{CO}}\left( {\text{g}} \right)\, + {{\text{O}}_{\text{2}}}\left( {\text{g}} \right) \to \,2{\text{C}}{{\text{O}}_2}\left( {\text{g}} \right)$
$\Delta {{\text{n}}_g} = \,2 - 3$
$\Delta {{\text{n}}_g} = - 1$
So, on substituting $\Delta {{\text{n}}_g} = - 1$ in $\Delta {\text{H}}$ and $\Delta {\text{E}}$ relation we get,
\[\Delta {\text{H}}\,{\text{ = }}\,\Delta {\text{E}}\, - \left( { - 1 \times {\text{RT}}} \right)\]
\[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]
So, for ${\text{2}}\,{\text{CO}}\left( {\text{g}} \right)\, + {{\text{O}}_{\text{2}}}\left( {\text{g}} \right) \to \,2{\text{C}}{{\text{O}}_2}\left( {\text{g}} \right)$ reaction, \[\Delta {\text{H}}\, \ne \,\Delta {\text{E}}\]. So, option (D) is incorrect.

Therefore, option (A) ${{\text{H}}_{\text{2}}}\left( {\text{g}} \right)\, + {\text{B}}{{\text{r}}_{\text{2}}}\left( {\text{g}} \right) \to \,2\,{\text{HBr}}\,\left( {\text{g}} \right)$, is correct.

Note: The change in the number of the mole is calculated only for gaseous species A chemical reaction for which\[\sum {n_p} > \sum {n_R}\]the relation between $\Delta {\text{H}}$and$\Delta {\text{E}}$is \[\Delta {\text{H}}\,\, < \Delta {\text{E}}\]. A chemical reaction for which\[\sum {n_p} < \sum {n_R}\]the relation between $\Delta {\text{H}}$and$\Delta {\text{E}}$is \[\Delta {\text{H}}\,\, > \Delta {\text{E}}\].