Question

for which of the following reactions, \[\Delta H{\text{ }} = {\text{ }}\Delta U\]
A.$2$$HI$$(g)$ $ = $ ${H_2}$$(g)$$ + $ ${I_2}$$(g)$
B.\[\;2S{O_2}{\text{ }} + {\text{ }}{{\text{O}}_2}{\text{ }} = {\text{ }}2S{O_3}\left( g \right)\]
C.\[{N_2}{\text{ }} + {\text{ }}3{H_2}{\text{ }} = {\text{ }}2N{H_3}\]
D.\[2N{O_2} = {\text{ }}{{\text{N}}_2}{O_2}\]

Answer 1

Hint: Enthalpy as it is known, is the measure of energy in an observed thermodynamic system. Basically it is the total heat present in a system equalising to the system’s internal energy and the product of volume present and the pressure.

Complete step by step solution
We know that,
 \[\Delta H{\text{ }} = {\text{ }}\Delta U{\text{ }} + {\text{ }}\Delta n{\text{ }}RT\]
Where we know that $\Delta H$ is enthalpy change
$\Delta U$ is internal energy
And $\Delta n$ is the change is the moles of the product
$R$ is gas constant and $T$ is temperature
Now, to solve the above question -
$2$$HI$$(g)$ $ = $ ${H_2}$$(g)$$ + $ ${I_2}$$(g)$ where it must be$\Delta H$$ = $ $\Delta Q$ (as said by the question to prove)
Now when the equation \[\Delta H\]$ = $ \[\Delta U\] $ + $ \[\Delta n\]$R$$T$ is applied
In this chemical reaction from the options
$2$$HI$$(g)$ $ = $ ${H_2}$$(g)$$ + $ ${I_2}$$(g)$ we will get,
$\Delta n$ $ = $ $1$$ + $ $1$ $ - $ $2$
therefore ,
\[\Delta H{\text{ }} = {\text{ }}\Delta U{\text{ }} + {\text{ }}0{\text{ }}RT\]
Hence, we conclude that -
\[\Delta H{\text{ }} = {\text{ }}\Delta U{\text{ }}\;{\text{ }}\;\]as the change in the number of moles is $0$ , for as \[0 \times RT{\text{ }} = {\text{ }}0\]
Therefore we can see,
$2$$HI$$(g)$ $ = $${H_2}$$(g)$$ + $ ${I_2}$$(g)$ is the correct choice for the mentioned question.

So, the correct answer is option A.

Notes: We know, the enthalpy change depends on the following factors such as -
The temperature of the system taken into consideration
Concentrations of the reactants taken and the products formed
And the change in the number of moles of gases i.e. if any present.
And an important thing to take into notice is that in the equation
\[\Delta H\]$ = $\[\Delta U\] $ + $\[\Delta n{\text{ }}RT\], the internal energy i.e. \[\Delta U\] , does not mean the whole energy of the system but only the kinetic energy and the potential energy in association with the random movement made the molecules present of the object or reactants. For an increase in the heat of the object, the internal energy of the system will increase and for a decrease in the heat of the object, the internal energy of the system will decrease.