Question

When a reaction is carried out in a closed vessel:
(A) $q_p < q_v$
(B) $q_p > q_v$
(C) $q_p = q_v$
(D) $q_v = 0$

Answer 1

Hint: $q_p$ denotes the heat of a system at constant pressure, while $q_v$ denotes the heat of a system at constant volume. When a reaction is carried out in a closed vessel, there is no increase or decrease in the volume of the gaseous reactants placed inside it. It means that there is no change in the volume of the system when a reaction is carried out in a closed vessel.

Complete step by step answer:
The relation between $q_p$ and $q_v$ is given by the formula:
$q_p = q_v + P\Delta V$ …$(i)$
Where $P$ is the pressure of the system;
$\Delta V$ is the change in volume of the system.
Since it has been mentioned in the question that the reaction takes place in a closed vessel, it means that the change in volume of the system is zero as there is no exchange of particles with the surroundings, and no particle escapes the system. Hence, $\Delta V$, in this case, is $0$.
Putting the value of $\Delta V$ as $0$ in equation $(i)$, we get;
$q_p = q_v + P\times 0$
Or, $q_p = q_v + 0$
Or, $q_p = q_v$
Therefore, it can be concluded that when a reaction is carried out in a closed vessel, $q_p = q_v$.

So, the correct answer is Option C .

Note: $q_p$ is also called the change in enthalpy of a system, denoted as $\Delta H$. Change in enthalpy of a system is defined as the total heat change taking place during a reaction in a vessel at a constant pressure. $q_v$ is also called the change in internal energy of a system, denoted as $\Delta E$. Energy change during a reaction is defined as the total heat change occurring in a vessel at a constant volume.