A gaseous reaction was carried out first keeping the volume constant and next keeping the pressure constant. In the second experiment, there was an increase in volume. The heats of reactions were different because

In the second case, the energy was spent to expand the gases.

The  correct answer is option 2. In the second case, the energy was spent to expand the gases.

The correct explanation for why the heats of reactions were different when the gaseous reaction was carried out first keeping the volume constant and next keeping the pressure constant, resulting in an increase in volume in the second case, is in the second case, the energy was spent to expand the gases.

Here is the detailed explanation:

Volume Constant Experiment (Isochoric Process):

When the gaseous reaction is carried out at constant volume (isochoric process), the volume of the gas remains unchanged. The heat transferred in this case, \(q_V\), is related to the change in internal energy (\(\Delta U\)) of the system because there is no work done by the gas against external pressure (\(W = 0\)). The change in internal energy (\(\Delta U\)) for the reaction can directly contribute to the heat of reaction at constant volume.

Pressure Constant Experiment (Isobaric Process):

When the gaseous reaction is carried out at constant pressure (isobaric process), the volume of the gas may change if the reaction produces gases that occupy more volume than the reactants. In this case, the heat transferred, \(q_P\), is related to both the change in internal energy (\(\Delta U\)) and the work done by the gas against constant external pressure (\(W = -P \Delta V\)). If the reaction results in an increase in volume (\(\Delta V > 0\)), the gas expands against the constant pressure, requiring energy to perform work (\(W\)). Therefore, in the second case (keeping pressure constant), additional energy \(q_P\) is spent to expand the gases, which contributes to the total heat of reaction at constant pressure.

Specific Heats:

Specific heats of gases (like molar heat capacities at constant volume \(C_V\) and constant pressure \(C_P\)) are properties that relate to how much heat is required to change the temperature of a substance. The specific heats of gases being more or less do not directly explain why the heats of reactions were different between the two experiments.

Conclusion:

The difference in heats of reactions between the two experiments (constant volume and constant pressure) primarily arises because in the second case (constant pressure with increase in volume), energy \(q_P\) is spent to expand the gases against the external pressure. This additional energy expenditure (work done by the gas) increases the total heat transferred (\(q_P\)) compared to the heat transferred at constant volume (\(q_V\)), where no work is done. Therefore, the correct explanation for why the heats of reactions were different in the two experiments is option (2): In the second case (constant pressure), the energy was spent to expand the gases, leading to a different heat of reaction compared to the case where volume was kept constant.