Question

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 becanse (1) In the first ease, the energy was spent to keep the volume constant. (2) In the second case, the energy was spent to expand the gases. (3) Specific heats of compressed gases are more. (4) Specific heats of rarefied gases are more.

Short answer

The difference in heats of reactions is because, in the second case, energy was spent to expand the gases. So, option (2) is correct.

Step-by-step solution

Understanding the Conditions

Recognize that there are two different conditions for the gaseous reaction:

Heat in Constant Volume Reaction

At constant volume, the work done is zero because the volume does not change.

Heat and Work in Constant Pressure Reaction

At constant pressure, there is an increase in volume and hence the gas does work against the external pressure.

Comparing Heats of Reaction

Compare the heats of reaction in both cases:

Conclusion

Therefore, the difference in heats of reactions is mainly because: In the second case,

Key concepts

Constant Volume

In a constant volume process, the volume of the gas does not change. Because of this, there is no work done by the gas. Work done by the gas can be expressed as \( W = P \Delta V \). Since \( \Delta V = 0 \) (no change in volume), \( W = 0 \). As a result, any heat added to the system changes only the internal energy of the gas. This is typically represented by the equation \( Q = \Delta U \), where \( Q \) is the heat added and \( \Delta U \) is the change in internal energy. This means the heat of reaction at constant volume is purely due to changes in internal energy.

Constant Pressure

When a reaction occurs at constant pressure, the system can expand or contract. This means there is a change in volume. In this case, the work done by the gas is not zero. The work done can be calculated using \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume. The heat added at constant pressure is split into changing the internal energy and doing work. The relationship is given by \( Q_P = \Delta U + W \), where \( Q_P \) is the heat at constant pressure. It is crucial to understand that the heat of reaction at constant pressure includes both the change in internal energy and the work done by the gas.

Heat of Reaction

The heat of reaction is the amount of heat absorbed or released during a chemical reaction. It is considered under different conditions: constant volume or constant pressure.
In a constant volume condition, the heat of reaction is totally converted into internal energy.
In a constant pressure condition, it includes both internal energy change and work done by the gas. This is why, in a constant pressure experiment, the observed heat of reaction may differ from that at constant volume.
The difference is primarily due to the work term \( P \Delta V \), as noted earlier. If a gas expands, some of the heat is used to do work on the surroundings, making the heat of reaction measured at constant pressure different from that at constant volume.

Work Done by Gas

In gaseous reactions, the work done by the gas is significant, especially under constant pressure. The work done by a gas during expansion or compression is given by the formula \( W = P \Delta V \).
At constant volume, \( \Delta V = 0 \) and thus \( W = 0 \), meaning no work is done.
Under constant pressure, if the gas expands, \( \Delta V > 0 \) and \( W = P \Delta V \) becomes a positive value. This signifies the gas does work on the surroundings. Conversely, if the gas contracts, \( \Delta V < 0 \) and \( W \) becomes negative, meaning work is done on the gas. Hence, in constant pressure reactions involving gas expansion, the heat of reaction is distributed between internal energy change and work done by the gas.

Specific Heats

Specific heats are vital in understanding how a substance heats up or cools down. They are defined as the amount of heat per unit mass required to raise the temperature by one degree Celsius. Gases have two specific heats: \( C_V \) (at constant volume) and \( C_P \) (at constant pressure).
\( C_V \) is used when the volume is kept constant, and no work is done by the gas, so all the heat goes into changing the internal energy.
\( C_P \) is used when the pressure is constant. Here, the heat added goes into changing internal energy and doing external work. Therefore, \( C_P \) is greater than \( C_V \) because it includes the energy required to do the work due to expansion. The relationship between them is given by \( C_P = C_V + R \) for ideal gases, where \( R \) is the gas constant.