NEET 2023 Chemistry Enthalpy and Internal Energy MCQ Question

To understand the relationship between the change in enthalpy ($\Delta H$) and the change in internal energy ($\Delta U$) in thermodynamics, we need to consider the definitions and the derived relationships that involve the number of moles of gas and temperature.

Explanation of the Correct Answer (B)

The correct relationship between the change in enthalpy and the change in internal energy is given by:

$\Delta H - \Delta U = -\Delta n_g RT$

Where:

• $\Delta H$ is the change in enthalpy.
• $\Delta U$ is the change in internal energy.
• $\Delta n_g$ is the change in the number of moles of gas during the reaction.
• $R$ is the universal gas constant.
• $T$ is the temperature in Kelvin.

This equation can be derived from the definition of enthalpy:

$H = U + PV$

For constant pressure processes, we can express the change in enthalpy as:

$\Delta H = \Delta U + \Delta (PV)$

Using the ideal gas law, for an ideal gas, we can express $PV = nRT$. If the number of moles of gas changes during a reaction ($\Delta n_g$), then:

$\Delta (PV) = \Delta n_g RT$

Substituting this back into the expression for $\Delta H$, we get:

$\Delta H = \Delta U + \Delta n_g RT$

Rearranging this gives us the correct relationship:

$\Delta H - \Delta U = \Delta n_g RT$

However, this is often presented in the context of reactions where gases are produced or consumed, leading to the negative sign when considering the change in moles of gases, thus:

$\Delta H - \Delta U = -\Delta n_g RT$

Clarification of Incorrect Options

Option A: $\Delta H = \Delta U + \Delta n_g RT$

This is a misrepresentation of the relationship. While it resembles the correct equation, it does not account for the sign of the change in moles of gases. The correct form has a negative sign associated with the change in moles.

Option C: $\Delta H + \Delta U = \Delta n R$

This option is incorrect because it suggests a direct addition of $\Delta H$ and $\Delta U$ equating to $\Delta nR$. This does not reflect the established relationship in thermodynamics and misrepresents the roles of enthalpy and internal energy in terms of gas moles.

Option D: $\Delta H = \Delta U - \Delta n_g RT$

This equation is also incorrect because it has the wrong sign in front of the term $\Delta n_g RT$. It implies that the change in enthalpy is less than the change in internal energy by the product of the change in gas moles and temperature, which contradicts the correct relationship established in thermodynamic principles.

Summary

In summary, the correct relationship is:

$\Delta H - \Delta U = -\Delta n_g RT$

This reflects that changes in enthalpy and internal energy are interconnected via the behavior of gases in a reaction. The incorrect options either misrepresent the sign or misinterpret the relationship altogether. Understanding these concepts is crucial for solving problems related to thermodynamics in the NEET/JEE examinations.