Question

Which amongst the following options is the correct relation between change in enthalpy and change in internal energy

• A. \(ΔH = ΔU + Δn_gRT\)
• B. \(ΔH - ΔU = - ΔnRT\)
• C. \(ΔH + ΔU = ΔnR\)
• D. \(ΔH = ΔU - Δn_gRT\)

Answer 1

The Correct Option is A

In the context of thermodynamics, the relationship between the change in enthalpy (\(ΔH\)) and the change in internal energy (\(ΔU\)) is crucial in understanding how energy is transferred in a chemical reaction or process, particularly when gases are involved.

To derive this relationship, consider the definition of enthalpy:

H = U + PV,

where \(H\) is the enthalpy, \(U\) is the internal energy, \(P\) is the pressure, and \(V\) is the volume.

When there is a change in these quantities, we can express this as:

ΔH = ΔU + Δ(PV).

For ideal gases, the term \(Δ(PV)\) can be further expressed using the ideal gas equation \(PV = nRT\), where \(n\) represents the number of moles, \(R\) is the universal gas constant, and \(T\) is the temperature.

Therefore,

Δ(PV) = Δ(nRT) = Δn_gRT,

where \(Δn_g\) is the change in the number of moles of gaseous reactants and products.

Thus, the relation becomes:

ΔH = ΔU + Δn_gRT.

Conclusion: The correct relation between the change in enthalpy and the change in internal energy is given by ΔH = ΔU + Δn_gRT.

Explanation of Other Options:

• ΔH - ΔU = - ΔnRT: Incorrect, as it does not correctly account for the change in enthalpy due to the work done by expanding or contracting gases.
• ΔH + ΔU = ΔnR: Incorrect, the signs and the expression are not consistent with thermodynamic principles.
• ΔH = ΔU - Δn_gRT: Incorrect, the change in enthalpy includes a positive term \(Δn_gRT\) for work done during expansion or contraction of gases.