Question

The Gibbs-Helmholtz equation is used to determine:

• A. The change in internal energy at constant volume
• B. The change in enthalpy at constant pressure
• C. The relationship between the Gibbs free energy change and temperature
• D. The efficiency of an engine cycle

Hint:

Use the Gibbs-Helmholtz equation to assess how \( \Delta G \) changes with temperature—essential for equilibrium and spontaneity analysis.

Answer 1

The Correct Option is C

Step 1: The Gibbs-Helmholtz equation is a thermodynamic relationship that links the change in Gibbs free energy \( \Delta G \) of a system to temperature and enthalpy. It is useful for understanding how \( \Delta G \) varies with temperature.
Step 2: The equation is given by: \[ \left( \frac{\partial (\Delta G/T)}{\partial T} \right)_P = -\frac{\Delta H}{T^2} \] where:

• \( \Delta G \) is the Gibbs free energy change,
• \( \Delta H \) is the enthalpy change,
• \( T \) is the absolute temperature.

Step 3: This relation is particularly important in chemical thermodynamics to predict the spontaneity and equilibrium position of reactions as temperature changes. Why the other options are incorrect:

• (A) Internal energy change at constant volume is addressed by the first law of thermodynamics.
• (B) Enthalpy change at constant pressure is covered by basic enthalpy definitions, not this equation.
• (D) Engine efficiency involves different thermodynamic principles like the Carnot cycle.