Question

Gibbs-Helmholtz equation relates

• A. Gibbs free energy, enthalpy and temperature
• B. Entropy and work
• C. Internal energy and volume
• D. Heat and temperature

Hint:

To easily identify the Gibbs-Helmholtz relation, remember its key application: it allows you to compute the change in Gibbs Free Energy (\(G\)) at different temperatures if you already know the reaction Enthalpy (\(H\)). It serves as a bridge connecting \(G\), \(H\), and \(T\).

Answer 1

The Correct Option is A

Concept: The Gibbs-Helmholtz equation is a fundamental thermodynamic relation used to determine how the Gibbs free energy (\(G\)) of a chemical system shifts as a function of temperature. It explicitly calculates the temperature dependence of the function \((G/T)\) using the system's enthalpy (\(H\)). Mathematical Derivation and Expressions:
We begin with the fundamental definition of Gibbs free energy at a constant state: \[ G = H - TS \] Differentiating this expression with respect to temperature (\(T\)) at constant pressure (\(P\)) yields: \[ \left(\frac{\partial G}{\partial T}\right)_P = -S \] Substituting this expression for \(-S\) back into our initial definition equation gives: \[ G = H + T \left(\frac{\partial G}{\partial T}\right)_P \] We can reformulate this relationship by analyzing the derivative of \((G/T)\) with respect to temperature using the quotient rule: \[ \left(\frac{\partial (G/T)}{\partial T}\right)_P = \frac{T\left(\frac{\partial G}{\partial T}\right)_P - G}{T^2} \] Substituting \(G - T\left(\frac{\partial G}{\partial T}\right)_P = H\) into this expression results in the classic form of the Gibbs-Helmholtz Equation: \[ \left(\frac{\partial (G/T)}{\partial T}\right)_P = -\frac{H}{T^2} \] Alternatively, expressed in terms of changes during a chemical transition (\(\Delta G\) and \(\Delta H\)): \[ \left(\frac{\partial (\Delta G/T)}{\partial T}\right)_P = -\frac{\Delta H}{T^2} \] This equation shows that the Gibbs-Helmholtz relation explicitly couples Gibbs free energy (\(G\)), enthalpy (\(H\)), and temperature (\(T\)), which matches Option (1). The other options describe standard thermodynamic parameters but do not represent the variables coupled by the Gibbs-Helmholtz equation.