Question

Which one of the following is correct?
A.\[ - \Delta G = \Delta H - T\Delta S\]
B.\[\Delta H = \Delta G - T\Delta S\]
C.\[\Delta S = \dfrac{1}{T}(\Delta G - \Delta H)\]
D.\[\Delta S = \dfrac{1}{T}(\Delta H - \Delta G)\]

Answer 1

Hint: The Gibbs Helmholtz equation defines the relation between Gibbs free energy (\[G\]), enthalpy (\[H\]) and entropy (\[S\]).
Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter).
Enthalpy is a property of a thermodynamic system and it is a state function. It is defined as the sum of the system's internal energy and the product of its pressure and volume.
Entropy is a state function and is defined as a measure of the unavailable energy in a closed thermodynamic system that is also usually considered to be a measure of the system's disorder.

Complete answer: The Gibbs Helmholtz equation states that the Gibbs free energy is equal to the change in enthalpy subtracted from the product of temperature and change in entropy. The equation is:
\[\Delta G = \Delta H - T\Delta S\]
On rearranging this equation, we get
$
  \Delta G - \Delta H = - T\Delta S \\
  \Delta H - \Delta G = T\Delta S \\
  \Delta S = \dfrac{1}{T}(\Delta H - \Delta G) \\
$
Hence, Option (d) is correct.

Note:
We can predict whether the reaction is spontaneous or not by using the value of \[\Delta G\], in the following way-
If \[\Delta G\] is negative ( \[\Delta G < 0\]), then the reaction will be spontaneous.
If \[\Delta G\] is positive (\[\Delta G > 0\]), then the reaction will be non-spontaneous.
If \[\Delta G\] is zero, the reaction is at equilibrium.