Question

For a system in equilibrium, $\Delta G = 0$ , under conditions of constant______.
A.Temperature and pressure.
B.Temperature and volume.
C.Pressure and volume.
D.Energy and volume.

Answer 1

We can use the formula $\Delta G = \Delta {G^ \odot } + RT\ln K$ where $\Delta G$ is free energy change and $\Delta {G^ \odot }$ is free energy change under standard conditions,$R = 8.314{\text{ Jmol}}{{\text{C}}^{ - 1}}$ is gas constant, T=Temperature and K is equilibrium constant of a reaction. We can also use the formula-
$\Delta {\text{G = }}\Delta {\text{H - T}}\Delta {\text{S}}$ where $\Delta {\text{G}}$ is change in free energy, $\Delta {\text{S}}$ is entropy change, $\Delta {\text{H}}$ is enthalpy change and ${\text{T}}$ is the temperature in Kelvin.

Complete step by step answer:
$\Delta G$ is Gibbs free energy for a system. It will be zero for a system in equilibrium only if the temperature and pressure are constant. It is also given as –
$\Rightarrow \Delta G = \Delta {G^ \odot } + RT\ln K$
Where$\Delta {G^ \odot }$ is free energy change under standard conditions, $R = 8.314{\text{ Jmol}}{{\text{C}}^{ - 1}}$ is gas constant, T=Temperature and K is equilibrium constant of a reaction.
Now if $\Delta G = 0$then we get the free energy change under standard conditions,
$\Rightarrow \Delta {G^ \odot } = - RT\ln K$
Gibbs free energy is also given as-
$\Delta G = \Delta H - T\Delta S$ Where $\Delta H$= change in enthalpy, $\Delta S$ is change in entropy and T is the temperature.
We can write-
$\Delta H = \Delta U + P\Delta V$ where P is constant pressure, V is volume and U is internal energy.
Then we can write –
$\Rightarrow \Delta G = \Delta U + P\Delta V - T\Delta S$
In the above equation only pressure and temperature are constant in equilibrium when $\Delta G = 0$

Hence the correct answer is A.

Note:
The direction of a chemical reaction is indicated by the sign of $\Delta G$ and it also tells –
If $\Delta G < 0$ then, the reaction is spontaneous in the direction it is written (backward or forward).This means that no external energy is needed for the reaction to occur.
If $\Delta G = 0$ then, the system is at equilibrium. No changes occur in either forward or backward direction.
If $\Delta G > 0$ then the reaction is not spontaneous. This means the reaction needs input of free energy to make the reaction go forward instead of backward.