Question

How does delta G change with pressure?

Answer 1

The chemical thermodynamics is a branch of chemistry which deals with heat of a system, work done etc. Delta G is the change in free energy of the reaction and the equation related to free enthalpy will give the relation with P.

Complete answer:
In the question we are asked to comment on how delta G changes with pressure. Before going into the solution, let us discuss how pressure influences the volume of gas, what delta G refers to, the factors influencing delta G etc.
First let's talk about the effect of pressure on a gas kept in a cylinder along with a piston. As we know that the arrangement of gaseous molecules are very loose and they have greater value of intermolecular distance etc. When we apply pressure to a gas by compressing the piston of the cylinder the volume of the gas will reduce. We know when a gas is compressed its volume is reduced.
Now let us relate the pressure with enthalpy and entropy. The pressure affects the enthalpy and entropy and as the enthalpy and entropy gets affected, internal energy also varies.
But for an ideal gas enthalpy is not affected by the variation in pressure but the entropy of the gas varies.
We could explain this as, when there is no role of pressure, the volume of the gas will be greater than when the pressure is applied. Greater volume means greater value of entropy. Since we know that entropy is disorderness of state. When the pressure is applied volume decreases and the molecules of gas have to move in a lesser area hence lesser entropy value.
So we may conclude that at low pressure and high volume, entropy will be greater. And at high pressure and lower volume the entropy will be lesser.
Now let us discuss delta G, which refers to the change in free energy. Free energy of a system is the useful work done or can be said as the maximum amount of work done in a closed system. And we could related pressure with internal energy and write the equation as:
$G={{G}^{0}}+RT\ln \left( P \right)$
G is the free energy of gas, ${{G}^{0}}$ is the free of the gas at 1atm, R is Universal constant. T is the absolute temperature, P is the pressure of the gas.
We can also write as, $G={{G}^{0}}+RT\ln Q$
Q is the reaction quotient
For example: We can find the relation of pressure and internal energy in ammonia synthesis as follows:
${{N}_{2}}_{\left( g \right)}+3{{H}_{2}}_{\left( g \right)}\to 2N{{H}_{3\left( g \right)}}$
$G={{G}^{0}}+RT\ln Q$
$Q=\dfrac{{{({{P}_{N{{H}_{3}}}})}^{2}}}{({{P}_{{{N}_{2}}}}){{\left( {{P}_{{{H}_{2}}}} \right)}^{3}}}$
$G={{G}^{0}}+RT\ln \dfrac{{{({{P}_{N{{H}_{3}}}})}^{2}}}{({{P}_{{{N}_{2}}}}){{\left( {{P}_{{{H}_{2}}}} \right)}^{3}}}$

Note:
If change in internal energy i.e. $\Delta G$has negative sign then it means that the reaction is spontaneous if the internal energy ($\Delta G$) is positive then the reaction is nonspontaneous and if $\Delta G$ has a value zero, then the reaction is in equilibrium.