Question

What is an example of free energy?

Answer 1

1. Gibbs free energy is a state function and it is a calculation of maximum work done or useful work done from a reversible reaction at constant temperature and pressure.
2. The free energy of a system is the enthalpy of the system minus the product of absolute temperature and entropy.i.e, $\mathrm{G}=\mathrm{H}-\mathrm{TS}.$ Here G is Gibbs free energy, H is enthalpy, T is temperature and S is entropy.
3. The change in Gibbs free energy is expressed as$∆\mathrm{G}$. Hence, $∆\mathrm{G}=∆\mathrm{H}-\mathrm{T}∆{\mathrm{S}}_{\mathrm{system}}$.
4. Generally, it is used to measure whether a reaction is spontaneous or not.
5. The spontaneity is related to free energy change as shown below.
6. The process is spontaneous only if it leads to a net following: a decrease in Gibb's free energy, i.e.,$∆\mathrm{G}<0.$
7. If $∆\mathrm{G}=0,$ then the process is in equilibrium
8. If $∆\mathrm{G}>0$, then the process will be non-spontaneous.

Example

For the reaction;

$$\begin{gathered} {\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)...................∆\mathrm{H}=-285.8{\mathrm{kJmol}}^{-1}{\mathrm{K}}^{-1}, \\ ∆\mathrm{S}=-0.163{\mathrm{kJmol}}^{-1}{\mathrm{K}}^{-1} \end{gathered}$$

Identify the value of $∆\mathrm{G}$ at ${27}^0\mathrm{C}$ for the reaction?

Solution:

$$\begin{gathered} ∆\mathrm{G}=∆\mathrm{H}-\mathrm{T}∆\mathrm{S}, \\ \mathrm{T}=27+273=300\mathrm{K} \\ ∆\mathrm{G}=\left(-285.8\right)-300\left(-0.163\right) \\ =-236.9{\mathrm{kJmol}}^{-1} \end{gathered}$$

Hence, the value of $∆\mathrm{G}$ at ${27}^0\mathrm{C}$ for the reaction is $-236.9{\mathrm{kJmol}}^{-1}$.