Consider the production of ammonia from nitrogen and hydrogen,

$N_2+3H_2\to 2N{H}_3$

at 298 K and 1 bar. From the values of ΔH and S tabulated at the back of this book, compute ΔG for this reaction and check that it is consistent with the value given in the table.

Temp, T = 298 K and the
pressure P= 1 bar.
The table from the book

Gibbs energy can be calculated by the equation below.

G=H-T S
Where, G= Gibbs energy, H= enthalpy, T= absolute temperature and S= entropy.

Lets assume there is an infinitesimal change is Gibbs energy, then

ΔG = ΔH - TΔS ........................................(1)

Similarly equation for the change in enthalpy for the given reaction is written as

$\Delta H=2\Delta H_{{\mathrm{NH}}_3}-\Delta H_{{\mathrm{N}}_2}-3\Delta H_{{\mathrm{H}}_2}$

Now substitute the value from the table , we get

$$\begin{gathered} \Delta H=2(-46.11\mathrm{kJ})-0-0 \\ =-92.2\mathrm{kJ} \\ =-92.2\mathrm{kJ}\left(\frac{1000\mathrm{J}}{1\mathrm{kJ}}\right) \\ =-92.2\times {10}^3\mathrm{J} \end{gathered}$$

Change in entropy for the reaction

Substitute values

$$\begin{gathered} \Delta S=2\left(192.45{\mathrm{JK}}^{-1}\right)-\left(191.61{\mathrm{JK}}^{-1}\right)-3\left(130.68{\mathrm{JK}}^{-1}\right) \\ =-198.75{\mathrm{JK}}^{-1} \end{gathered}$$

Substitute calculated values in equation (1), we get
$$\begin{gathered} \Delta G=\left(-92.2\times {10}^3\mathrm{J}\right)-(298\mathrm{K})\left(-198.75{\mathrm{JK}}^{-1}\right) \\ =-32972.5\mathrm{J} \end{gathered}$$