Question

Consider the production of ammonia from nitrogen and hydrogen,

N₂ + 3H₂ $\to$2NH₃
at 298 K and 1 bar. From the values of $△H$and S tabulated at the back of this book, compute $△G$for this reaction and check that it is consistent with the value given in the table.

Short answer

The value of change in Gibbs energy $\Delta G=-32972.5\mathrm{J}$

Step-by-step solution

Given

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

Explanation

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

$\Delta G=\Delta H-T\Delta S\dots ..........\left(1\right)$

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

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

Put the values from table, we get

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

Now, substitute $\Delta S=-198.75{\mathrm{JK}}^{-1}and\Delta H=-92.2\times {10}^3\mathrm{J}$ in the equation (1), we get$$\begin{gathered} \Delta G=\left(-92.2\times {10}^3\mathrm{J}\right)-(298\mathrm{K})\left(-198.75{\mathrm{JK}}^{-1}\right) \\ =-32972.5\mathrm{J} \end{gathered}$$