Question

The value of ${\Delta }_f{G}^0$ for $C{r}_2{O}_3$ is $540{\text{kJ mol}}^{-1}$ and that of $A{l}_2{O}_3$ is $-827{\text{kJ mol}}^{-1}$. Is the reduction of $C{r}_2{O}_3$ by $Al$ is feasible reaction?

• A. The data is incomlete
• B. The reaction is feasible
• C. The reaction is not feasible
• D. The reaction may or may not be feasible

Answer 1

The correct option is B The reaction is feasible

The free energy of formation of alumina is more negative than $C{r}_2{O}_3$ . According to thermodynamics if $\Delta G^0$, is more negative then reaction is more fealible.

Free energy of formation of $A{l}_2{O}_3=-827{\text{kJ mol}}^{-1}$
$\frac{4}{3}Al+O_2\to \frac{2}{3}A{l}_2{O}_3\Delta G_f=-827{\text{kJ mol}}^{-1}$

Free energy of formation of $C{r}_2{O}_3=-540{\text{kJ mol}}^{-1}$
So, $\frac{2}{3}C{r}_2{O}_3\to \frac{4}{3}Cr+O_2\Delta G_f=540{\text{kJ mol}}^{-1}$

Hence the free energy of reaction between $Al$ and $C{r}_2{O}_3$
$2Al+C{r}_2{O}_3\to A{l}_2{O}_3+2Cr$
$\Delta G^0=-827+540=-287\text{kJ mol}$
Hence the reaction is feasible.