Question

2WO3(s)+3C(s)→2W(s)+3CO2(g)Tungsten(VI) oxide can also be reduced to tungsten by heating it with carbon in an electric furnace:

$\mathbf{2}\mathit{W}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{3}\mathbf{C}\left(s\right)\mathbf{\to }\mathbf{2}\mathbf{W}\left(s\right)\mathbf{+}\mathbf{3}\mathit{C}{\mathit{O}}_{\mathbf{2}}\left(g\right)$

(a)Calculate the standard free energy change $\mathbf{△}\mathit{G}\mathbf{°}$for this reaction and comment on the feasibility of the process under room conditions.

(Blue- color code (#000A64)

Short answer

1. The standard free energy change for the given reaction is 345.08 kJ.Since the reaction is non-spontaneous at room temperature, the process is not feasible.

Step-by-step solution

Given information

The reaction between the tungsten oxide and carbon is given below:

$2{\mathrm{WO}}_3\left(\mathrm{s}\right)+3\mathrm{C}\left(\mathrm{s}\right)\to 2\mathrm{W}\left(\mathrm{s}\right)+3{\mathrm{CO}}_2\left(\mathrm{g}\right)$

The temperature at room condition, T=298 K

Step 2: Feasibility of a process

A thermodynamic process is said to be feasible if the total change in entropy is a positive value; change in Gibb’s free energy is less than zero.

Standard Gibbs free energy values

The standard Gibbs free energy value of W, $\Delta {\mathrm{G}}_{\mathrm{W}}°=0{\mathrm{kJmol}}^{-1}$

Standard Gibbs free energy value of C, $\Delta {\mathrm{G}}_{\mathrm{C}}°=0{\mathrm{kJmol}}^{-1}$

Standard Gibbs free energy of WO₃ $\Delta {\mathrm{G}}_{{\mathrm{WO}}_3}°=-764.08{\mathrm{kJmol}}^{-1}$

Standard Gibbs free energy of CO_{2$\Delta {\mathrm{G}}_{{\mathrm{CO}}_2}°=-394.36{\mathrm{kJmol}}^{-1}$}

Calculation of standard Gibbs free energy change of the reaction

The standard Gibbs free energy change of the reaction at room temperature is calculated as follows:$\begin{array}{c}\Delta \mathrm{G}°=2\left(\Delta {\mathrm{G}}_{{\mathrm{WO}}_3}°\right)+3\left(\Delta {\mathrm{G}}_{\mathrm{C}}°\right)+2\left(\Delta {\mathrm{G}}_{\mathrm{W}}°\right)+3\left(\Delta {\mathrm{G}}_{{\mathrm{CO}}_2}°\right)\\ =2\left(0{\mathrm{kJmol}}^{-1}\right)+3\left(-394.36{\mathrm{kJmol}}^{-1}\right)-2\left(-764.08{\mathrm{kJmol}}^{-1}\right)-3\left(0{\mathrm{kJmol}}^{-1}\right)+\\ =-1183.08{\mathrm{kJmol}}^{-1}+1528.16{\mathrm{kJmol}}^{-1}\\ =+345.08{\mathrm{kJmol}}^{-1}\end{array}$

Hence,the standard Gibbs free energy change of the reaction is 345.08 kJ.

Feasibility of the reaction

For a reaction to be feasible, its Gibbs free energy change must be less than zero.Since the Gibbs free energy change is greater than zero, the reaction is said to be non-spontaneous and non-feasible.