SATHEE: Thermodynamics and Thermochemistry 1 Question 11

Thermodynamics and Thermochemistry 1 Question 11

11. The reaction, $MgO (s) + C (s) \to Mg (s) + CO (g)$ ,

for which $Δ_{r} H^{\circ} = + 491.1 kJ {mol}^{- 1}$ and $Δ_{r} S^{\circ} = 198.0 {JK}^{- 1} {mol}^{- 1}$ , is not feasible at $298 K$ .

Temperature above which reaction will be feasible is

(a) $2040.5 K$

(b) $1890.0 K$

(c) $2380.5 K$

(d) $2480.3 K$

Show Answer

Solution:

According to Gibbs-Helmholtz equation,

$Δ_{r} G^{\circ} = Δ_{r} H^{\circ} - T Δ_{r} S^{\circ}$

For a reaction to be feasible (spontaneous)

$\begin{aligned} Δ_{r} G^{\circ} < 0 & Δ_{r} H^{\circ} - T Δ_{r} S^{\circ} < 0 \end{aligned}$

Given, $Δ_{r} H^{\circ} = + 491.1 kJ {mol}^{- 1}$ ,

$Δ_{r} S^{\circ} = 198 {JK}^{- 1} {mol}^{- 1}$

$∴ 491.1 \times 10^{3} - T \times 198 < 0$

$T > \frac{491.1 \times 10^{3}}{198} = 2480.3 K$

$∴$ Above $2480.3 K$ reaction will become spontaneous.

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