For complete combustion of ethene, the amount of heat produced as measured in a bomb calorimeter is at 300 K. The minimum value of needed to reach equilibrium is (–) _____ kJ. (Nearest integer) [2023]

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Solution

Q.
For complete combustion of ethene,

$C_{2} H_{4} (g) + 3 O_{2} (g) \to 2 {CO}_{2} (g) + 2 H_{2} O (l)$

the amount of heat produced as measured in a bomb calorimeter is $- {1406 kJ mol}^{- 1}$ at 300 K.

The minimum value of $T Δ S$ needed to reach equilibrium is (–) _____ kJ. (Nearest integer)

$Given: R = {8.3 J K}^{- 1} {mol}^{- 1}$ [2023]

Ans.
(1411)

$For equilibrium Δ G = 0$

$Δ H - T Δ S = 0$

$T Δ S = Δ H = Δ E + Δ n_{g} R T$

$Δ H = - 1406 + [- 2] \times 8.3 \times 10^{- 3} \times 300$

$= - 1410.98 \approx - 1411 kJ/mol$

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