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Gibbs Free Energy & Spontaneity

The equilibri...

Question

The equilibrium constant $K_{p}$ for the reaction
$A (g) ⇌ B (g) + C (g)$
is 1 at $27 C a n d 4 a t 47 .$
For the reaction calculate enthalpy change for the
$B (g) + C (g) ⇌ A (g)$
$(G i v e n : R = 2 c a l / m o l - K)$

A

13.31 k c a l / m o l

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B

14.31 k c a l / m o l

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C

19.2 k c a l / m o l

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D

55.63 k c a l / m o l

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Solution

The correct option is A $13.31 k c a l / m o l$
The equilibrium constant $K_{p}$ for the reaction
$A (g) ⇌ B (g) + C (g)$
$K_{p 1} = 1 a t 300 k; K_{p 2} = 4 a t 320 k$
$l o g_{10} \frac{4}{1} = \frac{Δ H}{2.303 R} [\frac{1}{300} - \frac{1}{320}]$
$0.6 = \frac{Δ H}{2.303 \times 2} \times \frac{20}{300 \times 320}$
$Δ H = 13.31 K c a l / m o l e .$
$f o r B (g) + C (g) ⇌ A (g)$
$Δ H = - 13.31 K c a l / m o l e .$

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