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Relation between Kp and Kc

In the reacti...

Question

In the reaction

$C S_{2} (l) + 3 O_{2} (g) \to C O_{2} (g) + 2 S O_{2} (g) Δ H = - 265 k c a l$

The enthalpies of formation of $C O_{2}$ and $S O_{2}$ are both negative and are in the ratio 4 : 3. The enthalpy of formation of $C S_{2}$ is $+ 26 k c a l / m o l$ . Calculate the enthalpy of formation of $S O_{2}$ .

A

−90 kcal/mol

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B

−52 kcal/mol

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C

−78 kcal/mol

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D

−71.7 kcal/mol

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Solution

The correct option is D
−71.7 kcal/mol

$C S_{2} (l) + 3 O_{2} (g) \to C O_{2} (g) + 2 S O_{2} (g)$

$Δ H = - 256 K c a l$

Let $Δ H_{r} (C O_{2}, g) = - 4 x$ and $Δ H_{r} (S O_{2}, g) = - 3 x$

$Δ H_{r e a c t i o n} = Δ H_{f} (C O_{2}, g) + 2 Δ Δ_{f} (S O_{2}, g) - Δ H_{f} (C S_{2} I)$

$- 265 = - 4 x - 6 x - 26$

$x = + 23.9$

$∴ Δ_{f} (S O_{2}, g) = 3 x = - 71.7 K c a l / m o l$

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