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In the decomposition of solid metallic carbonate $(M C O_{3})$ into solid metal oxide and carbon dioxide gas, the partial pressure is increases by 10 times when temperature changes from 400 K to 500 K. The average value of enthalpy change $(Δ H)$ for the reaction in the given temperature range in $k cal / mole$ is ____?
$(take R = 2 cal . K^{- 1} . {mole}^{- 1})$

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answer is 9.212.

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Detailed Solution

$M C O_{3 (s)} ⇌ M O_{(s)} + C O_{2_{(g})}$

$vont Hoff equation K_{P} = P_{C O_{2}}$

$\log (\frac{K_{P_{2}}}{K_{P_{1}}}) = \frac{Δ H}{2.303 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$

$\log 10 = \frac{Δ H}{2.303 \times 2 cal} [\frac{100}{200000}]$

$Δ H = 9.212 {kcal . mole}^{- 1}$

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