Chemical EquilibriumHard

Question

In the decomposition equilibrium of a certain alkaline earth metal carbonate, the partial pressure of CO2 becomes a hundred fold when the temperature is increased from 400 K to 500 K. What is the mean value of ΔH° for the given range of temperature?

Options

A.18.4 kcal/mol
B.13.84 kcal/mol
C.14.83 kcal/mol
D.10.83 kcal/mol

Solution

MCO3(S) $\rightleftharpoons$MO(S) + CO2(g): $K_{p} = P_{CO_{2}}$

Now, $\ln\frac{K_{2}}{K_{1}} = \frac{\Delta H^{o}}{R}\left( \frac{1}{T_{1}} - \frac{1}{T_{2}} \right)$

$\text{Or, }2.303 \times \log 100 = \frac{\Delta H^{o}}{2}\left( \frac{1}{450} - \frac{1}{500} \right) \Rightarrow \Delta H^{o} = 18424\text{ cal}$

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