Thermodynamics and Thermochemistry 2 Question 14
14. The thermal dissociation of equilibrium of $\mathrm{CaCO}_{3}(s)$ is studied under different conditions.
$\mathrm{CaCO}{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}{2}(g)$
(2013 Adv.)
For this equilibrium, the correct statement(s) is/are
(a) $\Delta H$ is dependent on $T$
(b) $K$ is independent of the initial amount of $\mathrm{CaCO}_{3}$
(c) $K$ is dependent on the pressure of $\mathrm{CO}_{2}$ at a given $T$
(d) $\Delta H$ is independent of the catalyst, if any
Subjective Questions
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Solution:
- PLAN Heat of reaction is dependent on temperature (Kirchhoff’s equation) in heterogeneous system, equilibrium constant is independent on the molar concentration of solid species.
Heat of reaction is not affected by catalyst. It lowers activation energy.
$$ \mathrm{CaCO}{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}{2}(g) $$
By Kirchhoff’s equation,
$$ \Delta H_{2}^{\circ}\left(\text { at } T_{2}\right)=\Delta H_{1}^{\circ}\left(\text { at } T_{1}\right)+\Delta C_{p}\left(T_{2}-T_{1}\right) $$
$\Delta H^{\circ}$ varies with temperature. Thus, (a) is correct.
$$ K=p_{\mathrm{CO}_{2}} $$
$K$ is dependent on pressure of $\mathrm{CO}{2}$ but independent of molar concentration of $\mathrm{CaCO}{3}$. Thus, (b) and (c) are correct. At a given temperature, addition of catalysis lowers activation energy, $\Delta H$ remaining constant. Thus, (d) is also correct.
$E_{a}=$ Activation energy in absence of catalyst
$E_{a}^{\prime}=$ Activation energy in presence of catalyst
