Chemistry

Problem

298\,\text{K}

the industrial decomposition of calcium carbonate is represented in two overall steps. Step 1:

\mathrm{CaCO_3}(s) \rightarrow \mathrm{CaO}(s) + \mathrm{CO_2}(g)

Step 2:

\mathrm{CaO}(s) + \mathrm{H_2O}(l) \rightarrow \mathrm{Ca(OH)_2}(s)

(a) Calculate the change in the number of moles of gas,

\Delta n_{\text{gas}}

, for each step. (b) Based on your values of

\Delta n_{\text{gas}}

, determine the sign of

\Delta S^\circ

for each step and briefly explain your reasoning. (c) The two steps are carried out sequentially in an open vessel at atmospheric pressure. Which step, if any, is expected to be more sensitive to an increase in temperature with respect to its entropy term (

T\Delta S

) in the Gibbs free-energy expression? Justify your answer. (a) Calculation of

\Delta n_{\text{gas}}

for each step (b) Determination and explanation of the sign of

\Delta S^\circ

for each step (c) Identification of the temperature-sensitive step with justification

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