Question

Concrete is produced from a mixture of cement, water and small stones. Small amount of gypsum,$CaS{O_4}.2{H_2}O$ , is added in cement production to improve the subsequent hardening of concrete. The elevated temperature during the production of cement may lead to the formation of unwanted hemihydrate $CaS{O_4}.\dfrac{1}{2}{H_2}O$according to the reaction.
$CaS{O_4}.2{H_2}O(s) \to CaS{O_4}.\dfrac{1}{2}{H_2}O(s) + \dfrac{3}{2}{H_2}O(g)$
The ${\Delta _f}{H^ - }$of $CaS{O_4}.2{H_2}O(s),CaS{O_4}.\dfrac{3}{2}{H_2}O(s),{H_2}O(g)$ are $- 2021.0KJmo{l^{ - 1}}, - 1575.0KJmo{l^{ - 1}}$ and $- 241.8KJmo{l^{ - 1}}$.respectively. The respective values of their standard entropies are $194.0,130.0$ and $188.0J{K^{ - 1}}mo{l^{ - 1}}$. The values of $R = 8.314J{K^{ - 1}}mo{l^{ - 1}} = 0.0831Lbarmo{l^{ - 1}}{k^{ - 1}}$.
Answer the following question on the basis of above information.
The formation of $CaS{O_4}.\dfrac{1}{2}{H_2}O$ at $298K$ is:
$A)$Spontaneous
$B)$Endothermic and non-spontaneous
$C)$Endothermic and spontaneous
$D)$Exothermic and non-spontaneous

Answer 1

The formation of $CaS{O_4}.\dfrac{1}{2}{H_2}O$ is an endothermic and non-spontaneous process. A spontaneous endothermic reaction can occur when the changes in enthalpy and entropy yield a negative Gibbs free energy. An endothermic reaction can be spontaneous if entropy increases by more than the change in enthalpy.

Complete answer:
The heat produced by concrete during concrete curing is called heat of hydration. This exothermic reaction occurs when water and cement react. The amount of heat produced during the reaction is mostly related to the composition and fineness of the cement.
The formation of $CaS{O_4}.\dfrac{1}{2}{H_2}O$ at $298K$ is endothermic. Gypsum and other sulfate compounds react with calcium aluminate in the cement to form ettringite within the first few hours after mixing with water. Most of the sulfate in the cement is normally consumed to form ettringite at early ages.
It combines with the $C - S - C$, or concrete paste, and begins destroying the paste that holds the concrete together. As sulphate dries, new compounds are formed, often called ettringite.
Most endothermic reactions are nonspontaneous. Without a steady supply of energy, the reactions typically come to a stop. For endothermic reactions, enthalpy usually goes up. However, a spontaneous endothermic reaction can occur when the changes in enthalpy and entropy yield a negative Gibbs free energy.
So, the correct answer is $B)$ Endothermic and non-spontaneous .

Note:
The $CaS{O_4}$ forms are white solids, barely soluble in water. Its two common hydrates are Plaster of Paris and Gypsum. Plaster of Paris is a Hemi-hydrate of calcium sulphate which is obtained by heating gypsum to $393K$.