Question

Concrete is produced from a mixture of cement, water and small stones. Small amount of gypsum, $CaS{O}_4\cdot 2H_{2}O$ 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
$CaS{O}_4\cdot \frac{1}{2}{H}_{2}O$ according to reaction,
$CaS{O}_4\cdot 2H_{2}O(s)\to CaS{O}_4\cdot \frac{1}{2}{H}_{2}O(s)+\frac{3}{2}{H}_{2}O(g)$
The ${\Delta }_f{H}^{\ominus }$ of$CaS{O}_4\cdot 2H_{2}O(s),CaS{O}_4\cdot \frac{1}{2}{H}_{2}O(s),H_{2}O(g)$ 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 questions on the basis of above information
Heat change occurring during conversion of $1kg$ of $CaS{O}_4\cdot 2H_{2}O(s)($ molar mass $172gmo{l}^{-1})$ of ${}_{CaS{O}_4}$. $\frac{1}{2}{H}_{2}O(s)$ is equal to

• A. $484kJmo{l}^{-1}$
• B. $400kJ$
• C. $-484.0kJ,mo{l}^{-1}$
• D. $-1000kJ$

Answer 1

Answer: (A)

$\Delta H^{\ominus }=\Delta H_P^{\ominus }-\Delta H_R^{\ominus };($ for $1mol)$
$=\left[-1575.0kJmo{l}^{-1}-\frac{3}{2}\times 241.8\right]$
$-\left[-2021.0kJmo{l}^{-1}\right]$
$=+83.3kJmo{l}^{-1}$
For $1kgCaSO{}_4\cdot 2H_{2}O$
Number of moles $=\frac{1000}{172}=5.81$
$\therefore$ Heat change for $5.81mol$ of $CaS{O}_4\cdot 2H_{2}O$
$=5.81\times 83.3kJmo{l}^{-1}$
$=484kJmo{l}^{-1}$