Question

Concrete is produced from a mixture of cement, water and small stones. Small amount of gypsum, $CaSO _4 \cdot 2 H _2 O$ 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
$CaSO _4 \cdot \frac{1}{2} H _2 O$ according to reaction,
$CaSO _4 \cdot 2 H _2 O ( s ) \rightarrow CaSO _4 \cdot \frac{1}{2} H _2 O ( s )+\frac{3}{2} H _2 O ( g )$
The $\Delta_f H^{\ominus} $ of$ CaSO _4 \cdot 2 H _2 O ( s ), CaSO _4 \cdot \frac{1}{2} H _2 O ( s ), H _2 O ( g )$ are $-2021.0\, kJ \,mol ^{-1},-1575.0\, kJ \,mol ^{-1}$ and $-241.8 \,kJ \,mol ^{-1}$ respectively. The respective values of their standard entropies are $194.0,130.0$ and $188.0 \,J K ^{-1} \,mol ^{-1}$. The values of $R=8.314 \,J K ^{-1}\, mol ^{-1}=0.0831\, L\, bar\, mol ^{-1} \,K ^{-1}$
Answer the following questions on the basis of above information
Heat change occurring during conversion of $1 \,kg$ of $CaSO _4 \cdot 2 H _2 O ( s )\left(\right.$ molar mass $\left.{172 \,g \,mol ^{-1}}\right)$ of $_{ CaSO _4}$. $\frac{1}{2} H _2 O ( s )$ is equal to

• A. $484\, kJ \, mol ^{-1}$
• B. $400 \,kJ$
• C. $-484.0 \,kJ ,mol ^{-1}$
• D. $-1000 \,kJ$

Answer 1

Answer: (A)

$\Delta H^{\ominus}=\Delta H_P^{\ominus}-\Delta H_R^{\ominus} ;($ for $1 mol )$
$=\left[-1575.0\, kJ\, mol ^{-1}-\frac{3}{2} \times 241.8\right]$
$-\left[-2021.0 \, kJ \, mol ^{-1}\right]$
$=+83.3\, kJ\, mol^{-1}$
For $1 \, kg CaSO { }_4 \cdot 2 H _2 O$
Number of moles $=\frac{1000}{172}=5.81$
$\therefore$ Heat change for $5.81 mol$ of $CaSO _4 \cdot 2 H _2 O$
$=5.81 \times 83.3\, kJ \, mol^{-1}$
$=484 \, kJ \, mol ^{-1}$