Question

A certain hydrate has the formula $MgS{O}_4.x{H}_{2}O.A$ quantity of 54.2 g of the compound is heated in an oven to drive off the water. if the steam generated exerts a pressure of 24.8 atm in a 2.0 L container at ${120}^{0}C$, calculate x.

• A. 2
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (D)

A certain of steam generated has following properties.

pressure=$P=24.8atm$ $valueV=2.0L$

Temperature $={120}^{0}C+273=393K$

$n=\frac{PV}{Rt}=\frac{24.8\times 2}{0.0821\times 393}=1.53mole.....\left(i\right)$

Amount of compound taken $=54.29$

Mole man of compound $(MgS{O}_4.x{H}_{2}O)$

$M=24+32+4\times 16+x\times 18$

$120+18x$

No.of mole of water $=\frac{54.2}{120+18x}......\left(ii\right)$

Comparing equation (i) and (ii)

$1.537=\frac{54.2}{120+18x}$

$184.47+27.67x=54.2x$

$184.47=26.53x$

$x=\frac{184.47}{26.53}=6.95\simeq 7$

Hence, the correct option is $D$