Question

${CuSO}_{4^{.}}{5H}_{2}O\left(s\right)\rightleftharpoons {CuSO}_{4^{.}}{3H}_{2}O\left(s\right)+2H_{2}O\left(g\right)$
$K_p=4\times {10}^{-4}{atm}^2$ and vapour pressure of water is $22.4$ torr at $298$ K. Then find out relative humidity.

• A. $74.46$%
• B. $78.65$%
• C. $67.85$%
• D. $70.46$%

Answer 1

The correct option is C $67.85$%

Given

$Kp=4\ast {10}^{-4}at{m}^2$

Vapour pressure of water is 22.4 torr$=22.4/760=3\ast {10}^{-2}atm$

Solution

As in reaction only $H_{2}O$ is gas therefore

Kp= $p(H_{2}O{)}^2$

$p\left(H_{2}O\right)=(4\ast {10}^{-4}{)}^{\frac{1}{2}}$

$p\left(H_{2}O\right)=2\ast {10}^{-2}$atm

Relative Humidity= $\frac{p\left(H_{2}O\right)}{VP}$

$=\frac{2\ast {10}^{-2}}{3\ast {10}^{-2}}$=0.67=67.85%

The correct option is C