Question

Henry’s constant (in $kbar$) for four gases $\alpha ,\beta ,\gamma$and $\mathrm{\delta }$ in water at $298K$ is given below:

	$\alpha$	$\beta$	$\gamma$	$\delta$
$K_H$	$50$	$2$	$2\times {10}^{-5}$	$0.5$

Density of water$={10}^{3}kg{m}^{-3}$ at $298\mathrm{K}$

This table implies that:

• A. Solubility of $\mathrm{\gamma }$ at $308\mathrm{K}$ is lower than at $298\mathrm{K}$
• B. The pressure of a $5.55$ molal solution of $\mathrm{\delta }$is $250\mathrm{bar}$
• C. $ɑ$has the highest solubility in water at given pressure
• D. The pressure of a $55.5$molal solution of $\mathrm{\gamma }$ is $1\mathrm{bar}$

Answer 1

The correct option is A

Solubility of $\mathrm{\gamma }$ at $308\mathrm{K}$ is lower than at $298\mathrm{K}$

Explanation for the correct options:

A) Solubility of $\mathrm{\gamma }$ at $308\mathrm{K}$ is lower than at $298\mathrm{K}$

According to Henry's law, $P=K_{H}x$.

In this equation,$K_H$ is temperature dependent. When the temperature increases the value $K_H$ increases, which leads to a decrease in the solubility. In option A $300K>298K$. Thus, solubility decreases.

Explanation for the incorrect options:

B) The pressure of a $5.55$ molal solution of $\mathrm{\delta }$is $250\mathrm{bar}$

Step1:

$K_H=0.5\times {10}^3$

Molality of the solution = $55.5$

Step2:

$P=\frac{0.5\times {10}^3\times 55.5}{55.5+1000/18}$;

$P=249bar$

C) $ɑ$has the highest solubility in water at given pressure

The gas $\alpha$ has the highest $K_H$ value, the gas will have the lowest solubility according to the Henry's law$(P=K_{H}x)$

D) The pressure of a $55.5$molal solution of $\mathrm{\gamma }$ is $1\mathrm{bar}$

Step 1:

$K_H=2\times {10}^{-5}$ ,

Molality of the solution = $55.5$

Step 2:

$P=2\times {10}^{-5}\times \frac{55.5}{55.5}+\frac{1000}{18}$;

$P=2\times {10}^{-2}bar$

Thus, option A) is correct.