Question

Consider following gases and their respective $K_H$ values (Henry's constant) at different values of temperature. In reference to these values identify correct statement/s regarding solubility of these gases in water:

Gas	Temperature/K	$K_H$/kbar	Gas	Temperature/K	$K_H$/kbar
He	293	144.97	Argon	298	40.3
H$_2$	293	69.16	CO$_2$	298	1.67
N$_2$	293	76.48	Formaldehyde	298	1.83×10$^{-5}$
N$_2$	303	88.84
O$_2$	293	34.86	Methane	298	0.413
O$_2$	303	46.82	Vinyl chloride	298	0.611

• A. Solubility of gases decreases with increase in temperature
• B. Solubility of gases increases with increase with pressure
• C. $CH_{4(g)}$ is more soluble in water than $CO_{2(g)}$ but less soluble than $HCHO_{(g)}$
• D. Henry's constant $K_H$ depends upon nature of the gas, temperature and the solvent

Answer 1

Answer: (A), (B), (C), (D)

All statements are correct.

Answer 2

Henry's Law states that the partial pressure of a gas in the vapor phase ($p$) is proportional to the mole fraction of the gas in the solution ($x$), given by $p = K_H \cdot x$. Solubility can be represented by the mole fraction $x = p / K_H$. For a given partial pressure, solubility is inversely proportional to Henry's constant ($K_H$).

Statement 1: Solubility of gases decreases with increase in temperature.
From the table, for N$_2$, $K_H$ increases from 76.48 kbar at 293 K to 88.84 kbar at 303 K. For O$_2$, $K_H$ increases from 34.86 kbar at 293 K to 46.82 kbar at 303 K. Since solubility is inversely proportional to $K_H$, an increase in $K_H$ with temperature indicates a decrease in solubility with temperature. This statement is correct.

Statement 2: Solubility of gases increases with increase with pressure.
According to Henry's Law, $x = p / K_H$. For a given temperature and gas (constant $K_H$), the mole fraction $x$ (solubility) is directly proportional to the partial pressure $p$ of the gas. Therefore, increasing the pressure increases the solubility. This statement is correct.

Statement 3: $CH_{4(g)}$ is more soluble in water than $CO_{2(g)}$ but less soluble than $HCHO_{(g)}$.
At 298 K, the $K_H$ values are: $K_H(CH_4) = 0.413$ kbar, $K_H(CO_2) = 1.67$ kbar, $K_H(HCHO) = 1.83 \times 10^{-5}$ kbar.
Comparing the $K_H$ values: $K_H(HCHO) < K_H(CH_4) < K_H(CO_2)$.
Since solubility is inversely proportional to $K_H$, the order of solubility is: Solubility($HCHO$) > Solubility($CH_4$) > Solubility($CO_2$).
This means $CH_4$ is more soluble than $CO_2$ and less soluble than $HCHO$. This statement is correct.

Statement 4: Henry's constant $K_H$ depends upon nature of the gas, temperature and the solvent.
The table shows different $K_H$ values for different gases (e.g., He, H$_2$, N$_2$, O$_2$ at 293 K), indicating dependence on the nature of the gas. The table also shows different $K_H$ values for the same gas (N$_2$ or O$_2$) at different temperatures, indicating dependence on temperature. Henry's constant is also known to depend on the nature of the solvent, although the table only provides data for water. This statement is correct.

All four statements are correct.