Question

The K_H value (K bar) of Argon (I), Carbondioxide (II) formuldehyde (III) and methane (IV) are respectively 40.3, 167, 1.83×10^-5 and 0.413 at 298 K. The increasing order of solubility of gas in liquid is

• A. I < II < IV < III
• B. III < IV < II < I
• C. I < III < II < IV
• D. I < IV < II < III

Answer 1

The Correct Option is A

Given the Henry's law constant (\( K_H \)) values (in bar) for the gases:
Argon (I): 40.3
Carbon dioxide (II): 1.67
Formaldehyde (III): \( 1.83 \times 10^{-5} \)
Methane (IV): 0.413

According to Henry's law, the solubility of a gas in a liquid is inversely proportional to its \( K_H \) value. Hence, the solubility increases as \( K_H \) decreases.

Argon (I) has the highest \( K_H \) value, so it has the lowest solubility.
Carbon dioxide (II) has a moderate \( K_H \) value, so it has a moderate solubility.
Formaldehyde (III) has the lowest \( K_H \) value, so it has the highest solubility.
Methane (IV) has a \( K_H \) value higher than formaldehyde but lower than argon, so its solubility lies between carbon dioxide and argon.

Therefore, the increasing order of solubility is:
\( \text{I} < \text{IV} < \text{II} < \text{III} \)

The correct answer is (A) : I < II < IV < III.

Answer 2

1. Recall Henry's Law
Henry's Law states: $p = K_H c$, where $p$ is the partial pressure, $K_H$ is Henry's constant, and $c$ is the concentration (solubility). We can rearrange this to $c = \frac{p}{K_H}$. This means that solubility ($c$) is inversely proportional to $K_H$.

2. Analyze the given $K_H$ values
We are given the following $K_H$ values in K bar at 298 K:

Argon (I): 40.3
Carbon dioxide (II): 1.67
Formaldehyde (III): 1.83 x 10^-5 = 0.0000183
Methane (IV): 0.413

3. Determine the order of $K_H$ values
Arranging the $K_H$ values in increasing order:
III < IV < II < I
(0.0000183 < 0.413 < 1.67 < 40.3)

4. Determine the order of solubility
Since solubility is inversely proportional to $K_H$, the order of solubility will be the reverse of the order of $K_H$ values. Thus, the order of solubility is:
I < II < IV < III

5. Compare with the given options
Comparing the derived order of solubility (I < II < IV < III) with the options, we find that it matches option (A).

Final Answer:
(A) I < II < IV < III