The value of Henry's law constant for some gases at 293 K is given below. Arrange the gases in the increasing order of their solubility .
He:144.97 kbar, `H_2`:69.16 kbar, `N_2`:76.48 kbar, `O_2`: 34.86 kbar

Options

A. `He lt N_2 lt H_2 lt O_2`
B. `O_2 lt H_2 lt N_2 lt He`
C. `H_2 lt N_2 lt O_2 lt He`
D. `He lt O_2 lt N_2 lt H_2`

Explanation

To solve the problem of arranging the gases in increasing order of their solubility based on the provided Henry's law constants, we can follow these steps:

### Step 1: Understand Henry's Law
Henry's law states that the amount of gas that dissolves in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid. Mathematically, it can be expressed as:
\[ C = k_H \cdot P \]
where:
- \( C \) = concentration of the gas in the solution (solubility)
- \( k_H \) = Henry's law constant (higher values indicate lower solubility)
- \( P \) = partial pressure of the gas

### Step 2: Analyze the Given Data
We have the following Henry's law constants for the gases at 293 K:
- Helium (He): 144.97 kbar
- Hydrogen (H₂): 69.16 kbar
- Nitrogen (N₂): 76.48 kbar
- Oxygen (O₂): 34.86 kbar

### Step 3: Determine the Solubility Order
Since the solubility is inversely proportional to the Henry's law constant (\( k_H \)), we can determine the order of solubility by looking at the values of \( k_H \):
- Higher \( k_H \) means lower solubility.
- Lower \( k_H \) means higher solubility.

Now, let's arrange the gases based on their \( k_H \) values:
1. O₂: 34.86 kbar (lowest \( k_H \), highest solubility)
2. H₂: 69.16 kbar
3. N₂: 76.48 kbar
4. He: 144.97 kbar (highest \( k_H \), lowest solubility)

### Step 4: Final Arrangement
Based on the analysis, the increasing order of solubility of the gases is:
\[ \text{He} < \text{N}_2 < \text{H}_2 < \text{O}_2 \]

### Conclusion
Thus, the final answer is:
- Helium (He) has the lowest solubility.
- Nitrogen (N₂) has a moderate solubility.
- Hydrogen (H₂) has a higher solubility.
- Oxygen (O₂) has the highest solubility.