`K_(H)` value for `Ar(g),CO_(2)(g),HCHO(g)and CH_(4)(g)` are `40.39,1.67,1.83xx10^(-5)and0.413` respectively.
Arrange these gases in the order of their increasing solubility.

Options

A. `HCHOltCH_(4)ltCO_(2)ltAr`
B. `HCHOltCO_(2)ltCH_(4)ltAr`
C. `ArltCO_(2)ltCH_(4)ltHCHO`
D. `ArltCH_(4)ltCO_(2)ltHCHO`

Explanation

To solve the problem of arranging the gases Ar(g), CO₂(g), HCHO(g), and CH₄(g) in the order of their increasing solubility based on their Henry's law constants (K_H), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Henry's Law**:
Henry's law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The proportionality constant is known as Henry's law constant (K_H). A lower K_H value indicates higher solubility.

2. **List the Given K_H Values**:
- K_H for Ar(g) = 40.39
- K_H for CO₂(g) = 1.67
- K_H for HCHO(g) = 1.83 x 10⁻⁵ (which can be rewritten as 0.0000183)
- K_H for CH₄(g) = 0.413

3. **Convert K_H Values for Comparison**:
To compare the K_H values easily, we can rewrite them in a more comparable format:
- K_H for Ar(g) = 40.39
- K_H for CO₂(g) = 1.67
- K_H for HCHO(g) = 0.0000183
- K_H for CH₄(g) = 0.413

4. **Identify the Order of K_H Values**:
Now, we can arrange these K_H values in ascending order:
- HCHO(g): 0.0000183 (lowest K_H, highest solubility)
- CH₄(g): 0.413
- CO₂(g): 1.67
- Ar(g): 40.39 (highest K_H, lowest solubility)

5. **Conclusion**:
Based on the K_H values, we can conclude that the order of increasing solubility of the gases is:
HCHO(g) < CH₄(g) < CO₂(g) < Ar(g)

### Final Order of Increasing Solubility:
HCHO(g) < CH₄(g) < CO₂(g) < Ar(g)