`K_(H)` value for Ar(g),CO(g), HCHO(g) and `CH_(4)(g)` are 40.39 , 1.67 ,`1.83xx10^(-5)` and 0.413 respectively. Arrange these gases in the order of their increastively solubility.

Options

A. HCHO lt `CH_4` lt `CO_2` lt Ar
B. HCHO lt `CO_2 lt CH_4 lt Ar`
C. `Ar lt CO_2 lt CH_4 lt HCHO`
D. `Ar lt CH_4 lt CO_2 lt HCHO`

Explanation

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

### Step 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 relationship can be expressed as:
\[ P = K_H \cdot x \]
Where:
- \( P \) = partial pressure of the gas
- \( K_H \) = Henry's law constant
- \( x \) = solubility of the gas

From this equation, we can infer that:
\[ K_H \propto \frac{1}{x} \]
This means that a higher \( K_H \) value indicates lower solubility, and a lower \( K_H \) value indicates higher solubility.

### Step 2: List the Given K_H Values
The K_H values for the gases are:
- Ar(g): 40.39
- CO(g): 1.67
- HCHO(g): \( 1.83 \times 10^{-5} \)
- CH4(g): 0.413

### Step 3: Arrange K_H Values in Ascending Order
To find the order of increasing solubility, we first arrange the K_H values from lowest to highest:
1. HCHO(g): \( 1.83 \times 10^{-5} \) (lowest)
2. CO(g): 1.67
3. CH4(g): 0.413
4. Ar(g): 40.39 (highest)

### Step 4: Determine the Order of Increasing Solubility
Since solubility is inversely proportional to K_H, we can now determine the order of increasing solubility by reversing the order of K_H values:
1. HCHO(g) (highest solubility)
2. CO(g)
3. CH4(g)
4. Ar(g) (lowest solubility)

### Final Order of Increasing Solubility
Thus, the order of increasing solubility of the gases is:
**HCHO(g) < CO(g) < CH4(g) < Ar(g)**

### Step 5: Write the Final Answer
The final answer, arranged in order of increasing solubility, is:
**HCHO, CO, CH4, Ar**