Given below are the dissociation constant values of few acids. Arrange them in order of increasing acidic strength.
`H_(2)SO_(3)=1.3xx10^(-2),HNO_(2)=4xx10^(-4)`
`CH_(3)COOH=1.8xx10^(-5),HCN=4xx10^(-10)`

Options

A. a. `HCNltCH_(3)COOHltHNO_(2)ltH_(2)SO_(3)`
B. b. `CH_(3)COOHltHNO_(2)ltHCNltH_(2)SO_(3)`
C. c.`CH_(3)COOHltHCNltH_(2)SO_(3)ltHNO_(2)`
D. d.`HNO_(2)ltH_(2)SO_(3)ltCH_(3)COOHltHCN`

Explanation

To arrange the given acids in order of increasing acidic strength based on their dissociation constant values (Ka), we can follow these steps:

### Step 1: Understand the concept of acid dissociation constant (Ka)
The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. A higher Ka value indicates a stronger acid, as it means the acid dissociates more completely in solution.

### Step 2: List the given dissociation constant values
We have the following dissociation constant values for the acids:
- \( H_2SO_3 = 1.3 \times 10^{-2} \)
- \( HNO_2 = 4 \times 10^{-4} \)
- \( CH_3COOH = 1.8 \times 10^{-5} \)
- \( HCN = 4 \times 10^{-10} \)

### Step 3: Compare the Ka values
To arrange the acids in order of increasing acidic strength, we need to compare their Ka values. The smaller the Ka value, the weaker the acid.

1. \( HCN = 4 \times 10^{-10} \) (smallest Ka, weakest acid)
2. \( CH_3COOH = 1.8 \times 10^{-5} \)
3. \( HNO_2 = 4 \times 10^{-4} \)
4. \( H_2SO_3 = 1.3 \times 10^{-2} \) (largest Ka, strongest acid)

### Step 4: Arrange in order of increasing acidic strength
Based on the comparison, we can arrange the acids from weakest to strongest:
- \( HCN < CH_3COOH < HNO_2 < H_2SO_3 \)

### Final Answer
The order of increasing acidic strength is:
\[ HCN < CH_3COOH < HNO_2 < H_2SO_3 \]