The dissociation constant of two acids ` HA_(1) " and " HA_(2)` are ` 3.14 xx 10^(-4) " and " 1.96 xx 10^(-5)` respectively . The relative strength of the acids will be approximately

Options

A. `1:4 `
B. `4:1`
C. ` 1: 16`
D. `16 : 1`

Explanation

To determine the relative strength of the two acids \( HA_1 \) and \( HA_2 \) based on their dissociation constants (\( K_a \)), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given dissociation constants**:
- For \( HA_1 \): \( K_{a1} = 3.14 \times 10^{-4} \)
- For \( HA_2 \): \( K_{a2} = 1.96 \times 10^{-5} \)

2. **Understand the relationship between \( K_a \) and acid strength**:
- The strength of an acid is directly related to its dissociation constant \( K_a \). A higher \( K_a \) value indicates a stronger acid because it means the acid dissociates more in solution.

3. **Calculate the ratio of the dissociation constants**:
- To find the relative strength of the acids, we can calculate the ratio of their dissociation constants:
\[ \text{Relative Strength} = \frac{K_{a1}}{K_{a2}} = \frac{3.14 \times 10^{-4}}{1.96 \times 10^{-5}} \]

4. **Perform the division**:
- First, calculate the numerical part:
\[ \frac{3.14}{1.96} \approx 1.60 \]
- Next, handle the powers of ten:
\[ \frac{10^{-4}}{10^{-5}} = 10^{1} = 10 \]
- Now combine the two results:
\[ \text{Relative Strength} \approx 1.60 \times 10 \approx 16 \]

5. **Express the result in terms of a ratio**:
- The relative strength of the acids can be expressed as:
\[ \text{Relative Strength} \approx 16:1 \]

6. **Conclusion**:
- Therefore, the relative strength of the acids \( HA_1 \) and \( HA_2 \) is approximately \( 16:1 \).