The dissociation constants of two acids `HA_(1)` and `HA_(2)` are `3.0xx10^(-4)` and `1.8xx10^(-5)` respectively. The relative strengths of the acids will be approximately

Options

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

Explanation

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

### Step 1: Identify the dissociation constants
The dissociation constants for the two acids are given as:
- \( K_a(HA_1) = 3.0 \times 10^{-4} \)
- \( K_a(HA_2) = 1.8 \times 10^{-5} \)

### Step 2: Understand the relationship between dissociation constant and 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 dissociates more in solution, producing more \( H^+ \) ions.

### Step 3: Calculate the relative strength
To find the relative strength of the two acids, we can use the formula:
\[ \text{Relative Strength} = \sqrt{\frac{K_a(HA_1)}{K_a(HA_2)}} \]
Substituting the values:
\[ \text{Relative Strength} = \sqrt{\frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}}} \]

### Step 4: Simplify the fraction
First, simplify the fraction inside the square root:
\[ \frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}} = \frac{3.0}{1.8} \times 10^{(-4) - (-5)} = \frac{3.0}{1.8} \times 10^{1} \]
Calculating \( \frac{3.0}{1.8} \):
\[ \frac{3.0}{1.8} \approx 1.6667 \]
So,
\[ \frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}} \approx 1.6667 \times 10^{1} = 16.667 \]

### Step 5: Take the square root
Now, take the square root of the result:
\[ \text{Relative Strength} \approx \sqrt{16.667} \approx 4.08 \]

### Conclusion
The relative strength of the acids \( HA_1 \) and \( HA_2 \) is approximately \( 4.08 \). This means that \( HA_1 \) is about 4 times stronger than \( HA_2 \).