The ratio of acid strength of `HOCN` and `HCN` is about
Given `K_(a)` of `HOCN=1.2xx10^(-4) and K_(a)" of "HCN "=4.2 xx10^(-10)`

Options

A. `535:1`
B. `1:535`
C. `2.86xx10^(5):1`
D. `2.86xx10^(4):1`

Answer

To find the ratio of acid strength of HOCN and HCN, we will use the given dissociation constants (Ka) for both acids. The acid strength can be compared using the formula:

\[ \text{Acid Strength Ratio} = \left( \frac{K_{a, \text{HOCN}}}{K_{a, \text{HCN}}} \right)^{1/2} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- \( K_{a, \text{HOCN}} = 1.2 \times 10^{-4} \)
- \( K_{a, \text{HCN}} = 4.2 \times 10^{-10} \)

2. **Set up the ratio of the acid dissociation constants:**
\[ \frac{K_{a, \text{HOCN}}}{K_{a, \text{HCN}}} = \frac{1.2 \times 10^{-4}}{4.2 \times 10^{-10}} \]

3. **Perform the division:**
- First, divide the coefficients:
\[ \frac{1.2}{4.2} \approx 0.2857 \]
- Next, subtract the exponents:
\[ 10^{-4} \div 10^{-10} = 10^{(-4) - (-10)} = 10^{6} \]
- Combine the results:
\[ \frac{K_{a, \text{HOCN}}}{K_{a, \text{HCN}}} \approx 0.2857 \times 10^{6} = 2.857 \times 10^{5} \]

4. **Take the square root of the ratio:**
\[ \left( \frac{K_{a, \text{HOCN}}}{K_{a, \text{HCN}}} \right)^{1/2} \approx (2.857 \times 10^{5})^{1/2} \approx 535.0 \]

5. **Express the final ratio:**
- The ratio of the acid strengths of HOCN to HCN is approximately:
\[ 535 : 1 \]

### Final Answer:
The ratio of acid strength of HOCN to HCN is approximately **535:1**.