If the dissociation constant of HCN is `1.3 xx 10^(-9)` the value of hydrolysis constant of HCN will be

Options

A. `1.3 xx 10^(-9)`
B. `10^(-14)`
C. `7.7 xx 10^(-5)`
D. `0.77 xx 10^(-5)`

Answer

To find the hydrolysis constant (\(K_h\)) of HCN given its dissociation constant (\(K_a\)), we can use the relationship between these constants. Here’s the step-by-step solution:

### Step 1: Understand the relationship between \(K_h\) and \(K_a\)
The hydrolysis constant (\(K_h\)) for a weak acid can be calculated using the formula:
\[ K_h = \frac{K_w}{K_a} \]
where:
- \(K_w\) is the ion product of water, which is \(1.0 \times 10^{-14}\) at 25°C.
- \(K_a\) is the dissociation constant of the weak acid.

### Step 2: Identify the values
From the question, we have:
- \(K_a = 1.3 \times 10^{-9}\)
- \(K_w = 1.0 \times 10^{-14}\)

### Step 3: Substitute the values into the formula
Now, substituting the values into the formula for \(K_h\):
\[ K_h = \frac{1.0 \times 10^{-14}}{1.3 \times 10^{-9}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ K_h = \frac{1.0}{1.3} \times 10^{-14 + 9} = \frac{1.0}{1.3} \times 10^{-5} \]
Calculating \(\frac{1.0}{1.3}\):
\[ \frac{1.0}{1.3} \approx 0.769 \]
Thus,
\[ K_h \approx 0.769 \times 10^{-5} = 0.769 \times 10^{-5} \]

### Step 5: Round off the result
Rounding \(0.769 \times 10^{-5}\) gives:
\[ K_h \approx 0.77 \times 10^{-5} \]

### Conclusion
The value of the hydrolysis constant (\(K_h\)) for HCN is approximately \(0.77 \times 10^{-5}\).