At what pH at `100^(@) C`, the solution will be basic `(K_(w) " at " 100^(@) C " is " 5.6 xx 10^(-13))`

Options

A. `6.02`
B. `6.56`
C. `5.4`
D. `5.9`

Explanation

To determine the pH at which a solution is basic at 100°C, we start with the dissociation constant of water (Kw) at that temperature, which is given as \(5.6 \times 10^{-13}\).

### Step-by-Step Solution:

1. **Understand the relationship between Kw and pH**:
The dissociation of water can be represented as:
\[ H_2O \rightleftharpoons H^+ + OH^- \]
The equilibrium constant for this reaction is given by:
\[ K_w = [H^+][OH^-] \]
At any temperature, for pure water, the concentrations of \(H^+\) and \(OH^-\) are equal:
\[ [H^+] = [OH^-] \]
Therefore, we can express \(K_w\) as:
\[ K_w = [H^+]^2 \]

2. **Calculate the concentration of \(H^+\)**:
From the expression for \(K_w\):
\[ [H^+]^2 = K_w \]
Taking the square root gives:
\[ [H^+] = \sqrt{K_w} = \sqrt{5.6 \times 10^{-13}} \]

3. **Calculate the value**:
\[ [H^+] = \sqrt{5.6 \times 10^{-13}} \approx 7.48 \times 10^{-7} \, \text{mol/L} \]

4. **Calculate the pH**:
The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
Substituting the value we found:
\[ pH = -\log(7.48 \times 10^{-7}) \approx 6.125 \]

5. **Determine the pH for a basic solution**:
A solution is considered basic when its pH is greater than the neutral pH. Since we calculated the neutral pH at 100°C to be approximately 6.125, a basic solution will have:
\[ pH > 6.125 \]

### Final Answer:
The solution will be basic at a pH greater than 6.125 at 100°C.