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 becomes basic at 100°C, we can follow these steps:

### Step 1: Understand the Ion Product of Water (Kw)
At 100°C, the ion product of water (Kw) is given as:
\[ K_w = 5.6 \times 10^{-13} \]

### Step 2: Relate Kw to H⁺ and OH⁻ Concentrations
The ion product of water is defined as:
\[ K_w = [H^+][OH^-] \]
In a neutral solution, the concentrations of H⁺ and OH⁻ are equal:
\[ [H^+] = [OH^-] = x \]
Thus, we can express Kw as:
\[ K_w = x^2 \]

### Step 3: Solve for H⁺ Concentration
From the equation:
\[ x^2 = 5.6 \times 10^{-13} \]
We can find x (which represents the concentration of H⁺ ions):
\[ x = \sqrt{5.6 \times 10^{-13}} \]
Calculating this gives:
\[ x \approx 7.48 \times 10^{-7} \, \text{M} \]

### Step 4: Calculate the pH of Neutral Solution
The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the value of H⁺ concentration:
\[ \text{pH} = -\log(7.48 \times 10^{-7}) \]
Calculating this gives:
\[ \text{pH} \approx 6.13 \]

### Step 5: Determine the pH for Basic Solution
A solution is considered basic when its pH is greater than that of a neutral solution. Since the neutral pH at 100°C is approximately 6.13, any pH greater than this indicates a basic solution. Therefore, the pH must be greater than 6.13 for the solution to be basic.

### Conclusion
At 100°C, the solution will be basic if the pH is greater than approximately 6.13.

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