At some high temperature, `K_(w)` of water is `10^(-13)` Then the `P^(H)` of the water at the same temperature is

Options

A. `7.0`
B. `6.5`
C. `7.5`
D. `7.23`

Answer

To find the pH of water at a high temperature where the ionic product of water (Kw) is \(10^{-13}\), we can follow these steps:

### Step 1: Understand the Ionic Product of Water
The ionic product of water (\(K_w\)) is defined as:
\[ K_w = [H^+][OH^-] \]
For pure water, the concentration of hydrogen ions \([H^+]\) is equal to the concentration of hydroxide ions \([OH^-]\).

### Step 2: Set Up the Equation
Since \([H^+] = [OH^-]\) in pure water, we can express \(K_w\) as:
\[ K_w = [H^+]^2 \]

### Step 3: Substitute the Given Value of \(K_w\)
From the question, we know that:
\[ K_w = 10^{-13} \]
Thus, we can write:
\[ [H^+]^2 = 10^{-13} \]

### Step 4: Solve for \([H^+]\)
To find \([H^+]\), we take the square root of both sides:
\[ [H^+] = \sqrt{10^{-13}} = 10^{-6.5} \]

### Step 5: Calculate the pH
The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
Substituting the value of \([H^+]\):
\[ pH = -\log(10^{-6.5}) = 6.5 \]

### Conclusion
Therefore, the pH of water at this high temperature is:
\[ \text{pH} = 6.5 \]