At certain temperature the `K_(w)` of `D_(2)`O is `10^(=-16)` M. Then the pH of pure `D_(2)`O at that temperature is

Options

A. 7
B. 16
C. 8
D. 6

Answer

To find the pH of pure D₂O (heavy water) at a given temperature where the ion product of water (K_w) is \(10^{-16}\) M, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ion Product of Water (K_w)**:
The ion product of water is defined as:
\[ K_w = [H^+][OH^-] \]
In pure water, the concentration of hydrogen ions \([H^+]\) is equal to the concentration of hydroxide ions \([OH^-]\).

2. **Set Up the Equation**:
Since \([H^+] = [OH^-]\) in pure D₂O, we can denote this concentration as \(x\). Therefore, we can rewrite \(K_w\) as:
\[ K_w = x \cdot x = x^2 \]
Given that \(K_w = 10^{-16}\) M, we can substitute this into the equation:
\[ x^2 = 10^{-16} \]

3. **Solve for x**:
To find \(x\), we take the square root of both sides:
\[ x = \sqrt{10^{-16}} = 10^{-8} \text{ M} \]
This means that \([H^+] = 10^{-8} \text{ M}\).

4. **Calculate the pH**:
The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
Substituting the value of \([H^+]\):
\[ pH = -\log(10^{-8}) = 8 \]

### Final Answer:
The pH of pure D₂O at that temperature is **8**.

---