At some high temperature the value of `K_(w)` is equal to `10^(-12) M^(2)`. Calculate the `H^(+)` ion concentration of water at same temperature is

Options

A. `10^(-12) M`
B. `10^(-8) M`
C. `10^(-7) M`
D. `10^(-6) M`

Explanation

To solve the problem, we need to find the concentration of hydrogen ions \([H^+]\) in water when the ionic product of water \(K_w\) is given as \(10^{-12} \, M^2\).

### Step-by-Step Solution:

1. **Understand the Ionic Product of Water**:
The ionic product of water (\(K_w\)) is defined as:
\[ K_w = [H^+][OH^-] \]
where \([H^+]\) is the concentration of hydrogen ions and \([OH^-]\) is the concentration of hydroxide ions.

2. **Neutrality of Water**:
In pure water, the concentration of hydrogen ions is equal to the concentration of hydroxide ions:
\[ [H^+] = [OH^-] \]

3. **Substituting into the Ionic Product Expression**:
Since \([H^+] = [OH^-]\), we can denote the concentration of hydrogen ions as \(x\):
\[ K_w = [H^+][OH^-] = x \cdot x = x^2 \]

4. **Setting Up the Equation**:
Given \(K_w = 10^{-12} \, M^2\), we can write:
\[ x^2 = 10^{-12} \]

5. **Solving for \(x\)**:
To find \(x\), we take the square root of both sides:
\[ x = \sqrt{10^{-12}} = 10^{-6} \, M \]

6. **Conclusion**:
Therefore, the concentration of hydrogen ions \([H^+]\) in water at this temperature is:
\[ [H^+] = 10^{-6} \, M \]

### Final Answer:
The concentration of \(H^+\) ion in water at the given temperature is \(10^{-6} \, M\).

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