What is the pH of a ` 10^(-4)` M ,MOH solution at 330K, if , if ` K_(w)` at 330 is ` 10^(-13.6)` ?

Options

A. 4
B. `9.0`
C. 10
D. `9.6`

Explanation

To find the pH of a `10^(-4)` M MOH solution at 330 K, given that `K_w` at this temperature is `10^(-13.6)`, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between pH, pOH, and pKw**:
\[ pK_w = pH + pOH \]
Rearranging gives:
\[ pH = pK_w - pOH \]

2. **Calculate pK_w**:
Given that \( K_w = 10^{-13.6} \),
\[ pK_w = -\log(K_w) = -\log(10^{-13.6}) = 13.6 \]

3. **Determine the concentration of OH⁻ ions**:
Since MOH is a strong base, it dissociates completely in solution:
\[ MOH \rightarrow M^+ + OH^- \]
Therefore, the concentration of OH⁻ ions is equal to the concentration of the MOH solution:
\[ [OH^-] = 10^{-4} \, M \]

4. **Calculate pOH**:
Using the concentration of OH⁻ ions:
\[ pOH = -\log([OH^-]) = -\log(10^{-4}) = 4 \]

5. **Calculate pH**:
Now, substitute the values of pK_w and pOH into the rearranged equation:
\[ pH = pK_w - pOH = 13.6 - 4 = 9.6 \]

### Final Answer:
The pH of the `10^(-4)` M MOH solution at 330 K is **9.6**.

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