The hydroxide ion concentration of a wine is `8xx10^(-11)` M. What is the pH of the wine?

Options

A. `2.10`
B. `2.9`
C. `3.9`
D. `4.9`

Answer

To find the pH of the wine given the hydroxide ion concentration, we can follow these steps:

### Step 1: Calculate pOH
We start with the hydroxide ion concentration, which is given as \( [OH^-] = 8 \times 10^{-11} \, \text{M} \).

To find the pOH, we use the formula:
\[ pOH = -\log[OH^-] \]

Substituting the value:
\[ pOH = -\log(8 \times 10^{-11}) \]

### Step 2: Simplify the logarithm
Using the properties of logarithms, we can separate the terms:
\[ pOH = -\log(8) - \log(10^{-11}) \]
\[ pOH = -\log(8) + 11 \]

The logarithm of 8 can be approximated as:
\[ \log(8) \approx 0.903 \]

Thus, we can substitute this value:
\[ pOH = -0.903 + 11 \]
\[ pOH = 10.097 \]

### Step 3: Calculate pH
Now that we have the pOH, we can find the pH using the relationship:
\[ pH + pOH = 14 \]

Rearranging gives us:
\[ pH = 14 - pOH \]
Substituting the value of pOH:
\[ pH = 14 - 10.097 \]
\[ pH \approx 3.903 \]

### Step 4: Round the pH value
Rounding this to one decimal place, we get:
\[ pH \approx 3.9 \]

### Final Answer
The pH of the wine is approximately **3.9**.

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