Calculate `[OH^(-)]` for a solution whose pH is 6.2

Answer

To calculate the hydroxide ion concentration \([OH^-]\) for a solution with a given pH of 6.2, we can follow these steps:

### Step 1: Calculate the \([H^+]\) concentration from pH
The pH is related to the hydrogen ion concentration \([H^+]\) by the formula:
\[ [H^+] = 10^{-\text{pH}} \]
Substituting the given pH value:
\[ [H^+] = 10^{-6.2} \]

### Step 2: Calculate \([H^+]\)
Using a calculator:
\[ [H^+] = 10^{-6.2} \approx 6.31 \times 10^{-7} \, \text{M} \]

### Step 3: Use the ion product of water to find \([OH^-]\)
The product of the concentrations of hydrogen ions and hydroxide ions at 25°C is given by:
\[ K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \]
We can rearrange this equation to find \([OH^-]\):
\[ [OH^-] = \frac{K_w}{[H^+]} \]

### Step 4: Substitute the values into the equation
Now substituting the values we have:
\[ [OH^-] = \frac{1.0 \times 10^{-14}}{6.31 \times 10^{-7}} \]

### Step 5: Calculate \([OH^-]\)
Performing the calculation:
\[ [OH^-] \approx 1.58 \times 10^{-8} \, \text{M} \]

### Final Answer
Thus, the hydroxide ion concentration \([OH^-]\) for a solution with a pH of 6.2 is approximately:
\[ [OH^-] \approx 1.58 \times 10^{-8} \, \text{M} \]

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