The number of hydroxyl ions in 100 mL of a solution having pH 10 is

Options

A. `1 xx 10^(4)`
B. `3.012 xx 10^(4)`
C. `6.02 xx 10^(18)`
D. `6.023 xx 10^(19)`

Answer

To solve the problem of finding the number of hydroxyl ions (OH⁻) in 100 mL of a solution with a pH of 10, we can follow these steps:

### Step-by-Step Solution:

1. **Understand pH Definition**:
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter.

2. **Calculate [H⁺] from pH**:
Given that the pH is 10, we can find the concentration of hydrogen ions:
\[ [H^+] = 10^{-\text{pH}} = 10^{-10} \text{ moles per liter} \]

3. **Use the Ion Product of Water**:
At 25°C, the product of the concentrations of hydrogen ions and hydroxyl ions is constant:
\[ [H^+][OH^-] = 10^{-14} \]
We can rearrange this to find \([OH^-]\):
\[ [OH^-] = \frac{10^{-14}}{[H^+]} = \frac{10^{-14}}{10^{-10}} = 10^{-4} \text{ moles per liter} \]

4. **Convert to 100 mL**:
Since we need the concentration in 100 mL, we convert the concentration from moles per liter to moles per 100 mL:
\[ \text{Moles of } OH^- = [OH^-] \times \text{Volume in liters} = 10^{-4} \times \frac{100}{1000} = 10^{-5} \text{ moles} \]

5. **Calculate the Number of Hydroxyl Ions**:
To find the number of hydroxyl ions, we use Avogadro's number (\(6.022 \times 10^{23}\) ions per mole):
\[ \text{Number of } OH^- \text{ ions} = 10^{-5} \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} = 6.022 \times 10^{18} \text{ ions} \]

### Final Answer:
The number of hydroxyl ions in 100 mL of a solution having pH 10 is:
\[ 6.022 \times 10^{18} \text{ OH}^- \text{ ions} \]