The number of hydrogen ions in 10 ml of a solution with pH=13 is

Options

A. `10^(13)`
B. `6.023 xx 10^8`
C. `6.023 xx 10^(10)`
D. `6.023 xx 10^(13)`

Answer

To find the number of hydrogen ions in 10 ml of a solution with a pH of 13, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Volume from ml to Liters**:
- Given volume = 10 ml
- To convert ml to liters:
\[ \text{Volume in liters} = \frac{10 \text{ ml}}{1000} = 0.01 \text{ L} \]

2. **Use the pH to Find the Concentration of Hydrogen Ions**:
- The formula relating pH to hydrogen ion concentration \([H^+]\) is:
\[ \text{pH} = -\log[H^+] \]
- Given pH = 13, we can rearrange the formula:
\[ 13 = -\log[H^+] \]
- This implies:
\[ -13 = \log[H^+] \]
- Converting from logarithmic form to exponential form:
\[ [H^+] = 10^{-13} \text{ M} \]

3. **Calculate the Number of Moles of Hydrogen Ions**:
- We know that concentration (Molarity) is defined as:
\[ \text{Concentration} = \frac{\text{moles}}{\text{volume in liters}} \]
- Rearranging gives us:
\[ \text{moles} = \text{Concentration} \times \text{Volume} \]
- Substituting the values:
\[ \text{moles of } H^+ = 10^{-13} \text{ M} \times 0.01 \text{ L} = 10^{-13} \times 10^{-2} = 10^{-15} \text{ moles} \]

4. **Calculate the Number of Hydrogen Ions**:
- To find the number of ions, we use Avogadro's number (\(6.022 \times 10^{23}\) ions/mole):
\[ \text{Number of } H^+ \text{ ions} = \text{moles} \times \text{Avogadro's number} \]
- Substituting the values:
\[ \text{Number of } H^+ \text{ ions} = 10^{-15} \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} \]
- This gives:
\[ \text{Number of } H^+ \text{ ions} = 6.022 \times 10^{8} \text{ ions} \]

### Final Answer:
The number of hydrogen ions in 10 ml of a solution with pH = 13 is approximately:
\[ \boxed{6.022 \times 10^{8} \text{ ions}} \]