Calculate the number of H+ ion present in 1 mL of solution having pH = 13

To calculate the number of hydrogen ions (\( \text{H}^+ \)) present in a 1 mL solution with a pH of 13, we can follow these steps:

### Step-by-Step Solution

1. **Understand the pH Definition**:
   The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([\text{H}^+]\):
   \[
   \text{pH} = -\log_{10}([\text{H}^+])
   \]

2. **Find the Hydrogen Ion Concentration**:
   Given the pH is 13, we can find \([\text{H}^+]\) using the formula:
   \[
   [\text{H}^+] = 10^{-\text{pH}}
   \]

   For pH = 13:
   \[
   [\text{H}^+] = 10^{-13} \, \text{mol/L}
   \]

3. **Calculate the Number of Moles of \(\text{H}^+\) in 1 mL**:
   To find the number of moles of \(\text{H}^+\) in 1 mL (0.001 L) of the solution, multiply the concentration by the volume:
   \[
   \text{Moles of } \text{H}^+ = [\text{H}^+] \times \text{Volume} = 10^{-13} \, \text{mol/L} \times 0.001 \, \text{L}
   \]
   \[
   \text{Moles of } \text{H}^+ = 10^{-16} \, \text{mol}
   \]

4. **Convert Moles to Number of Ions**:
   To convert the moles of \(\text{H}^+\) to the number of ions, use Avogadro's number (\(6.022 \times 10^{23} \, \text{ions/mol}\)):
   \[
   \text{Number of } \text{H}^+ \text{ ions} = 10^{-16} \, \text{mol} \times 6.022 \times 10^{23} \, \text{ions/mol}
   \]

   Let's calculate this:

\[
\text{Number of } \text{H}^+ \text{ ions} = 6.022 \times 10^{23 - 16}
\]
\[
\text{Number of } \text{H}^+ \text{ ions} = 6.022 \times 10^7
\]

### Conclusion

There are approximately \(6.022 \times 10^7\) hydrogen ions (\(\text{H}^+\)) present in 1 mL of a solution with a pH of 13.

Would you like more details or have any questions?

### Related Questions:
1. How does pH affect the concentration of hydroxide ions (\(\text{OH}^-\)) in a solution?
2. What is the pH of a solution if it contains \(1 \times 10^{-7}\) mol/L of \(\text{H}^+\)?
3. How would the number of \(\text{H}^+\) ions change if the volume of the solution was increased to 10 mL?
4. What are the real-world applications of calculating hydrogen ion concentration in chemistry?
5. How does temperature affect the pH of a solution?

**Tip**: Remember that pH is a logarithmic scale; a change of 1 pH unit represents a tenfold change in hydrogen ion concentration.

Learn how to calculate the number of hydrogen ions (H+) in a 1 mL solution with pH 13 using logarithms and molarity concepts. Understand the pH scale and its relation to hydrogen ion concentration. Suitable for Grades 11-12.

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