The number of `H^(o+)` ions present in `1mL` of solution having `pH = 13` is

Options

A. `6.023 xx 10^(10)`
B. `6.023 xx 10^(7)`
C. `6.023 xx 10^(13)`
D. `10^(13)`

Explanation

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

### Step 1: Understand the relationship between pH and \( H^+ \) concentration
The pH of a solution is defined by the formula:
\[ \text{pH} = -\log[H^+] \]
Given that the pH is 13, we can set up the equation:
\[ -\log[H^+] = 13 \]

### Step 2: Solve for \( [H^+] \)
To find \( [H^+] \), we can rearrange the equation:
\[ \log[H^+] = -13 \]
Now, we take the antilogarithm (base 10) of both sides:
\[ [H^+] = 10^{-13} \text{ M} \]
This means the concentration of \( H^+ \) ions in the solution is \( 10^{-13} \) moles per liter.

### Step 3: Convert concentration to moles in 1 mL
Since we need to find the number of \( H^+ \) ions in 1 mL of solution, we first convert the concentration from moles per liter to moles per milliliter:
\[ \text{Concentration in mL} = 10^{-13} \text{ moles/L} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 10^{-16} \text{ moles/mL} \]

### Step 4: Calculate the number of \( H^+ \) ions
To find the number of \( H^+ \) ions in 1 mL, we multiply the number of moles by Avogadro's number (\( 6.022 \times 10^{23} \) ions/mole):
\[ \text{Number of } H^+ \text{ ions} = 10^{-16} \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} \]
Calculating this gives:
\[ \text{Number of } H^+ \text{ ions} = 6.022 \times 10^{7} \text{ ions} \]

### Final Answer
The number of \( H^+ \) ions present in 1 mL of solution with a pH of 13 is:
\[ 6.022 \times 10^{7} \text{ ions} \]

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