How many hydrogen ions are present in `1ml` of a solution of `pH=13`?

Options

A. `6.02xx10^(13)`
B. `6.02xx10^(12)`
C. `6.02xx10^(7)`
D. `6.02xx10^(5)`

Explanation

To find the number of hydrogen ions present in 1 ml of a solution with a pH of 13, we can follow these steps:

### Step 1: Understand the pH scale
The pH scale is a measure of the hydrogen ion concentration in a solution. The formula to calculate the concentration of hydrogen ions \([H^+]\) from pH is given by:
\[ [H^+] = 10^{-\text{pH}} \]

### Step 2: Calculate the concentration of hydrogen ions
Given that the pH of the solution is 13, we can substitute this value into the formula:
\[ [H^+] = 10^{-13} \]
This means the concentration of hydrogen ions in the solution is \(10^{-13}\) moles per liter (M).

### Step 3: Convert the concentration to moles in 1 ml
Since we want to find the number of hydrogen ions in 1 ml of solution, we need to convert the concentration from liters to milliliters. There are 1000 ml in 1 liter, so:
\[ \text{Moles of } H^+ \text{ in 1 ml} = [H^+] \times \frac{1 \text{ ml}}{1000 \text{ ml}} = 10^{-13} \times \frac{1}{1000} = 10^{-16} \text{ moles} \]

### Step 4: Use Avogadro's number to find the number of ions
Avogadro's number (\(N_A\)) is \(6.022 \times 10^{23}\) entities (atoms, molecules, ions, etc.) per mole. To find the number of hydrogen ions in 1 ml, we multiply the number of moles by Avogadro's number:
\[ \text{Number of } H^+ \text{ ions} = 10^{-16} \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} \]

### Step 5: Calculate the final number of ions
Now we perform the multiplication:
\[ \text{Number of } H^+ \text{ ions} = 10^{-16} \times 6.022 \times 10^{23} = 6.022 \times 10^{7} \text{ ions} \]

### Final Answer
Thus, the number of hydrogen ions present in 1 ml of a solution with a pH of 13 is approximately \(6.022 \times 10^{7}\) ions.

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