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 1: Understand the relationship between pH and hydrogen ion concentration
The pH of a solution is defined as:
\[ \text{pH} = -\log[\text{H}^+] \]
Where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter (M).

### Step 2: Calculate the hydrogen ion concentration
Given that the pH is 13, we can rearrange the formula to find \([\text{H}^+]\):
\[ 13 = -\log[\text{H}^+] \]
To find \([\text{H}^+]\), we can take the antilogarithm:
\[ [\text{H}^+] = 10^{-13} \, \text{M} \]

### Step 3: Convert the concentration to moles in 10 ml
Since the concentration is given in moles per liter, we need to convert the volume from ml to liters:
\[ 10 \, \text{ml} = 0.010 \, \text{L} \]

Now, we can calculate the number of moles of hydrogen ions in 10 ml:
\[ \text{moles of } \text{H}^+ = [\text{H}^+] \times \text{Volume in L} \]
\[ \text{moles of } \text{H}^+ = 10^{-13} \, \text{mol/L} \times 0.010 \, \text{L} \]
\[ \text{moles of } \text{H}^+ = 10^{-13} \times 10^{-2} \]
\[ \text{moles of } \text{H}^+ = 10^{-15} \, \text{mol} \]

### Step 4: Calculate the number of hydrogen ions
To find the total number of hydrogen ions, we multiply the number of moles by Avogadro's number (\(6.022 \times 10^{23} \, \text{ions/mol}\)):
\[ \text{Number of } \text{H}^+ = \text{moles of } \text{H}^+ \times \text{Avogadro's number} \]
\[ \text{Number of } \text{H}^+ = 10^{-15} \, \text{mol} \times 6.022 \times 10^{23} \, \text{ions/mol} \]
\[ \text{Number of } \text{H}^+ = 6.022 \times 10^{8} \, \text{ions} \]

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

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