Number of hydrogen ions present in 10 millionth part of `1.33 cm^(3)` of pure water at `25^(@)C` is

Options

A. 6.023 million
B. 60 million
C. 8.01 million
D. 80.23 million

Explanation

To find the number of hydrogen ions present in 10 millionth part of 1.33 cm³ of pure water at 25°C, we can follow these steps:

### Step 1: Calculate the volume of water in liters
Given that we have 1.33 cm³ of water, we first need to convert this volume into liters.

1 cm³ = 1 mL, so:
\[ 1.33 \, \text{cm}^3 = 1.33 \, \text{mL} = 1.33 \times 10^{-3} \, \text{L} \]

Now, we need to find 10 millionth part of this volume:
\[ \text{Volume} = \frac{1.33 \times 10^{-3} \, \text{L}}{10^7} = 1.33 \times 10^{-10} \, \text{L} \]

### Step 2: Determine the concentration of hydrogen ions
At 25°C, the concentration of hydrogen ions \([H^+]\) in pure water is:
\[ [H^+] = 10^{-7} \, \text{mol/L} \]

### Step 3: Calculate the number of moles of hydrogen ions in the given volume
To find the number of moles of hydrogen ions in the calculated volume, we use the formula:
\[ \text{Moles of } H^+ = [H^+] \times \text{Volume} \]
Substituting the values:
\[ \text{Moles of } H^+ = 10^{-7} \, \text{mol/L} \times 1.33 \times 10^{-10} \, \text{L} \]
\[ \text{Moles of } H^+ = 1.33 \times 10^{-17} \, \text{mol} \]

### Step 4: Convert moles to number of hydrogen ions
To find the number of hydrogen ions, we use Avogadro's number (\(6.022 \times 10^{23} \, \text{ions/mol}\)):
\[ \text{Number of } H^+ = \text{Moles of } H^+ \times N_A \]
\[ \text{Number of } H^+ = 1.33 \times 10^{-17} \, \text{mol} \times 6.022 \times 10^{23} \, \text{ions/mol} \]
\[ \text{Number of } H^+ \approx 8.01 \times 10^{6} \, \text{ions} \]

### Final Answer
The number of hydrogen ions present in 10 millionth part of 1.33 cm³ of pure water at 25°C is approximately \(8.01 \times 10^{6}\) ions.

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