Calculate how many Hions are present in one millionth part of 1 mL of pure waler. The ionic product of water is `1 xx 10^(-14)("mol/L") ?`

Answer

To solve the problem of calculating how many H⁺ ions are present in one millionth part of 1 mL of pure water, we can follow these steps:

### Step 1: Understand the Ionic Product of Water
The ionic product of water (Kw) is given as:
\[ K_w = [H^+][OH^-] = 1 \times 10^{-14} \, \text{mol/L} \]

In pure water, the concentration of H⁺ ions is equal to the concentration of OH⁻ ions. Therefore, we can say:
\[ [H^+] = [OH^-] = \sqrt{K_w} \]

### Step 2: Calculate the Concentration of H⁺ Ions
Using the value of Kw:
\[ [H^+] = \sqrt{1 \times 10^{-14}} = 1 \times 10^{-7} \, \text{mol/L} \]

### Step 3: Convert the Volume from mL to Liters
Since we need to calculate the number of H⁺ ions in one millionth part of 1 mL, we first convert this volume to liters:
\[ 1 \, \text{mL} = 0.001 \, \text{L} \]
Thus, one millionth part of 1 mL is:
\[ \frac{1 \, \text{mL}}{1,000,000} = 1 \times 10^{-6} \, \text{mL} = 1 \times 10^{-9} \, \text{L} \]

### Step 4: Calculate the Number of Moles of H⁺ Ions in the Given Volume
Now, we can calculate the number of moles of H⁺ ions in \( 1 \times 10^{-9} \, \text{L} \):
\[ \text{Moles of } H^+ = [H^+] \times \text{Volume in L} \]
\[ \text{Moles of } H^+ = (1 \times 10^{-7} \, \text{mol/L}) \times (1 \times 10^{-9} \, \text{L}) \]
\[ \text{Moles of } H^+ = 1 \times 10^{-16} \, \text{mol} \]

### Step 5: Convert Moles to Number of Ions
To find the number of H⁺ ions, we use Avogadro's number (\(6.022 \times 10^{23} \, \text{ions/mol}\)):
\[ \text{Number of } H^+ \text{ ions} = \text{Moles of } H^+ \times \text{Avogadro's number} \]
\[ \text{Number of } H^+ \text{ ions} = (1 \times 10^{-16} \, \text{mol}) \times (6.022 \times 10^{23} \, \text{ions/mol}) \]
\[ \text{Number of } H^+ \text{ ions} \approx 6.022 \times 10^{7} \]

### Final Answer
Thus, the number of H⁺ ions present in one millionth part of 1 mL of pure water is approximately \(6.022 \times 10^{7}\).

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