The number of hydroxyl ions in 100 mL of a solution having pH 10 is

Options

A. `1 xx 10^(4)`
B. `3.012 xx 10^(4)`
C. `6.02 xx 10^(18)`
D. `6.023 xx 10^(19)`

Answer

To find the number of hydroxyl ions (OH⁻) in 100 mL of a solution with a pH of 10, we can follow these steps:

### Step 1: Calculate the concentration of hydrogen ions (H⁺)
The pH of a solution is related to the concentration of hydrogen ions by the formula:
\[ \text{pH} = -\log[H^+] \]
To find the concentration of H⁺ ions, we can rearrange this formula:
\[ [H^+] = 10^{-\text{pH}} = 10^{-10} \]

### Step 2: Calculate the concentration of hydroxyl ions (OH⁻)
We can use the ion product of water (K_w) to find the concentration of hydroxyl ions. At 25°C, \(K_w = 10^{-14}\):
\[ K_w = [H^+][OH^-] \]
We can rearrange this to find [OH⁻]:
\[ [OH^-] = \frac{K_w}{[H^+]} = \frac{10^{-14}}{10^{-10}} = 10^{-4} \]

### Step 3: Convert the concentration of hydroxyl ions to millimoles
Since we want to find the number of hydroxyl ions in 100 mL, we first convert the concentration from molarity to millimolarity:
\[ \text{Millimolarity} = [OH^-] \times 1000 = 10^{-4} \times 1000 = 10^{-1} \text{ mM} \]

### Step 4: Calculate the number of moles of hydroxyl ions in 100 mL
Now, we can find the number of moles of hydroxyl ions in 100 mL:
\[ \text{Number of moles} = \text{Millimolarity} \times \text{Volume in L} = 10^{-1} \times 0.1 = 10^{-2} \text{ moles} \]

### Step 5: Convert moles to number of hydroxyl ions
To find the total number of hydroxyl ions, we multiply the number of moles by Avogadro's number (\(6.022 \times 10^{23}\)):
\[ \text{Number of OH}^- = 10^{-2} \times 6.022 \times 10^{23} = 6.022 \times 10^{21} \]

### Final Answer
The number of hydroxyl ions in 100 mL of a solution having pH 10 is approximately \(6.022 \times 10^{21}\).

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