40 mg of pure NaOH is dissolved in 10 litres of distilled water. The pH of the solution is

Options

A. `9 `
B. ` 10 `
C. ` 11`
D. `12`

Answer

To find the pH of a solution made by dissolving 40 mg of pure NaOH in 10 liters of distilled water, we can follow these steps:

### Step 1: Convert the mass of NaOH to grams
Given:
- Mass of NaOH = 40 mg

To convert milligrams to grams:
\[ \text{Mass in grams} = \frac{40 \text{ mg}}{1000} = 0.040 \text{ g} \]

### Step 2: Calculate the number of moles of NaOH
The molar mass of NaOH is approximately 40 g/mol.

Using the formula:
\[ \text{Moles of NaOH} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}} \]
Substituting the values:
\[ \text{Moles of NaOH} = \frac{0.040 \text{ g}}{40 \text{ g/mol}} = 0.001 \text{ moles} \]

### Step 3: Calculate the concentration of NaOH in the solution
The volume of the solution is given as 10 liters.

Using the formula for concentration:
\[ \text{Concentration (M)} = \frac{\text{moles}}{\text{volume in liters}} \]
Substituting the values:
\[ \text{Concentration of NaOH} = \frac{0.001 \text{ moles}}{10 \text{ L}} = 0.0001 \text{ M} = 10^{-4} \text{ M} \]

### Step 4: Calculate the pOH of the solution
Since NaOH is a strong base, it dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, the concentration of OH⁻ ions is also \(10^{-4} \text{ M}\).

Using the formula for pOH:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the concentration:
\[ \text{pOH} = -\log(10^{-4}) = 4 \]

### Step 5: Calculate the pH of the solution
We know the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the value of pOH:
\[ \text{pH} + 4 = 14 \]
Thus,
\[ \text{pH} = 14 - 4 = 10 \]

### Final Answer
The pH of the solution is **10**.

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