The molar mass of the solute sodium hydrdoxide obtained from the measurement of the osmotic pressure of its aqueous solution at `27^(@)C` is `25 g mol^(-1)`. Therefore its ionization percentage in this solution is

Options

A. 75
B. 60
C. 80
D. 70

Explanation

To find the ionization percentage of sodium hydroxide (NaOH) in the solution, we can follow these steps:

### Step 1: Determine the Molar Mass of Sodium Hydroxide
The molar mass of sodium hydroxide (NaOH) can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Adding these together:
\[ \text{Molar mass of NaOH} = 23 + 16 + 1 = 40 \text{ g/mol} \]

### Step 2: Identify the Observed Molar Mass
The observed molar mass from the osmotic pressure measurement is given as:
\[ \text{Observed molar mass} = 25 \text{ g/mol} \]

### Step 3: Calculate the Van 't Hoff Factor (i)
The Van 't Hoff factor (i) is the ratio of the molar mass of the solute (calculated) to the molar mass obtained from the osmotic pressure measurement:
\[ i = \frac{\text{Molar mass of NaOH (calculated)}}{\text{Observed molar mass}} \]
Substituting the values:
\[ i = \frac{40 \text{ g/mol}}{25 \text{ g/mol}} = 1.6 \]

### Step 4: Relate the Van 't Hoff Factor to Ionization
For NaOH, which dissociates into Na⁺ and OH⁻ ions, the relationship for the Van 't Hoff factor is:
\[ i = 1 + \alpha(n - 1) \]
where \( \alpha \) is the degree of ionization and \( n \) is the number of particles produced per formula unit of the solute. For NaOH, \( n = 2 \) (Na⁺ and OH⁻).

Substituting the values into the equation:
\[ 1.6 = 1 + \alpha(2 - 1) \]
This simplifies to:
\[ 1.6 = 1 + \alpha \]

### Step 5: Solve for the Degree of Ionization (α)
Rearranging the equation gives:
\[ \alpha = 1.6 - 1 = 0.6 \]

### Step 6: Calculate the Ionization Percentage
To find the ionization percentage, we multiply the degree of ionization by 100:
\[ \text{Ionization percentage} = \alpha \times 100 = 0.6 \times 100 = 60\% \]

### Final Answer
The ionization percentage of sodium hydroxide in this solution is **60%**.

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