1 molal aqueous solution of an electrolyte `A_2B_3` is 60% ionised. The boiling point of the solution at 1 atm is `"______"` K. (Rounded-off to the nearest integer)
[given `K_b` for `(H_2O)=0.52 K mol^(-1)]`

Answer

To solve the problem, we need to determine the boiling point of a 1 molal aqueous solution of the electrolyte \( A_2B_3 \) that is 60% ionized. We will use the formula for boiling point elevation, which is given by:

\[ \Delta T_b = i \cdot K_b \cdot m \]

where:
- \( \Delta T_b \) is the elevation in boiling point,
- \( i \) is the van 't Hoff factor,
- \( K_b \) is the ebullioscopic constant of the solvent (water in this case),
- \( m \) is the molality of the solution.

### Step 1: Determine the van 't Hoff factor (i)

The electrolyte \( A_2B_3 \) dissociates in solution as follows:

\[ A_2B_3 \rightarrow 2A^+ + 3B^{3-} \]

From this dissociation, we can see that 1 mole of \( A_2B_3 \) produces \( 2 + 3 = 5 \) moles of ions. Therefore, the theoretical van 't Hoff factor \( N \) is 5.

Since the solution is 60% ionized, we can calculate the effective van 't Hoff factor \( i \):

\[ \alpha = 0.6 \quad (\text{where } \alpha \text{ is the degree of ionization}) \]

Using the formula for the van 't Hoff factor:

\[ i = 1 + (N - 1) \cdot \alpha \]

Substituting the values:

\[ i = 1 + (5 - 1) \cdot 0.6 = 1 + 4 \cdot 0.6 = 1 + 2.4 = 3.4 \]

### Step 2: Calculate the boiling point elevation (\( \Delta T_b \))

Now we can use the boiling point elevation formula:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Given:
- \( K_b = 0.52 \, \text{K kg/mol} \)
- \( m = 1 \, \text{molal} \)

Substituting the values:

\[ \Delta T_b = 3.4 \cdot 0.52 \cdot 1 = 1.768 \, \text{K} \]

### Step 3: Calculate the new boiling point (\( T_b \))

The normal boiling point of water (\( T_{b0} \)) is 373 K. Therefore, the new boiling point \( T_b \) is:

\[ T_b = T_{b0} + \Delta T_b = 373 + 1.768 = 374.768 \, \text{K} \]

Rounding off to the nearest integer, we get:

\[ T_b \approx 375 \, \text{K} \]

### Final Answer

The boiling point of the solution at 1 atm is approximately **375 K**.

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