Step 1 (Formula / Governing Law & Given Data): [1 Mark]

The boiling point elevation is given by the formula:

$$\Delta T_b = i \cdot K_b \cdot m$$

Where:

• $w_2 (\text{solute}) = 0.61\text{ g}$
• $M_2 (\text{molar mass}) = 122\text{ g mol}^{-1}$
• $w_1 (\text{solvent}) = 5\text{ g} = 0.005\text{ kg}$
• $K_b = 2.3\text{ K kg mol}^{-1}$
• $\alpha = 0.88$ (degree of association)

For dimerization ($n=2$), the van't Hoff factor $i$ is calculated as:

$$i = 1 + \left(\frac{1}{n} - 1\right)\alpha = 1 + \left(\frac{1}{2} - 1\right)0.88 = 1 - 0.44 = 0.56$$

Step 2 (Step-by-Step Mathematical Working): [1.5 Marks]

First, calculate the molality ($m$):

$$m = \frac{w_2 \times 1000}{M_2 \times w_1 (\text{in g})} = \frac{0.61 \times 1000}{122 \times 5} = \frac{610}{610} = 1\text{ mol kg}^{-1}$$

Now, substitute the values into the elevation formula:

$$\Delta T_b = 0.56 \times 2.3 \times 1 = 1.288\text{ K}$$

Step 3 (Final Concluded Answer): [0.5 Mark]

The boiling point of the solution ($T_b$) is:

$$T_b = T_b^\circ + \Delta T_b = 46.2 + 1.288 = 47.488\text{ }^\circ\text{C}$$

Final Answer: The boiling point of the solution is $47.488\text{ }^\circ\text{C}$.

💡 EL10 Concept Insight: Think of the van't Hoff factor ($i$) as a "crowd counter." Because benzoic acid molecules pair up (dimerize), there are fewer individual particles floating around than you'd expect, which makes the boiling point rise less than it would if they stayed separate.