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Step-by-Step Solution
Step 1: Determine the Van’t Hoff Factor for K4Fe(CN)6
Potassium ferrocyanide, K4Fe(CN)6, on complete dissociation would produce 5 ions in solution: 4 K+ ions and 1 Fe(CN)64− ion.
Given its degree of dissociation ( \alpha = 0.4 ), the van’t Hoff factor i is calculated using: i = 1 + (n - 1)\alpha , where n is the maximum number of ions.
Thus, n = 5 , so: i = 1 + (5 - 1)\times 0.4 = 1 + 4\times 0.4 = 1 + 1.6 = 2.6.
Step 2: Relate Van’t Hoff Factor to Effective Molality
Since the given solution is 1 molal in K4Fe(CN)6, the effective molality (taking dissociation into account) becomes: 1 \times i = 1 \times 2.6 = 2.6\text{ molal}.
This 2.6 molal value determines the total particle concentration that affects colligative properties.
Step 3: Equate the Boiling Point of the Non-Electrolyte Solution
Another solution with a non-electrolytic solute A has the same boiling point, implying that its molality must also be 2.6 molal.
Step 4: Determine Composition of the Non-Electrolyte Solution
The non-electrolyte solution contains 18.1% by mass of the solute A, meaning 18.1 g of solute is present in 100 g of the overall solution. Hence, the mass of the solvent (water) is 100\text{ g} - 18.1\text{ g} = 81.9\text{ g}.
Since the density of water is 1.0 g/cm3, we treat 81.9 g of water as 0.0819 kg of water.
Step 5: Set Up the Molality Expression
Molality (m) for the non-electrolyte is given by: m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}.
In symbols: 2.6 = \frac{(\frac{18.1}{M})}{0.0819},
where M is the molar mass of the solute A.
Step 6: Solve for the Molar Mass
From 2.6 = \frac{18.1/M}{0.0819}, we get \frac{18.1}{M} = 2.6 \times 0.0819.
Hence, \frac{18.1}{M} = 0.21294\ldots
Therefore, M = \frac{18.1}{0.21294\ldots} \approx 85\text{ u.}
Final Answer
The molar mass of the non-electrolytic solute A, rounded to the nearest integer, is 85 u.
