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Question: A solution of 2.5 g of a non-volatile solid in 100 g benzene is boiled at \( {0.42^o}C \) higher tha...

A solution of 2.5 g of a non-volatile solid in 100 g benzene is boiled at 0.42oC{0.42^o}C higher than the boiling point of pure benzene. Calculate the molecular mass of the substance. Molal elevation constant of benzene is 2.67 K kg moll - 1{\text{K kg mol}}{{\text{l}}^{{\text{ - 1}}}}

Explanation

Solution

Hint : When another substance is added to a liquid (a solvent), the boiling point of the liquid (a solvent) increases, implying that a solution has a higher boiling point than a pure solvent. When a non-volatile solute, such as salt, is introduced to a pure solvent, such as water, this occurs. An ebullioscope may be used to precisely determine the boiling point.

Complete Step By Step Answer:
When one mole of solute is dissolved in 1 kg of solvent, the molal elevation constant is the increase in boiling point. The ebullioscopic constant is another name for it. When a nonvolatile solute is added to a solvent, its vapour pressure drops, requiring more heat to raise the vapour pressure of the solution to one atmosphere. As a result, when a nonvolatile solute is introduced, the boiling point of the solvent rises. It indicates that the boiling point of the solution is higher than that of the pure solvent. This rise in boiling point is referred to as elevation in boiling point, or the difference between the boiling point of the solution and the boiling point of pure solvent.,
M=1000  Kb×wW×ΔT{\text{M}} = \dfrac{{1000\;{{\text{K}}_{\text{b}}} \times {\text{w}}}}{{{\text{W}} \times \Delta {\text{T}}}}
Given, Kb=2.67  K.kg⋅mol−1{{\mathbf{K}}_{\text{b}}} = 2.67\;{\text{K}}.{\text{kg}} \cdot {\text{mo}}{{\text{l}}^{ - 1}}
From the question we obtain
w=2.5  g{\text{w}} = 2.5\;{\text{g}}
W=100  g{\text{W}} = 100\;{\text{g}}
ΔT=0.42  K\Delta {\text{T}} = 0.42\;{\text{K}}
Now, upon substituting
M=1000×2.67×2.5100×0.42=158.9gM = \dfrac{{1000 \times 2.67 \times 2.5}}{{100 \times 0.42}} = 158.9g
The molecular weight of the substance is 158.9  g mol−1158.9\;{\text{g mo}}{{\text{l}}^{ - 1}} .

Note :
The boiling point elevation is a colligative characteristic, meaning it is affected by the presence and amount of dissolved particles, but not by their identity. It's a result of the solvent being diluted in the presence of a solute. It is a phenomenon that occurs for all solutes in all solutions, even perfect solutions, and is unaffected by specific solute–solvent interactions. When the solute is an electrolyte, such as different salts, or a nonelectrolyte, the boiling point rises.