Answer :
Final answer:
By using Raoult's Law and the given values for vapor pressures, mass of solute, and number of moles of solvent in the equation, we can calculate the molar mass of the solute, which comes out to approximately 342 g/mol.
Explanation:
To find the molar mass of the solute, we need to use the formula for Raoult's Law, which states that the vapor pressure depression (ΔP) is equal to the molar fraction of the solute (χ) times the vapor pressure of the pure solvent (P0). Here, ΔP = P0 - P = 107.9 torr - 97.3 torr = 10.6 torr. χ can be expressed as number of moles of solute (nsolute) over total number of moles (ntotal).
The total number of moles (ntotal) is equal to number of moles of solvent + nsolute, and since nsolute = mass of solute/molar mass of solute, that gives us:
10.6 torr = [(43.8 g/molar mass of solute) / ((43.8 g/molar mass of solute) + 2.07 mol)] * 107.9 torr.
Solving this equation results in a molar mass of the solute of about 342 g/mol.
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