Answer to Question #296170 in General Chemistry for acks

Question

1. What is the vapor pressure of the pure solvent if the vapor pressure of a solution of 15g sucrose (C₁₂H₂₂O₁₁) in 100g of ethanol (C₂H₅OH) is 58 mmHg?

Answer 1

Given vapor pressure of the solution,P_solution = 55 mmHg

Given the mass of sucrose (C6H12O6) = 10 g

molar mass of sucrose (C6H12O6) = 180 g/mol

Hence moles of sucrose in the solution = mass / molar mass = 10 g / 180 g = 0.05556 mol

mass of ethanol = 100 g

molar mass of ethanol = 46 g/mol

Hence moles of ethanol = mass / molar mass = 100 g / 46 g/mol = 2.174 mol

Hence mole fraction of solvent, ethanol, X_ethanol = 2.174 mol / (2.174 + 0.05556) mol = 0.975

Now applying Raoult's Law

P_solution = X_ethanol*P⁰_ethanol

=> P⁰_ethanol = P_solution / X_ethanol  = 55 mmHg / 0.975 = 56.4 mm Hg