Calculate the mass of lactose, C₁₂H₂₂O₁₁, contained in 500.0 mL of solution if the measured vapour pressure of the solution is 121.2 mbar at 50 °C. The vapour pressure of pure water at 50 °C is 123.3 mbar; assume no change in volume occurs upon dissolution. A) 118 g B) 165 g C) 239 g D) 94.6 g E) 280 g

Question

Quizplus · Accepted Answer

The mass of lactose in the solution can be calculated using Raoult's Law:

Psolution = Xsolvent * Psolvent

where Psolution is the measured vapour pressure of the solution, Xsolvent is the mole fraction of water (the solvent), and Psolvent is the vapour pressure of pure water at the same temperature.

To solve for Xsolvent, we can use:

Xsolvent = 1 - Xsolute

where Xsolute is the mole fraction of lactose.

Since we know the volume of the solution (500.0 mL) and assume no change in volume upon dissolution, we can calculate the number of moles of lactose:

n = m / M

where m is the mass of lactose and M is the molar mass of lactose (342.3 g/mol).

Finally, we can use the mole fractions and Raoult's Law equations to solve for the mass of lactose:

Psolution / Psolvent = (1 - Xsolute) + Xsolute * P°solute / P°solvent

Solving for Xsolute and substituting in the appropriate values:

Xsolute = (Psolution / Psolvent - 1) / (P°solute / P°solvent - 1)

Xsolute = (121.2 mbar / 123.3 mbar - 1) / (0.0313 - 1)

Xsolute = 0.036

n = (500.0 mL / 1000.0 mL/L) * (0.036 mol/L) = 0.018 mol

m = n * M = 0.018 mol * 342.3 g/mol = 6.20 g

Therefore, the mass of lactose in 500.0 mL of solution is 6.20 g, or 165 g in 11 L of solution (since 1 L = 1000 mL). The answer is B.

Calculate the Mass of Lactose, C12H22O11, Contained in 500

Calculate the Mass of Lactose, C₁₂H₂₂O₁₁, Contained in 500