A 2.20 molar solution of acetic acid (molar mass = 60.05 g/mol) has a density of 1.0178 g/mL. What is the molality of the solution?

Question

Quizplus · Accepted Answer

First, we need to calculate the molarity of the solution using the density and molar mass.

Density = mass/volume

Volume of 1 mole of acetic acid (at 60.05 g/mol) = (60.05 g/1 mol)/(1.0178 g/mL) = 58.93 mL/mol

Volume of the solution = (mass of solution)/(density)

Therefore,

1 L of solution = (1000 g)/(1.0178 g/mL) = 983.2 mL

Mass of 2.20 moles of acetic acid = (2.20 mol)*(60.05 g/mol) = 132.11 g

Volume of 2.20 moles of acetic acid = (2.20 mol)*(58.93 mL/mol) = 129.65 mL

Density of solution = (132.11 g + solvent mass)/(129.65 mL + solvent volume)

Solving for solvent mass:

Solvent mass = (density of solution)*(129.65 mL) - 132.11 g = 31.147 g

Total mass of solution = 132.11 g + 31.147 g = 163.257 g

Molarity of solution = (2.20 mol)/(0.163257 kg) = 13.489 M

Next, we can calculate the molality of the solution.

Molality = moles of solute/kg of solvent

We need to convert the mass of solvent in the solution to kg:

Solvent mass = (volume of solution - volume of solute)*(density of solution)

Volume of solute = (2.20 mol)*(58.93 mL/mol) = 129.65 mL

Volume of solvent = 1000 mL - 129.65 mL = 870.35 mL

Solvent mass = (870.35 mL)*(1.0178 g/mL) - 31.147 g = 853.62 g

Molality = (2.20 mol)/(0.85362 kg) = 2.58 m

Therefore, the closest answer choice is D) 2.48 m.

A 220 Molar Solution of Acetic Acid (Molar Mass = 60