Question

A solution is prepared by dissolving 21.0mL of methanol in 160.0mL of water at 25 ?C. The final volume of the solution is 177.9mL . The densities of methanol and water at this temperature are 0.782g/mL and 1.00g/mL , respectively. For this solution, calculate each of the following.

Molarity, Molality, percent by mass, mole fraction, and mole percent

Answer 1

V = 21 ml methanol

V =160 ml water

V = 177.9 ml total

D1 = 0.782

D2 = 1

a) molarity

M = mol/volume

mass of water used = D*V = 160*1 = 160 g of Water

mass of ethanol used = D*V = 0.782*21 = 16.42 g of Ethanol

mol of water used = mass/MW = 160/18 = 8.88 mol of Water

mol of ethanol used = mass/MW = 16.42/46.1 = 0.356 mol of Ethanol

Vt = 177.9 ml or 0.1779 L

M water = 8.88/0.1779 = 49.92 mol per liter

M ethanol = 0.356/0.1779 = 2.00 mol per liter

b)

Molality

Mol per kg of solvent

kg of solvent = 0.16 kg of water

Molality Water = 1

Molality of Ethanol = 0.356/0.16 = 2.225 mol per kg of solvent

c) % mass

mass of solution = mass of water + mass of ethanol = 16.42+160 = 176.42g

% water = mass of water / mass of solution = 160/176.42 = 0.9069*100%

%water = 90.69%

% ethanol = mass of ethanol / mass of solution = 16.42/176.42 = 0.0931*100%

%ethanol = 9.31%

d) mole fraction

Total mol = 8.88+0.356 = 9.236

Mol Fraction of Water = mol water / total mol = 8.88/9.236 = 0.9615

Mol Frac. Water = 0.9615

Mol Fraction of Ethanol = mol ethanol / total mol = 0.356/9.236 = 0.038

Mol Frac. Ethanol = 0.038

e) Mole percent

Mole Fraction * 100%

For water= 0.9615*100 = 96.15%

For ethanol = 3.8%