Question

Molarity and molality of a solution of a liquid (mol. wt 50) in aqueous solution is 8and 10 respectively. what is the density of the solution

Answer 1

Molarity is number of moles of solute per 1000 mL of solution, and molality is the number of moles of solute per 1000 g of solvent.

Molarity = 8 means that 8 moles of the compound are present in 1000 mL of the solution. This means that 1 mole of the compound would be found in 1000/8 = 125 mL of the solution.

Molality = 10 means that 10 moles of the compound are present in 1000 g of water, the solvent. 10 moles of the compound translate to 10×50 = 500 g of the compound. This means that 10 moles of the compound are present in 1000 + 500 = 1500 g of solution i.e. 1 mole per 150 g.

Since 1 mole of the solute is found in 150 g or 125 ml of the solution, the density of the solution would be 150 g/125 mL = 1.2 g/mL.

Answer 2

A very simple formula is enough for solving this type of questions. you should memorize this one . Formula is 1/m = d/M - Ms/1000
Here, m is molality
M is molarity
d is density of solution
Ms is molar mass of solute .

Given, m = 10, M = 8 , Ms = 50 g/mol
∴ 1/10 = d/8 - 50/1000
⇒ 0.1 = d/8 - 0.05
⇒0.1 + 0.05 = d/8
⇒0.15 = d/8
⇒d = 0.15 × 8 = 1.2 g/ml

Hence, density of solution is 1.2 g/ml