Question

The density of a 20.3M CH3OH (methanol) solution is .858 g/mL. What is the molality of this solution? H2O is the solvent.

Answer 1

Let volume be 1 L
volume , V = 1 L


use:
number of mol ,
n = Molarity * Volume
= 20.3*1
= 20.3 mol
volume , V = 1 L
= 1*10^3 mL


density, d = 0.858 g/mL
use:
mass = density * volume
= 0.858 g/mL *1*10^3 mL
= 858.0 g
This is mass of solution

Molar mass of CH3OH,
MM = 1*MM(C) + 4*MM(H) + 1*MM(O)
= 1*12.01 + 4*1.008 + 1*16.0
= 32.042 g/mol

use:
mass of CH3OH,
m = number of mol * molar mass
= 20.3 mol * 32.042 g/mol
= 6.505*10^2 g
This is mass of solute

mass of solvent = mass of solution - mass of solute
= 858 - 650.4526
= 207.5474 g
= 0.20755 Kg

m(solvent)= 0.20755 Kg

use:
Molality,
m = number of mol / mass of solvent in Kg
=(20.3 mol)/(0.20755 Kg)
= 97.81 molal
Answer: 97.81 molal