Question 11.5: USING DENSITY TO CONVERT FROM MOLALITY TO MOLARITY Ethylene ...
USING DENSITY TO CONVERT FROM MOLALITY TO MOLARITY
Ethylene glycol, C_{2}H_{4}(OH)_{2}, is a colorless liquid used as automobile antifreeze. If the density at 20 °C of a 4.028 m solution of ethylene glycol in water is 1.0241 g/mL, what is the molarity of the solution? The molar mass of ethylene glycol is 62.07 g/mol.
STRATEGY
A 4.028 m solution of ethylene glycol in water contains 4.028 mol of ethylene glycol per kilogram of water. To find the solution’s molarity, we need to find the number of moles of solute per volume (liter) of solution. The volume, in turn, can be found from the mass of the solution by using density as a conversion factor.
The mass of the solution is the sum of the masses of solute and solvent. Assuming that 1.000 kg of solvent is used to dissolve 4.028 mol of ethylene glycol, the mass of the ethylene glycol is
Mass of ethylene glycol = 4.028 mol × 62.07 \frac{g}{mol} = 250.0 g
Dissolving this 250.0 g of ethylene glycol in 1.000 kg (or 1000 g) of water gives the total mass of the solution:
Mass of solution = 250.0 g + 1000 g = 1250 g
The volume of the solution is obtained from its mass by using density as a conversion factor:
Volume of solution = 1250 g × \frac{1 mL}{ 1.0241 g} = 1221 mL = 1.221 L
The molarity of the solution is the number of moles of solute divided by the volume of solution:
Molarity of solution = \frac{4.028 mol}{1.221 L} = 3.299 M