A 45.10 g sample of ethylene glycol (C2H6O2) is dissolved in 250.0 g of water at 25.0 °C. Determine the molarity (M), mole fraction of ethylene glycol (X), molality (m), percent mass to volume (w/v)%, percent mass to mass (w/w)%, and percent volume to volume (v/v)%. Molar mass of ethylene glycol = 62.10 g/mol; density of EG = 1.11 g/mL; density of solution= 1.10 g/mL. Show all work using dimensional analysis and report your final answers in the spaces provided. Be mindful of SFs and rounding errors.
1. Calculate the number of moles of ethylene glycol (C2H6O2).
n(C2H6O2) = mass / molar mass
n(C2H6O2) = 45.10 g / 62.10 g/mol
n(C2H6O2) = 0.726 moles
2. Calculate the number of moles of water (H2O).
Molar mass of water = 18.015 g/mol
n(H2O) = mass / molar mass
n(H2O) = 250.0 g / 18.015 g/mol
n(H2O) = 13.879 moles
3. Calculate the mole fraction of ethylene glycol (X).
X(C2H6O2) = n(C2H6O2) / (n(C2H6O2) + n(H2O))
X(C2H6O2) = 0.726 moles / (0.726 moles + 13.879 moles)
X(C2H6O2) = 0.0497
4. Calculate the volume of the solution.
Density of solution = 1.10 g/mL
Mass of solution = mass of ethylene glycol + mass of water
Mass of solution = 45.10 g + 250.0 g
Mass of solution = 295.10 g
Volume of solution (V) = mass of solution / density of solution
V = 295.10 g / 1.10 g/mL
V = 268.3 mL
5. Calculate the molarity (M) of ethylene glycol.
M(C2H6O2) = n(C2H6O2) / (V/1000)
M(C2H6O2) = 0.726 moles / (268.3 mL / 1000)
M(C2H6O2) = 2.707 mol/L
6. Calculate the molality (m) of ethylene glycol.
m(C2H6O2) = n(C2H6O2) / mass of water (in kg)
m(C2H6O2) = 0.726 moles / (250.0 g / 1000)
m(C2H6O2) = 2.904 mol/kg
7. Calculate the mass percent (w/w) of ethylene glycol.
wt% = (mass of solute / mass of solution) * 100
wt% = (45.10 g / 295.10 g) * 100
wt% = 15.28%
8. Calculate the volume of ethylene glycol.
Volume of ethylene glycol = mass of ethylene glycol / density of ethylene glycol = 45.10 g / 1.11 g/mL = 40.63 mL
9. Calculate the volume percent (v/v) of ethylene glycol.
vol% = (volume of solute / volume of solution) * 100
vol% = (40.63 mL / 268.3 mL) * 100
vol% = 15.14%
10. Calculate the mass to volume percent (w/v) of ethylene glycol.
wt/vol% = (mass of solute / volume of solution) * 100
wt/vol% = (45.10 g / 268.3 mL) * 100
wt/vol% = 16.81%
Results:
Molarity (M): 2.707 mol/L
Mole fraction (X): 0.0497
Molality (m): 2.904 mol/kg
Mass percent (w/w): 15.28%
Volume percent (v/v): 15.14%
Mass to volume percent (w/v): 16.81%