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%
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.
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