Question

What is the molecular weight of acetic acid if a solution that contains 30.0 grams of acetic acid per kilogram of water freezes at -0.93°C. Do these results agree with the assumption that acetic acid has the formula CH3CO2H?

Answer 1

The molecular mass from this experiment is 60 u. This agrees with the value of 60.05 u calculated from the formula CH₃CO₂H.

1. Calculate the molality of the solution.

`ΔT_"f" = iK_"f"m`, so

`m = (ΔT_"f")/( iK_"f")`

`T_"f" = T_"f"^° -ΔT_"f"` = 0.00 °C – (-0.93) °C= 0.93 °C
`K_"f" = "1.86 °C·kg·mol"^-1`

Assume that `i` = 1. Then

`m = (ΔT_"f")/( iK_"f") = "0.93 °C"/("1 ×1.86 °C·kg·mol"^-1)` = 0.50 mol/kg

2. Calculate the molar mass.

Molar mass = `"30.0 g"/"0.50 mol"` = 60 g/mol

So the molecular mass is 60 u.

You can do the above calculation in one step by rearranging the equation to read

Molar mass = `(iK_"f")/(ΔT_"f") × "mass of [solute](http://socratic.org/chemistry/solutions-and-their-behavior/solute)"/"kilograms of [solvent](http://socratic.org/chemistry/solutions-and-their-behavior/solvent)"`

3. Compare with the known value.

The molecular mass of CH₃COOH is 60.05 u.

The experimental and the theoretical values agree within experimental uncertainty.

Here's a video on calculating the molar mass from freezing point depression.