# Question 4b054

Sep 20, 2014

The molecular formula is C₁₂H₂₆O.

This is a boiling point elevation problem in which you use the boiling point elevation to determine the molar mass of the solute.

Step 1. Determine the molar mass.

We use the boiling point elevation expression

ΔT_"b" = K_"b"m

where ΔT_"b" is the change in boiling point, ${K}_{\text{b}}$ is the molal boiling point elevation constant for the solvent, and $m$ is the molality of the solute.

For benzene, ${K}_{\text{b}}$ = 2.53 °C·kg·mol⁻¹ and T_"b"^° = 80.10 °C.

ΔT_"b" = T_"b" – T_"b"^° = 80.78 °C – 80.10 °C = 0.68 °C

m = (ΔT_"b")/K_"b" = "0.68 °C"/("2.53 °C·kg·mol"^-1) = ${\text{0.27 mol·kg}}^{-} 1$

So we have 0.100 kg × $\text{0.27 mol"/"1 kg}$ = 0.027 mol of lauric acid

∴ Molar mass = $\text{5 g"/"0.027 mol}$ = 190 g /mol

If you want to calculate the molar mass in one step. The formula is

Molar mass = ${K}_{\text{b"/"ΔT"_"b}}$ × $\text{grams of solute"/"kilograms of solvent}$

Molar mass = ("2.53 °C·kg·mol"^-1)/"0.68°C"# × $\text{5 g"/"0.100 kg}$ = 190 g/mol

Step 2. Calculate the molecular formula.

EF = C₁₂H₂₆O; so EF mass = 186.33 u

Molecular Mass = 190 u

MF = $\text{(EF)"_"n}$

So Molecular mass = EF mass × n

and $\text{n" = "Molecular mass"/"EF mass}$ = $\text{190 u"/"186.33 u" = 1.0 ≈ 1}$.

The MF is ${\text{(C"_12"H"_26"O)}}_{n}$ = ${\text{(C"_12"H"_26"O)}}_{1}$ = $\text{C"_12"H"_26"O}$