# Question 9f5d4

May 2, 2017

The molar mass of β-carotene is 537 g/mol.

#### Explanation:

The formula for freezing point depression ΔT_text(f) is

color(blue)(bar(ul(|color(white)(a/a)ΔT_text(f) = iK_text(f)bcolor(white)(a/a)|)))" "

where

$i \textcolor{w h i t e}{l l} =$ the van't Hoff $i$ factor
${K}_{\textrm{f}} =$ the molal freezing point depression constant of the solvent
$b \textcolor{w h i t e}{l l} =$ the molality of the solute

We can rearrange the above formula to get

b = (ΔT_text(f))/(iK_text(f))

In this problem,

ΔT_text(f) = "1.17 °C"
$i = 1$ because β-carotene is a nonelectrolyte
${K}_{\textrm{f}} = \text{37.7 °C·kg·mol"^"-1}$

b = (1.17 color(red)(cancel(color(black)("°C"))))/(1 × 37.7 color(red)(cancel(color(black)("°C")))·"kg·mol"^"-1") = "0.031 03 mol·kg"^"-1" = "0.031 03 mol solute"/"1 kg solvent"#

Our solution contains

$\text{0.0250 g solute"/"0.00150 kg solvent" = "16.67 g solute"/"1 kg solvent}$

$\text{0.031 03 mol" = "16.67 g}$

and

$\text{Molar mass" = "16.67 g"/"0.031 03 mol" = "537 g/mol}$