# What is the molecular mass of a substance if 22.5 g dissolved in 250 g of water produces a solution whose freezing point is -0.930°C?

Aug 18, 2016

The molecular mass is 180 u.

#### Explanation:

color(blue)(|bar(ul(color(white)(a/a) ΔT_"f" = K_"f"mcolor(white)(a/a)|)))" "

where

ΔT_"f" = the decrease in the freezing point
${K}_{\text{f}}$ = the molal freezing point depression constant of the solvent
$m$ = the molality of the solution

We can rearrange the formula to get

m = (ΔT_"f")/K_"f"

ΔT_"f" = "0.930 °C"
${K}_{\text{f" = "1.86 °C·kg·mol"^"-1}}$
m = (0.930 color(red)(cancel(color(black)("°C"))))/(1.86 color(red)(cancel(color(black)("°C")))·"kg·mol"^"-1") = "0.500 mol·kg"^"-1"
Now, m = "0.500 mol"/(1 color(red)(cancel(color(black)("kg")))) = "22.5 g"/(0.250 color(red)(cancel(color(black)("kg"))))
$\text{1 mol" = "22.5 g"/0.250 × 1/0.500 = "180 g}$