Question

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?

Answer 1

The molecular mass is 180 u.

Explanation:

The formula for freezing point depression is

`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_"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"`

In your problem,

`ΔT_"f" = "0.930 °C"`
`K_"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"))))`

∴ `"1 mol" = "22.5 g"/0.250 × 1/0.500 = "180 g"`

The molar mass is 180 g/mol, so the molecular mass is 180 u.