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?

1 Answer
Ernest Z.
Aug 18, 2016

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.

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