Question

What is the freezing point of a 3.0 mol/kg aqueous solution of sodium chloride?

Answer 1

The freezing point is -11 °C.

Explanation:

The formula for calculating freezing point depression `ΔT_"f"` is

`color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = iK_fbcolor(white)(a/a)|)))" "`

where

`i` is the van't Hoff factor

`K_"f"` is the molal freezing point depression constant

`b` is the molality of the solution.

In this problem,

`icolor(white)(ll)= 2`, because 1 mol of `"NaCl"` forms 2 mol of ions
`K_text(f) = "1.86 °C·kg·mol"^"-1"`
`bcolor(white)(l) = "3.0 mol/kg"`

∴ `ΔT_"f" = 2 × "1.86 °C"·color(red)(cancel(color(black)("kg·mol"^"-1"))) × 3.0 color(red)(cancel(color(black)("mol·kg"^"-1"))) = "11 °C"`

`T_text(f) = T_text(f)^° - ΔT_text(f) = "0 °C - 11 °C" = "-11 °C"`