# How does molecular weight affect freezing point?

Aug 24, 2016

If everything else is kept constant, a compound with a higher molecular mass will have a smaller effect on the freezing point.

#### Explanation:

The formula for calculating freezing point depression is

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

where

ΔT_"f" is the decrease in freezing point
${K}_{\text{f}}$ is the molal freezing point depression constant
$\text{b}$ is the molal concentration of the solution.

$\text{Molal concentration" = "moles of solute"/"kilograms of solvent}$

Let's rewrite this formula in symbols as

$b = \frac{n}{m} _ 1$

Then

color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = K_fn/m_1color(white)(a/a)|)))" "

Now,

$\text{moles" = "mass"/"molar mass}$, or $n = \frac{m}{M}$

We can rearrange the formula to give

color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = K_fm/(Mm_1)color(white)(a/a)|)))" "

If ${K}_{f} , m$, and ${m}_{1}$ are held constant, then

color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" ∝ 1/Mcolor(white)(a/a)|)))" "

Thus, as the molar mass increases, the freezing point depression decreases.

That is, increasing the molar (or molecular) mass will have a smaller effect on the freezing point.