# Derivation of freezing-point depression equation

Can anyone provide me the real derivation of depression in freezing point? In almost all of the books and online articles that I have read, it says $$\Delta T_\mathrm{f}$$ is directly proportional to molality $$m,$$ which implies

$$\Delta T_\mathrm{f} = K_\mathrm{f}m,$$

where $$K_\mathrm{f}$$ is the constant of proportionality:

$$K_\mathrm{f} = \frac{MRT^2}{1000 \Delta_\mathrm{fus}H}.$$

• Nice concise derivation: doi.org/10.1021/ed018p393 (half-page long). Also, there are numerous YouTube videos of various quality that also somewhat cover the topic. You probably might want to add more details as to what seems unintuitive to you when you do the derivation yourself. – andselisk Dec 29 '19 at 8:43