Skip to content

Chemistry · Ch 1 — Liquid State

Determination of Molecular Mass Using Colligative Properties

1.11

Determination of Molecular Mass Using Colligative Properties

All four colligative properties covered in this chapter — relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure — can, in principle, each be rearranged into a formula for an unknown solute's molar mass M2M_2 once the corresponding property has been measured for a solution of known composition:

p1∘−p1p1∘=n2n1⇒M2=w2M1w1⋅p1∘p1∘−p1\frac{p_1^{\circ}-p_1}{p_1^{\circ}} = \frac{n_2}{n_1} \quad\Rightarrow\quad M_2 = \frac{w_2 M_1}{w_1}\cdot\frac{p_1^{\circ}}{p_1^{\circ}-p_1}

ΔTb=Kbm⇒M2=1000 Kb w2ΔTb w1\Delta T_b = K_b m \quad\Rightarrow\quad M_2 = \frac{1000\,K_b\,w_2}{\Delta T_b\, w_1}

ΔTf=Kfm⇒M2=1000 Kf w2ΔTf w1\Delta T_f = K_f m \quad\Rightarrow\quad M_2 = \frac{1000\,K_f\,w_2}{\Delta T_f\, w_1}

π=CRT⇒M2=w2RTπV\pi = CRT \quad\Rightarrow\quad M_2 = \frac{w_2 RT}{\pi V}

In practice, however, the four methods are not equally convenient for every kind of solute, and the choice between them depends heavily on the solute's own molar mass. For solutes of small-to-moderate molar mass (roughly up to a few hundred grams per mole) — sugars, simple organic acids, small inorganic molecules — boiling-point elevation and freezing-point depression are the traditional, technically simple laboratory methods, since a conveniently weighable amount of solute produces a ΔTb\Delta T_b or ΔTf\Delta T_f of several tenths of a degree or more, easily read on an ordinary precision thermometer. …

Start your 14-day free trial to unlock the full solution →
← Previous · 1.10Osmosis and Osmotic PressureNext · 1.12 →Abnormal Molar Mass and van't Hoff Factor