Ionic Equilibria and Colligative Properties

Freezing and boiling point depression

Freezing point depression and boiling point elevation are colligative properties. They depend on the number of solute particles relative to the amount of solvent, not on the chemical identity of the solute. For a non-volatile, non-electrolyte solute in a dilute ideal solution, the changes are \Delta T_f = K_f m and \Delta T_b = K_b m, where m is the molality (moles of solute per kilogram of solvent), K_f is the cryoscopic constant, and K_b is the ebullioscopic constant of the solvent. Molality is used rather than molarity because the constants are defined per kilogram of solvent. The ebullioscopic constant can be derived from thermodynamics as K_b = \dfrac{R T_b^2 M_{\text{solvent}}}{\Delta H_{\text{vap}}}, with M_{\text{solvent}} in kg mol^{-1} and T_b in kelvin. Temperatures must always be converted from degrees Celsius to kelvin before substitution. For a solvent with K_f = 3.9 K kg mol^{-1}, a depression of 7.8 K corresponds to a molality of 2.0 mol kg^{-1}. To find the molar mass of an unknown solute, first compute m = \Delta T / K, then find the moles as n = m \times (\text{solvent mass in kg}), and finally divide the solute mass by n. This method is valid only when the solute neither dissociates nor associates in the solvent.

The same logic applies to boiling point elevation. In an illustrative case where K_b = 2.5 K kg mol^{-1} and the boiling point rises by 0.25 K, the molality is 0.25/2.5 = 0.10 mol kg^{-1}. When the constant is not given directly, it can be computed from the boiling point and the enthalpy of vaporization of the solvent, as shown by the formula above.

For electrolytes, the van't Hoff factor i must be included: \Delta T = i K m. Ideal NaCl gives approximately i = 2 because it yields two ions, and an ideal 1:2 or 2:1 salt such as Na_2SO_4 gives i = 3. Therefore, solutions of equal molality give depressions proportional to the total number of ions. The ratio of depressions for 0.1 mol kg^{-1} NaCl and Na_2SO_4 is 2:3, so the salt with the larger van't Hoff factor depresses the freezing point more strongly.

Finally, when the solute is non-volatile and the solvent mass is given in grams, convert it to kilograms before using the formula. For a solute of molar mass 180 g mol^{-1} in a solvent with K_b = 0.51 K kg mol^{-1}, a boiling point rise of 0.153 K requires m = 0.30 mol kg^{-1}. For 500 g (0.5 kg) of solvent, this is 0.15 mol, or 27 g of solute.

Henderson-Hasselbalch buffer ratio

A buffer solution resists large changes in pH when small amounts of acid or base are added. It is formed from a weak acid (HA) together with its conjugate base (A^-), usually supplied as a salt such as a sodium salt of the anion. A mixture of a strong acid or strong base with a neutral salt does not buffer, because it contains no weak acid–conjugate base pair. Thus, acetic acid together with sodium acetate is a buffer, whereas acetic acid together with sodium chloride is not, because chloride is not the conjugate base of acetic acid. Similarly, a strong base with a salt of a weak acid gives a basic solution without a weak acid component, so it does not serve as a buffer.