mole per kilogram (molal)
Molalityexact by definition
The mole per kilogram, symbol m and spoken as molal, is the concentration expressed as moles of solute per kilogram of SOLVENT. Its factor of 1 is exact as the coherent SI form. Because it is built entirely on masses, it does not change when the solution is heated or cooled, which is why every colligative property is defined in terms of it.
Watch out: Molality and molarity are easily confused and are not the same quantity. Molarity is moles per litre of finished solution and shifts with temperature as the liquid expands; molality is moles per kilogram of solvent and does not. In dilute aqueous solution near room temperature the two are numerically close, since a litre of water weighs about a kilogram, but that coincidence fails in concentrated solutions and in any non-aqueous solvent.
| 1 mol/kg | 1 mol/kg |
About the mole per kilogram (molal)
Molality exists to solve one problem: volume is not conserved and mass is. A 1.00 M solution prepared at 20 °C is no longer 1.00 M at 80 °C, because the liquid expanded and the same moles now occupy more litres. A 1.00 molal solution is 1.00 molal at every temperature, at every pressure, forever, because it is defined as \(b = n_{solute}/m_{solvent}\) with both quantities on a mass basis and neither of them caring about thermal expansion.
That is why the colligative properties are written in molality and not molarity. Freezing point depression is \(\Delta T_f = i K_f b\) and boiling point elevation is \(\Delta T_b = i K_b b\), where \(i\) is the van 't Hoff factor counting the particles each formula unit releases. For water \(K_f = 1.86\) K·kg/mol and \(K_b = 0.512\) K·kg/mol. A 1 molal solution of sodium chloride, which dissociates into two ions so \(i \approx 2\), depresses water's freezing point by about 3.7 K. These equations would be temperature-dependent nonsense if written in molarity, since the temperature is the thing being calculated.
The practical distinction: to make one litre of 1 M NaCl you weigh 58.44 g into a flask and top up to the 1 L mark. To make 1 molal NaCl you weigh 58.44 g and add exactly 1.000 kg of water, giving somewhat more than a litre of brine. For dilute aqueous work near room temperature the two are within a percent or two and people use them loosely. In a 5 molal solution, or in ethanol, or in anything hot, they diverge badly and the distinction has to be respected.