Molality is a measure of solution composition defined as the amount of substance of a solute divided by the mass of the solvent. Usually represented by (b) or (m), it is expressed in moles per kilogram of solvent, mol kg⁻¹. Unlike molar concentration, which uses the volume of the entire solution as its denominator, molality uses only the solvent mass. This distinction makes it useful for describing solutions when their volume changes with temperature. (old.goldbook.iupac.org)
Definition and notation
For solute (B) dissolved in solvent (A), molality is
[ b_B=\frac{n_B}{m_A}, ]
where (n_B) is the amount of solute in moles and (m_A) is the solvent mass in kilograms. Its unit in the International System of Units is mol kg⁻¹. The symbol (b) helps distinguish molality from mass, since both mass and molality may otherwise be represented by (m). Subscripts identify the component being described. (old.goldbook.iupac.org)
A solution containing 0.50 mol of solute dissolved in 2.0 kg of solvent therefore has a molality of 0.25 mol kg⁻¹. This is a direct application of the definition: the denominator is neither the total solution mass nor its volume. Adding solute increases the solution mass but does not, by itself, increase the solvent mass used in the calculation. (old.goldbook.iupac.org)
For several solutes sharing one solvent, each component has its own molality, (b_i=n_i/m_A). The solvent basis must remain consistent. In mixed-solvent systems, reporting conventions should specify whether the denominator refers to the combined solvent mass or to a particular solvent component. (goldbook.iupac.org)
Calculation from measured masses
When the solute amount is obtained by weighing, its molar mass (M_B) provides the conversion:
[ n_B=\frac{m_B}{M_B}, \qquad b_B=\frac{m_B}{M_Bm_A}. ]
The units must be consistent; for example, grams of solute may be divided by a molar mass in g mol⁻¹, but solvent mass must then be expressed in kilograms to obtain mol kg⁻¹. These equations follow from the definitions of molar mass and molality. (iupac.org)
As a hypothetical example, dissolving 10.0 g of a substance with molar mass 100.0 g mol⁻¹ in 250.0 g of water gives 0.100 mol of solute and a molality of 0.400 mol kg⁻¹. The combined mass is 260.0 g, but using that value as the denominator would calculate a different quantity. (old.goldbook.iupac.org)
Relationship to other composition measures
Molality, molar concentration, mass fraction, and mole fraction describe different ratios. They are interconvertible when the necessary component properties are known, but they should not be treated as interchangeable units. (iupac.org)
For a binary solution containing one solute and one solvent, the following relationships can be derived from their definitions:
[ b_B=\frac{w_B}{M_B(1-w_B)}, ]
[ x_B=\frac{b_BM_A}{1+b_BM_A}, ]
where (w_B) is the solute mass fraction, (x_B) its mole fraction, and both molar masses are expressed in kg mol⁻¹. These expressions assume that the component amounts are counted consistently; dissociation requires distinguishing an added compound from the species present in solution. (iupac.org)
Conversion to molar concentration requires the solution’s density. With density (\rho) in kg L⁻¹ and (M_B) in kg mol⁻¹, the derived binary-solution relationship is
[ c_B=\frac{\rho b_B}{1+b_BM_B}. ]
Here (c_B) is in mol L⁻¹. The equation incorporates total solution mass and volume; the solvent density alone is generally insufficient. (iupac.org)
Temperature dependence and colligative properties
At unchanged composition, molality does not vary merely because temperature changes: solvent mass and solute amount remain fixed, whereas thermal expansion changes solution volume and thus molar concentration. This does not mean that liquid-phase molality remains constant if evaporation, precipitation, or a chemical reaction changes its composition. (openstax.org)
Molality appears in dilute-solution expressions for colligative properties, particularly boiling-point elevation and freezing-point depression:
[ \Delta T_b=iK_bb, \qquad \Delta T_f=iK_fb. ]
The positive quantities (\Delta T_b) and (\Delta T_f) represent the respective temperature changes. The constants (K_b) and (K_f) characterize the solvent, while the van ’t Hoff factor (i) accounts approximately for the number of dissolved particles produced per solute formula unit. These equations apply under dilute-solution assumptions; boiling-point elevation additionally assumes a nonvolatile solute. (openstax.org)
For an electrolyte, dissociation produces ions, so the particle amount can exceed the amount of compound added. Interactions between dissolved species cause departures from simple particle-counting predictions. (openstax.org)
Thermodynamic use
In thermodynamics, molality provides a composition scale for defining thermodynamic activity. On a molality basis,
[ a_B=\gamma_B\frac{b_B}{b^\circ}, ]
where (a_B) is dimensionless, (\gamma_B) is an activity coefficient, and (b^\circ) is the standard molality, conventionally 1 mol kg⁻¹. The associated solute standard state is hypothetical and uses limiting infinite-dilution behavior, rather than necessarily describing a real solution at that molality. (goldbook.iupac.org)
Activity enters the chemical potential relation
[ \mu_B=\mu_B^\circ+RT\ln a_B, ]
with (R) the gas constant and (T) absolute temperature. Consequently, molality specifies composition, while the activity coefficient accounts for nonideal behavior; molality alone does not determine thermodynamic activity. (goldbook.iupac.org)