Molar concentration

Molar concentration, or molarity, is most commonly expressed in units of moles of solute per litre of solution. For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c: : c = \frac{n}{V} = \frac{N}{N_\text{A}\,V} = \frac{C}{N_\text{A}}. Here, n is the amount of the solute in moles, The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution. Formality or analytical concentration If a molecule or salt dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes called formal concentration or formality (FA) or analytical concentration (cA). For example, if a sodium carbonate solution () has a formal concentration of c() = 1 mol/L, the molar concentrations are c() = 2 mol/L and c() = 1 mol/L because the salt dissociates into these ions. == Units ==

While there is clear consensus on the equivalence of units: : 1 mol/m3 = 10−3 mol/dm3 = 10−3 mol/L = 10−3 M = 1 mM = 1 mmol/L, guidance on unit names and abbreviations varies: The SI prefix "mega" (symbol M) has the same symbol. However, the prefix is never used alone, so "M" unambiguously denotes molar. Sub-multiples, such as "millimolar" (mM) and "nanomolar" (nM), consist of the unit preceded by an SI prefix: == Related quantities ==

Number concentration The conversion to number concentration C_i is given by : C_i = c_i N_\text{A}, where N_\text{A} is the Avogadro constant. Mass concentration The conversion to mass concentration \rho_i is given by : \rho_i = c_i M_i, where M_i is the molar mass of constituent i. Mole fraction The conversion to mole fraction x_i is given by : x_i = c_i \frac{\overline{M}}{\rho}, where \overline{M} is the average molar mass of the solution, \rho is the density of the solution. A simpler relation can be obtained by considering the total molar concentration, namely, the sum of molar concentrations of all the components of the mixture: : x_i = \frac{c_i}{c} = \frac{c_i}{\sum_j c_j}. Mass fraction The conversion to mass fraction w_i is given by : w_i = c_i \frac{M_i}{\rho}. Molality For binary mixtures, the conversion to molality b_2 is : b_2 = \frac{c_2}{\rho - c_1 M_1}, where the solvent is substance 1, and the solute is substance 2. For solutions with more than one solute, the conversion is : b_i = \frac{c_i}{\rho - \sum_{j\neq i} c_j M_j}. == Properties ==

Sum of molar concentrations – normalizing relations The sum of molar concentrations gives the total molar concentration, namely the density of the mixture divided by the molar mass of the mixture or by another name the reciprocal of the molar volume of the mixture. In an ionic solution, ionic strength is proportional to the sum of the molar concentration of salts. Sum of products of molar concentrations and partial molar volumes The sum of products between these quantities equals one: : \sum_i c_i \overline{V_i} = 1. Dependence on volume The molar concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature, the dependence is : c_i = \frac {c_{i,T_0}}{1 + \alpha\Delta T}, where c_{i,T_0} is the molar concentration at a reference temperature, \alpha is the thermal expansion coefficient of the mixture. == Examples ==