Molar Concentration

Molar concentration is the amount of substance of a specified constituent divided by the volume of the solution or mixture containing it. Commonly called molarity, it expresses how much of a constituent is present within a given volume, rather than its proportion by mass. It is usually reported in moles per litre and is widely used to describe solutions in chemistry. IUPAC uses the name amount concentration; substance concentration is also used in clinical chemistry. (goldbook.iupac.org)

Definition and units

For a constituent $B$, molar concentration is defined by

where $n_B$ is its amount of substance and $V$ is the total volume of the mixture. The notation $[B]$ is also common. Crucially, the denominator is the volume of the completed solution, not the initial volume of solvent used to prepare it. (goldbook.iupac.org)

In the International System of Units, the coherent derived unit is $\mathrm{mol\,m^{-3}}$. Laboratory practice commonly uses $\mathrm{mol\,L^{-1}}$, equivalent to $\mathrm{mol\,dm^{-3}}$. Thus,

The symbol “M” often denotes $\mathrm{mol\,L^{-1}}$: a 0.20 M solution contains 0.20 mol of the specified constituent per litre. Millimolar and micromolar correspond to $10^{-3}$ and $10^{-6}\ \mathrm{mol\,L^{-1}}$, respectively. (goldbook.iupac.org)

The entities being counted must be specified. They may be atoms, molecules, ions, or defined groups of particles. One mole contains exactly $6.02214076\times10^{23}$ specified entities, the number fixed by the Avogadro constant. Concentrations referring to different entities are therefore not automatically interchangeable. (bipm.org)

Calculation and dilution

For a pure solute of mass $m_B$ and molar mass $M_B$,

Mass, molar mass, and volume must be expressed in compatible units. As an illustrative calculation, 0.0500 mol of a solute in a final solution volume of 0.250 L gives a concentration of $0.200\ \mathrm{mol\,L^{-1}}$. A specified concentration and volume likewise determine the required amount through $n_B=c_BV$. (bipm.org)

Dilution lowers concentration by adding solvent while preserving the amount of the constituent under consideration. If no reaction, precipitation, or loss changes that amount,

For example, diluting 25.0 mL of a $0.400\ \mathrm{mol\,L^{-1}}$ stock solution to a final volume of 100.0 mL produces $0.100\ \mathrm{mol\,L^{-1}}$. The final volume is what matters: it need not equal the arithmetic sum of separately measured liquid volumes. (openstax.org)

Temperature dependence and related quantities

Because concentration contains a volume term, it depends on temperature whenever thermal expansion or contraction changes the solution volume. Even without any change in the amount of solute, heating or cooling can change molar concentration. Accurate comparisons consequently require attention to measurement temperature. (openstax.org)

Molar concentration differs from several other measures of composition:

• Molality, $b_B=n_B/m_{\mathrm{solvent}}$, expresses solute amount per mass of solvent, usually in $\mathrm{mol\,kg^{-1}}$. Unlike molar concentration, its denominator is not affected by thermal expansion. (old.goldbook.iupac.org)
• Mass concentration, $\rho_B=m_B/V$, expresses constituent mass per mixture volume. It is related to molar concentration by $\rho_B=c_BM_B$. Equal mass concentrations do not imply equal molar concentrations when molar masses differ. (goldbook.iupac.org)
• Mole fraction, $x_B=n_B/\sum_i n_i$, expresses a constituent’s amount relative to the total amount of all constituents. It is dimensionless, whereas molar concentration is amount divided by volume. (goldbook.iupac.org)

Constituents and dissolved species

A concentration based on the amount of material dissolved must be distinguished from the concentrations of individual species subsequently present. An electrolyte may dissociate into several ions. Under the assumption of complete dissociation, a $0.100\ \mathrm{mol\,L^{-1}}$ sodium chloride solution contains approximately $0.100\ \mathrm{mol\,L^{-1}}$ sodium ions and the same concentration of chloride ions—not that concentration of intact sodium chloride molecules. (openstax.org)

For a weak acid, the initial acid concentration is not generally equal to the equilibrium hydrogen-ion concentration, because ionization is incomplete. Calculations involving chemical equilibrium must distinguish the material introduced from the species actually present after equilibration. (openstax.org)

Applications

In analytical chemistry, titration determines an unknown concentration through reaction with a solution of known concentration. The measured titrant volume gives its amount through $n=cV$; stoichiometry then relates that amount to the analyte. Equal concentration–volume products apply directly only when the reacting amounts have a 1:1 ratio. (openstax.org)

In chemical kinetics, concentration appears in experimentally determined rate laws, such as $r=k[A]^p[B]^q$. The exponents describe how reaction rate responds to concentration and need not match the coefficients in the overall chemical reaction. (openstax.org)

For thermodynamic descriptions, molar concentration is distinguished from activity. On a concentration-based scale, activity can be expressed as $a_B=\gamma_Bc_B/c^\circ$, where $\gamma_B$ is an activity coefficient and $c^\circ$ is a standard concentration. Activity is dimensionless and accounts for nonideal behavior. The definition of pH, for example, uses hydrogen-ion activity rather than uncorrected molar concentration. (publications.iupac.org)