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Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
of a
chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entity, molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels ...
, in particular of a
solute In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
in a
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
, in terms of
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
per unit
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
of solution. In
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, the most commonly used unit for molarity is the number of
moles Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain * The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People *Abraham Moles, French engin ...
per
liter The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). ...
, having the unit symbol mol/L or mol/ dm3 in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.


Definition

Molar concentration or molarity is most commonly expressed in units of moles of
solute In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
per litre of
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
. For use in broader applications, it is defined as
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c: :c = \frac = \frac = \frac. Here, n is the amount of the solute in moles, N is the number of constituent particles present in volume V (in litres) of the solution, and N_\text is the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
, since 2019 defined as exactly . The ratio \frac is the
number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
C. In
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
the use of molar concentration is often not convenient because the volume of most solutions slightly depends on
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
due to
thermal expansion Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic ...
. This problem is usually resolved by introducing temperature correction
factors Factor, a Latin word meaning "who/which acts", may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, suc ...
, or by using a temperature-independent measure of concentration such as
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
. The
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...
quantity represents the dilution (volume) which can appear in Ostwald's
law of dilution Wilhelm Ostwald’s dilution law is a relationship proposed in 1888 between the dissociation constant ' and the degree of dissociation ' of a weak electrolyte. The law takes the form :K_d = \cfrac = \frac \cdot c_0 Where the square brackets deno ...
. ; Formality or analytical concentration If a molecular entity dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes called formal concentration or formality (''F''A) or analytical concentration (''c''A). 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

In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) the
coherent unit A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, inc ...
for molar concentration is mol/ m3. However, this is inconvenient for most laboratory purposes and most chemical literature traditionally uses mol/ dm3, which is the same as mol/ L. This traditional unit is often called a molar and denoted by the letter M, for example: : mol/ m3 = 10−3 mol/ dm3 = 10−3 mol/ L = 10−3 M = 1 mM = 1 mmol/L. To avoid confusion with
SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
mega Mega or MEGA may refer to: Science * mega-, a metric prefix denoting 106 * Mega (number), a certain very large integer in Steinhaus–Moser notation * "mega-" a prefix meaning "large" that is used in taxonomy * Gravity assist, for ''Moon-Eart ...
, which has the same abbreviation,
small caps In typography, small caps (short for "small capitals") are characters typeset with glyphs that resemble uppercase letters (capitals) but reduced in height and weight close to the surrounding lowercase letters or text figures. This is technicall ...
or
italicized In typography, italic type is a cursive font based on a stylised form of calligraphic handwriting. Owing to the influence from calligraphy, italics normally slant slightly to the right. Italics are a way to emphasise key points in a printed tex ...
''M'' are also used in journals and textbooks. Sub-multiples such as ''millimolar'' consist of the unit preceded by an
SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
:


Related quantities


Number concentration

The conversion to
number concentration A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
C_i is given by :C_i = c_i N_\text, where N_\text is the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
.


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 In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, p ...
of constituent i.


Mole fraction

The conversion to
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
x_i is given by :x_i = c_i \frac, where \overline is the average molar mass of the solution, \rho is the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
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 = \frac.


Mass fraction

The conversion to mass fraction w_i is given by :w_i = c_i \frac.


Molality

For binary mixtures, the conversion to
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
b_2 is :b_2 = \frac, 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.


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 = 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 , where c_ is the molar concentration at a reference temperature, \alpha is the
thermal expansion coefficient Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic ...
of the mixture.


Examples


See also

*
Molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
*
Orders of magnitude (molar concentration) This page lists examples of the orders of magnitude of molar concentration. Source values are parenthesized where unit conversions were performed. All orders SI multiples See also * Molarity * Osmolarity * Metric system * Scientific notation ...


References


External links


Molar Solution Concentration Calculator


{{DEFAULTSORT:Molar Concentration Chemical properties Amount of substance