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| {{Redirect-distinguish|Molarity|Molality}}
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| In chemistry, the '''molar concentration''', <math>c_i</math> is defined as the [[amount of substance|amount]] of a constituent <math>n_i</math> (usually measured in [[Mole (unit)|moles]] – hence the name) divided by the [[volume]] of the mixture <math>V</math>:<ref name="GoldBook">{{GoldBookRef|title=amount concentration, ''c''|file=A00295}}</ref>
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| :<math>c_i = \frac {n_i}{V}</math>
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| It is also called '''molarity''', '''amount-of-substance concentration''', '''amount concentration''', '''substance concentration''', or simply '''concentration'''. The volume <math>V</math> in the definition <math>c_i = n_i/V</math> refers to the volume of the solution, ''not'' the volume of the solvent. One litre of a solution usually contains either slightly more or slightly less than 1 litre of solvent because the process of dissolution causes volume of liquid to increase or decrease.
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| The [[reciprocal]] quantity represents the dilution (volume) which can appear in Ostwald's [[law of dilution]].
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| == Notation ==
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| In addition to the notation <math>c_i</math> there is a notation using brackets and the formula of a compound like [A]. This notation is encountered especially in [[equilibrium constant]]s and [[reaction quotient]]s.
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| == Units ==
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| The [[International System of Units|SI unit]] is mol/m<sup>3</sup>. However, more commonly the unit mol/[[Liter|L]] is used.
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| A solution of concentration 1 mol/L is also denoted as "1 molar" (1 M).
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| :1 mol/L = 1 mol/[[Decimetre|dm]]<sup>3</sup> = 1 mol dm<sup>−3</sup> = 1 M = 1000 mol/m<sup>3</sup>.
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| An [[SI prefix]] is often used to denote concentrations. Commonly used units are listed in the table hereafter:
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| {|class="wikitable" style="text-align: center; " border="0"
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| !Name
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| !Abbreviation
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| !Concentration
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| !Concentration (SI unit)
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| |-
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| |millimolar
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| |mM
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| |10<sup>−3</sup> mol/dm<sup>3</sup>
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| |10<sup>0</sup> mol/m<sup>3</sup>
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| |-
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| |micromolar
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| |μM
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| |10<sup>−6</sup> mol/dm<sup>3</sup>
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| |10<sup>−3</sup> mol/m<sup>3</sup>
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| |-
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| |nanomolar
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| |nM
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| |10<sup>−9</sup> mol/dm<sup>3</sup>
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| |10<sup>−6</sup> mol/m<sup>3</sup>
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| |-
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| |picomolar
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| |pM
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| |10<sup>−12</sup> mol/dm<sup>3</sup>
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| |10<sup>−9</sup> mol/m<sup>3</sup>
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| |-
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| |femtomolar
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| |fM
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| |10<sup>−15</sup> mol/dm<sup>3</sup>
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| |10<sup>−12</sup> mol/m<sup>3</sup>
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| |-
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| |attomolar
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| |aM
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| |10<sup>−18</sup> mol/dm<sup>3</sup>
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| |10<sup>−15</sup> mol/m<sup>3</sup>
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| |-
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| |zeptomolar
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| |zM
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| |10<sup>−21</sup> mol/dm<sup>3</sup>
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| |10<sup>−18</sup> mol/m<sup>3</sup>
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| |-
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| |yoctomolar
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| |yM<ref>{{cite web|url=http://www.sciencebase.com/yocto.html|title=How low can you go? The Y to Y|author=David Bradley}}</ref>
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| |10<sup>−24</sup> mol/dm<sup>3</sup><br />(1 particle per 1.6 L)
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| |10<sup>−21</sup> mol/m<sup>3</sup>
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| |}
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| == Related quantities ==
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| === Number concentration ===
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| {{main|Number concentration}}
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| The conversion to [[number concentration]] <math>C_i</math> is given by:
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| :<math>C_i = c_i \cdot N_{\rm A}</math>
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| where <math>N_{\rm A}</math> is the [[Avogadro constant]], approximately 6.022{{e|23}} [[Mole (unit)|mol]]<sup>−1</sup>.
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| === Mass concentration===
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| {{main|Mass concentration (chemistry)}}
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| The conversion to [[mass concentration (chemistry)|mass concentration]] <math>\rho_i</math> is given by:
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| :<math>\rho_i = c_i \cdot M_i</math>
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| where <math>M_i</math> is the [[molar mass]] of constituent <math>i</math>.
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| === Mole fraction===
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| {{main|Mole fraction}}
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| The conversion to [[mole fraction]] <math>x_i</math> is given by:
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| :<math>x_i = c_i \cdot \frac{M}{\rho} = c_i \cdot \frac{\sum_i x_i M_i}{\rho}</math>
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| :<math>x_i= c_i \cdot \frac{\sum x_j M_j}{\rho - c_i M_i}</math>
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| where <math>M</math> is the average molar mass of the solution, <math>\rho</math> is the [[density]] of the solution and j is the index of other solutes. | |
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| 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.
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| :<math>x_i = \frac{c_i}{c} = \frac{c_i}{\sum c_i}</math>
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| === Mass fraction===
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| {{main|Mass fraction (chemistry)}}
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| The conversion to [[mass fraction (chemistry)|mass fraction]] <math>w_i</math> is given by:
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| :<math>w_i = c_i \cdot \frac{M_i}{\rho}</math>
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| === Molality ===
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| {{main|Molality}}
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| The conversion to [[molality]] (for binary mixtures) is:
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| :<math> b_2 = \frac{{c_2}}{{\rho - c_2 \cdot M_2}} \,</math>
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| where the solute is assigned the subscript 2.
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| For solutions with more than one solute, the conversion is:
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| :<math> b_i = \frac{{c_i}}{{\rho - \sum c_i \cdot M_i}} \,</math>
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| == Properties ==
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| ===Sum of molar concentrations - normalizing relation===
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| 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 molar concentration of salts.
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| ===Sum of products molar concentrations-partial molar volumes===
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| The sum of products between these quantities equals one.
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| :<math>\sum_i c_i \cdot \bar{V_i} = 1</math>
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| ===Dependence on volume===
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| 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 :
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| :<math>c_i = \frac {{c_{i,T_0}}}{{(1 + \alpha \cdot \Delta T)}}</math>
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| where <math>c_{i,T_0}</math> is the molar concentration at a reference temperature, <math>\alpha</math> is the thermal expansion coefficient of the mixture.
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| ==Spatial variation and diffusion==
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| Molar and mass concentration have different values in space where diffusion happens.
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| == Examples ==
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| '''Example 1:''' Consider 11.6 g of [[NaCl]] dissolved in 100 g of water. The final mass concentration <math>\rho</math>(NaCl) will be: | |
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| :<math>\rho</math>(NaCl) = 11.6 g / (11.6 g + 100 g) = 0.104 g/g = 10.4 %
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| The density of such a solution is 1.07 g/mL, thus its volume will be:
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| :<math>V</math> = (11.6 g + 100 g) / (1.07 g/mL) = 104.3 mL
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| The molar concentration of NaCl in the solution is therefore:
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| :<math>c</math>(NaCl) = (11.6 g / 58 g/mol) / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L
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| Here, 58 g/mol is the molar mass of NaCl.
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| '''Example 2:''' Another typical task in chemistry is the preparation of 100 mL (= 0.1 L) of a 2 mol/L solution of NaCl in water. The mass of salt needed is:
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| :<math>m</math>(NaCl) = 2 mol/L * 0.1 L * 58 g/mol = 11.6 g
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| To create the solution, 11.6 g NaCl are placed in a [[volumetric flask]], dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL.
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| '''Example 3:''' The density of [[water]] is approximately 1000 g/L and its molar mass is 18.02 g/mol (or 1/18.02=0.055 mol/g). Therefore, the molar concentration of water is:
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| :<math>c</math>(H<sub>2</sub>O) = 1000 g/L / (18.02 g/mol) = 55.5 mol/L
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| Likewise, the concentration of [[solid hydrogen]] (molar mass = 2.02 g/mol) is:
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| :<math>c</math>(H<sub>2</sub>) = 88 g/L / (2.02 g/mol) = 43.7 mol/L | |
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| The concentration of pure [[osmium tetroxide]] (molar mass = 254.23 g/mol) is:
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| :<math>c</math>(OsO<sub>4</sub>) = 5.1 kg/L / (254.23 g/mol) = 20.1 mol/L.
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| '''Example 4:''' Proteins in [[bacterium|bacteria]], such as ''[[Escherichia coli|E. coli]]'', usually occur at about 60 copies, and the volume of a bacterium is about <math>10^{-15}</math> L. Thus, the number concentration <math>C</math> is:
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| :<math>C</math> = 60 / (10<sup>−15</sup> L)= 6{{e|16}} L<sup>−1</sup> | |
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| The molar concentration is:
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| :<math>c = C / N_A</math> = 6{{e|16}} L<sup>−1</sup> / (6{{e|23}} mol<sup>−1</sup>) = 10<sup>−7</sup> mol/L = 100 nmol/L
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| [[Image:Reference ranges for blood tests - by molarity.png|thumb|700px|center|[[Reference ranges for blood tests]], sorted by molar concentration.]]
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| If the concentration refers to original chemical formula in solution, the molar concentration is sometimes called ''formal concentration''. For example, if a sodium carbonate solution has a formal concentration of <math>c</math>(Na<sub>2</sub>CO<sub>3</sub>) = 1 mol/L, the molar concentrations are <math>c</math>(Na<sup>+</sup>) = 2 mol/L and <math>c</math>(CO<sub>3</sub><sup>2-</sup>) = 1 mol/L because the salt dissociates into these ions.
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.physiologyweb.com/calculators/molar_solution_concentration_calculator.html Molar Solution Concentration Calculator]
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| * [http://web.lemoyne.edu/~giunta/chm151L/vinegar.html Experiment to determine the molar concentration of vinegar by titration]
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| {{Chemical solutions}}
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| {{DEFAULTSORT:Molar Concentration}}
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| <!--Categories-->
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| [[Category:Chemical properties]]
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