Molar concentration
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In [[chemistry]], '''molar concentration''', also called '''molarity''', is a measure of the [[concentration]] of a [[solute]] in a [[solution]], or of any [[molecule|molecular]], [[ion]]ic, or [[atom]]ic [[Chemical species|species]] in a given [[volume]]. However, in [[thermodynamics]] the use of molar concentration is often not very convenient, because the volume of most solutions slightly depends on [[temperature]] due to [[thermal expansion]]. This problem is usually resolved by introducing temperature correction [[coefficient|factors]], or by using a temperature-independent measure of concentration such as [[molality]].<ref name=kaufman>{{Citation
| author = Myron Kaufman
| title = Principles of thermodynamics
| page = 213
| publisher = [[CRC Press]]
| year = 2002
| url =
| doi =
| id =
| isbn = 0-8247-0692-7}}</ref>
==Notation==
Molar concentration is sometimes denoted by ''C'' or ''M'', but more often by simply placing [[square bracket]]s around the [[chemical formula]] or [[element symbol]]. For example,
:''C''<sub>Na<sup>+</sup></sub> = <nowiki>[</nowiki>Na<sup>+</sup><nowiki>]</nowiki>
denotes the molar concentration of sodium ions.
==Definition==
'''Molar concentration''' or '''molarity''' ''C'' is defined as [[Mole (unit)|mole]]s of [[solute]] per unit volume of [[solution]], or per unit volume available to the species:<ref>{{Citation
| author = John Kenkel
| title = Analytical chemistry for technicians
| page = 67
| publisher = [[CRC Press]]
| year = 2002
| volume =
| edition =
| url =
| doi =
| id =
| isbn = 1-5667-0519-3}}</ref>
:<math>C=\frac{\nu}{V}=\frac{N}{N_A\,V}=\frac{n}{N_A}</math> .
Here, <math>\nu</math> is the number of moles of the solute,<ref name=kaufman/> ''N'' is the number of molecules present in the volume ''V'', the ratio ''N''/''V'' is the [[number density]] ''n'', and ''N''<sub>A</sub> is the [[Avogadro constant|Avogadro's number]], approximately 6.022×10<sup>23</sup> [[Mole (unit)|mol]]<sup>-1</sup>.
==Units==
The [[SI]] [[Units of measurement|units]] for molar concentration are [[Mole (unit)|mol]]/[[Metre|m]]<sup>3</sup>. However, most chemical literature traditionally uses [[Mole (unit)|mol]]/[[Decimetre|dm]]<sup>3</sup>, which is the same as [[Mole (unit)|mol]]/[[Litre|L]]. These traditional units are often denoted by a capital letter M (pronounced "molar"), sometimes preceded by an [[SI prefix]], as in:
:10<sup>-6</sup> [[Mole (unit)|mol]]/[[Metre|m]]<sup>3</sup> = 10<sup>-3</sup> [[Mole (unit)|mol]]/[[Decimetre|dm]]<sup>3</sup> = 10<sup>-3</sup> [[Mole (unit)|mol]]/[[Litre|L]] = 10<sup>-3</sup> M = 1 mM .
This way, words "millimolar" and "micromolar" refer to mM and μM (10<sup>-3</sup> [[Mole (unit)|mol]]/[[Litre|L]] and 10<sup>-6</sup> [[Mole (unit)|mol]]/[[Litre|L]]) respectively.
==Examples==
Most proteins are present in the [[bacteria]] such as [[E. coli]] at 60 copies or fewer. The volume of a bacterium is 10<sup>-15</sup> [[litre|L]], which gives us ''C'' = ''N'' / (''N''<sub>A</sub>·''V'') = 10<sup>-7</sup> M = 100 nM. (Here, nM is "nanomolar", ''i.e.'' 10<sup>-9</sup> moles per litre).
Consider 2 [[gram]]s of [[Sodium chloride|NaCl]] dissolved in 15 [[millilitre|mL]] of water. As 58 grams of NaCl is 1 mole of molecules (since [[molar mass]] of NaCl is 58 g/mol), and 1 millilitre is 0.001 litre, this gives ''C'' = (2/58 [[Mole (unit)|mol]])/(0.015 L) = 2.3 M.
==References==
{{Reflist}}
==See also==
*[[Molar solution]]
*[[Concentration#Normality|Normality]]
*[[Osmolarity]]
*[[Molecular weight]]
==External links==
*[http://web.lemoyne.edu/~giunta/chm151L/vinegar.html Experiment to determine the molar concentration of vinegar by titration]
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