Molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.
Contents
1 Definition
2 Units
3 Related quantities
3.1 Number concentration
3.2 Mass concentration
3.3 Mole fraction
3.4 Mass fraction
3.5 Molality
4 Properties
4.1 Sum of molar concentrations – normalizing relations
4.2 Sum of products molar concentrations-partial molar volumes
4.3 Dependence on volume
5 Spatial variation and diffusion
6 Examples
6.1 Orders of magnitude
7 Formal concentration
8 References
9 External links
Definition
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:[1]
- c=nV=NNAV=CNA.{displaystyle c={frac {n}{V}}={frac {N}{N_{rm {A}},V}}={frac {C}{N_{rm {A}}}}.}
Here, n is the amount of the solute in moles,[2]N is the number of molecules present in volume V (in litres), the ratio N/V is the number concentration C, and NA is the Avogadro constant, approximately 6.022×1023mol−1.
In thermodynamics the use of molar concentration is often not convenient because the volume of most solutions slightly depends on temperature due to thermal expansion. This problem is usually resolved by introducing temperature correction factors, or by using a temperature-independent measure of concentration such as molality.[2]
The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.
Units
In the International System of Units (SI) the base unit for molar concentration is mol/m3. However, this is impractical for most laboratory purposes and most chemical literature traditionally uses mol/dm3, which is the same as mol/L. These traditional units are often denoted by the letter M, optionally preceded by an SI prefix as needed to denote sub-multiples, for example:
mol/m3 = 10−3mol/dm3 = 10−3mol/L = 10−3 M = 1 mmol/L = 1 mM.
The adjectives "millimolar" and "micromolar" refer to mM and μM (10−3mol/L and 10−6mol/L), respectively.
| Name | Abbreviation | Concentration | Concentration (SI unit) |
|---|---|---|---|
millimolar | mM | 10−3 mol/L | 100 mol/m3 |
| micromolar | μM | 10−6 mol/L | 10−3 mol/m3 |
| nanomolar | nM | 10−9 mol/L | 10−6 mol/m3 |
| picomolar | pM | 10−12 mol/L | 10−9 mol/m3 |
| femtomolar | fM | 10−15 mol/L | 10−12 mol/m3 |
| attomolar | aM | 10−18 mol/L | 10−15 mol/m3 |
| zeptomolar | zM | 10−21 mol/L | 10−18 mol/m3 |
| yoctomolar | yM[3] | 10−24 mol/L (1 particle per 1.6 L) | 10−21 mol/m3 |
Related quantities
Number concentration
The conversion to number concentration Ci{displaystyle C_{i}}
- Ci=ci⋅NA{displaystyle C_{i}=c_{i}cdot N_{rm {A}}}
where NA{displaystyle N_{rm {A}}}
Mass concentration
The conversion to mass concentration ρi{displaystyle rho _{i}}
- ρi=ci⋅Mi{displaystyle rho _{i}=c_{i}cdot M_{i}}
where Mi{displaystyle M_{i}}
Mole fraction
The conversion to mole fraction xi{displaystyle x_{i}}
- xi=ci⋅Mρ=ci⋅∑jxjMjρ{displaystyle x_{i}=c_{i}cdot {frac {M}{rho }}=c_{i}cdot {frac {sum _{j}x_{j}M_{j}}{rho }}}
- xi=ci⋅∑jxjMjρ−ciMi{displaystyle x_{i}=c_{i}cdot {frac {sum _{j}x_{j}M_{j}}{rho -c_{i}M_{i}}}}
where M{displaystyle M}
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.
- xi=cic=ci∑ci{displaystyle x_{i}={frac {c_{i}}{c}}={frac {c_{i}}{sum c_{i}}}}
Mass fraction
The conversion to mass fraction wi{displaystyle w_{i}}
- wi=ci⋅Miρ{displaystyle w_{i}=c_{i}cdot {frac {M_{i}}{rho }}}
Molality
The conversion to molality (for binary mixtures) is:
- b2=c2ρ−c2⋅M2{displaystyle b_{2}={frac {c_{2}}{rho -c_{2}cdot M_{2}}},}
where the solute is assigned the subscript 2.
For solutions with more than one solute, the conversion is:
- bi=ciρ−∑ci⋅Mi{displaystyle b_{i}={frac {c_{i}}{rho -sum c_{i}cdot M_{i}}},}
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 molar concentration of salts.
Sum of products molar concentrations-partial molar volumes
The sum of products between these quantities equals one.
- ∑ici⋅Vi¯=1{displaystyle sum _{i}c_{i}cdot {bar {V_{i}}}=1}
Dependence on volume
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 :
- ci=ci,T0(1+α⋅ΔT){displaystyle c_{i}={frac {c_{i,T_{0}}}{(1+alpha cdot Delta T)}}}
where ci,T0{displaystyle c_{i,T_{0}}}
Spatial variation and diffusion
Molar and mass concentration have different values in space where diffusion happens.
Examples
- 11.6 g of NaCl is dissolved in 100 g of water. The final mass concentration ρ(NaCl) is:
ρ(NaCl) = 11.6 g/11.6 g + 100 g = 0.104 g/g = 10.4 %
The density of such a solution is 1.07 g/mL, thus its volume is:
V = 11.6 g + 100 g/1.07 g/mL = 104.3 mL
The molar concentration of NaCl in the solution is therefore:
c(NaCl) = 11.6 g/58 g/mol / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L
Here, 58 g/mol is the molar mass of NaCl.
- A 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:
m(NaCl) = 2 mol/L × 0.1 L × 58 g/mol = 11.6 g
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.
- 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:
c(H2O) = 1000 g/L/18.02 g/mol ≈ 55.5 mol/L
Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is:
c(H2) = 88 g/L/2.02 g/mol = 43.7 mol/L
The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is:
c(OsO4) = 5.1 kg/L/254.23 g/mol = 20.1 mol/L.
- A typical protein in bacteria, such as E. coli, may have about 60 copies, and the volume of a bacterium is about 10−15{displaystyle 10^{-15}}
L. Thus, the number concentration C is:
C = 60 / (10−15 L)= 6×1016 L−1
The molar concentration is:
c = C/NA = 6×1016 L−1/6×1023 mol−1 = 10−7 mol/L = 100 nmol/L
Reference ranges for blood tests, sorted by molar concentration:
Orders of magnitude
Examples of molar concentration grouped by orders of magnitude. Source values are parenthesized where unit conversions were performed.
| Factor (Molarity) | SI prefix | Value | Item |
|---|---|---|---|
| 10−24 | yM | 7000166000000000000♠1.66 yM | 1 elementary entity per litre[4] |
| 10−23 | |||
| 10−22 | |||
| 10−21 | zM | 7000360000000000000♠3.6 zM | solar neutrinos on Earth (7010650000000000000♠6.5×1010 /cm2⋅s)[5] |
| 10−20 | 7001120000000000000♠12 zM | radon in ambient, outdoor air in the United States (7001148000000000000♠0.4 pCi/L ≈ 7006700000000000000♠7000/L)[6] | |
| 10−19 | |||
| 10−18 | aM | ||
| 10−17 | |||
| 10−16 | |||
| 10−15 | fM | 7000200000000000000♠2 fM | bacteria in surface seawater (7012100000000000000♠1×109/L)[7] |
| 10−14 | 7001200000000000000♠20 fM | virions in surface layer North Atlantic seawater (7013100000000000000♠10×109/L)[8] | |
| 7001500000000000000♠50–100 fM | gold in seawater[9] | ||
| 10−13 | |||
| 10−12 | pM | 6988751000000000000♠7.51–9.80 pM | normal range for erythrocytes in blood in an adult male (7015452000000000000♠(4.52–5.90)×1012/L)[10][11] |
| 10−11 | 6989100000000000000♠10–100 pM | gold in undersea hydrothermal fluids[9] | |
| 10−10 | |||
| 10−9 | nM | 6991499999999999999♠5 nM | inhaled osmium tetroxide is immediately dangerous to life or health (7000100000000000000♠1 mg Os/m3)[12] |
| 10−8 | |||
| 10−7 | 6993101000000000000♠101 nM | hydronium and hydroxide ions in pure water at 7002298150000000000♠25 °C[13] | |
| 10−6 | µM | ||
| 10−5 | |||
| 10−4 | 7002180000000000000♠180–480 µM | normal range for uric acid in blood[10] | |
| 7002570000000000000♠570 µM | inhaled carbon monoxide induces unconsciousness in 2–3 breathes and death in < 7002180000000000000♠3 min (7001128000000000000♠12.8 ppt)[14] | ||
| 10−3 | mM | 6996320000000000000♠0.32–32 mM | normal range of hydronium ions in stomach acid (pH 1.5–3.5)[15] |
| 6997549999999999999♠5.5 mM | upper bound for healthy blood glucose when fasting[16] | ||
| 6997780000000000000♠7.8 mM | upper bound for healthy blood glucose 2 hours after eating[16] | ||
| 10−2 | cM | 6998200000000000000♠20 mM | neutrinos during a supernova, 7011149597870700000♠1 AU from the core[17] |
| 6998446000000000000♠44.6 mM | pure ideal gas at 7002273149999999999♠0 °C and 7005101325000000000♠101.325 kPa[18] | ||
| 10−1 | dM | 6999140000000000000♠140 mM | sodium ions in blood plasma[10] |
| 6999480000000000000♠480 mM | sodium ions in seawater[19] | ||
| 100 | M | ||
| 101 | daM | 7001250000000000000♠25 M | helium in the solar core[20] |
| 7001400000000000000♠40 M | pure solid hydrogen[21] | ||
| 7001555000000000000♠55.5 M | pure water at 7002277149999999999♠4 °C[22] | ||
| 102 | hM | 7002118800000000000♠118.8 M | pure osmium at 7002293150000000000♠20 °C[23] |
| 103 | kM | ||
| 106 | MM | ||
| 109 | GM | ||
| 1012 | TM | ||
| 1015 | PM | ||
| 1017 | 7002228000000000000♠228 PM | nucleons in atomic nuclei (7017229999999999999♠2.3×1017 kg/m3 = 7044137000000000000♠1.37×1044/m3)[24] | |
| 1077 | 7077390000000000000♠3.9×1077 M | the Planck concentration (7104240000000000000♠2.4×10104/m3), inverse of the Planck volume |
Formal concentration
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 c(Na2CO3) = 1 mol/L, the molar concentrations are c(Na+) = 2 mol/L and c(CO2−
3) = 1 mol/L because the salt dissociates into these ions.
References
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount concentration, c".
^ ab Kaufman, Myron (2002). Principles of thermodynamics. CRC Press. p. 213. ISBN 0-8247-0692-7..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
^ David Bradley. "How low can you go? The Y to Y".
^ 7003100000000000000♠1/L ÷ NA ≈ 7000166000000000000♠1.66 yM
^ Bahcall, John N.; Serenelli, Aldo M.; Basu, Sarbani (1 March 2005). "New Solar Opacities, Abundances, Helioseismology, and Neutrino Fluxes". The Astrophysical Journal. 621 (1): L85–L88. doi:10.1086/428929. Retrieved 26 November 2018.
^ "Radon Toxicity Case Study: What are the Standards and Regulations for Environmental Radon Levels? | ATSDR - Environmental Medicine & Environmental Health Education - CSEM". www.atsdr.cdc.gov. CDC. Retrieved 26 November 2018.
^ Gamfeldt, Lars; Lefcheck, Jonathan S.; Byrnes, Jarrett E. K.; Cardinale, Bradley J.; Duffy, J. Emmett; Griffin, John N. (March 2015). "Marine biodiversity and ecosystem functioning: what's known and what's next?". Oikos. 124 (3): 252–265. doi:10.1111/oik.01549.
^ Bergh, Øivind; Børsheim, Knut Yngve; Bratbak, Gunnar; Heldal, Mikal (August 1989). "High abundance of viruses found in aquatic environments". Nature. 340 (6233): 467–468. doi:10.1038/340467a0. ISSN 0028-0836. Retrieved 26 November 2018.
^ ab "Gold in seawater". Earth and Planetary Science Letters. 98 (2): 208–221. 1 May 1990. doi:10.1016/0012-821X(90)90060-B. ISSN 0012-821X. Retrieved 26 November 2018.
^ abc Reference ranges for blood tests
^ "Erythrocyte Count (RBC): Reference Range, Interpretation, Collection and Panels". Medscape. 7 January 2017. Retrieved 26 November 2018.
^ "CDC - Immediately Dangerous to Life or Health Concentrations (IDLH): Osmium tetroxide (as Os) - NIOSH Publications and Products". www.cdc.gov. CDC. 2 November 2018. Retrieved 28 November 2018.
^ Bandura, Andrei V.; Lvov, Serguei N. (2006). "The Ionization Constant of Water over Wide Ranges of Temperature and Density" (PDF). Journal of Physical and Chemical Reference Data. 35 (1): 15–30. Bibcode:2006JPCRD..35...15B. doi:10.1063/1.1928231.
^ Goldstein, Mark (December 2008). "Carbon Monoxide Poisoning". Journal of Emergency Nursing. 34 (6): 538–542. doi:10.1016/j.jen.2007.11.014. PMID 19022078.
^ Marieb EN, Hoehn K (2010). Human anatomy & physiology. San Francisco: Benjamin Cummings. ISBN 0-8053-9591-1.
^ ab "Type 2 diabetes - Diagnosis and treatment - Mayo Clinic". www.mayoclinic.org.
^ "nature physics portal - looking back - Neutrinos and neutrino mass from a supernova". www.nature.com. Nature Publishing Group 2006. Retrieved 26 November 2018.
^ Vm = 8.3145 × 273.15 / 101.325 = 22.414 dm3/mol
^ 0.469 mol/kg at an average density of 1.025 kg/L
^ "Helio- and Asteroseismology". solar-center.stanford.edu. Stanford SOLAR Center. Retrieved 26 November 2018.
^ c(H2) = ≈80 g/L/2.02 g/mol ≈ 7001400000000000000♠40 M
^ Riddick 1970, Table of Physical Properties, Water 0b. pg 67-8.
^ c(Os) = 22,590 g/L/190.23 g/mol = 7002118800000000000♠118.8 M
^ "The Atomic Nucleus". www.cyberphysics.co.uk. Retrieved 26 November 2018.
External links
- Molar Solution Concentration Calculator
- Experiment to determine the molar concentration of vinegar by titration
