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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, the mass concentration (or ) is defined as the
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
of a constituent divided by the
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). ...
of the mixture . :\rho_i = \frac For a pure chemical the mass concentration equals its
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. Mathematicall ...
(mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture. This explains the usage of (the lower case Greek letter
rho Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
), the symbol most often used for density.


Definition and properties

The volume in the definition refers to the volume of the solution, ''not'' the volume of the
solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
. 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. Sometimes the mass concentration is called titre.


Notation

The notation common with mass density underlines the connection between the two quantities (the mass concentration being the mass density of a component in the solution), but it can be a source of confusion especially when they appear in the same formula undifferentiated by an additional symbol (like a star superscript, a bolded symbol or varrho).


Dependence on volume

Mass concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature the dependence is : :\rho_i = \frac where is the mass concentration at a reference temperature, is the thermal expansion coefficient of the mixture.


Sum of mass concentrations - normalizing relation

The sum of the mass concentrations of all components (including the solvent) gives 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. Mathematicall ...
of the solution: :\rho = \sum_i \rho_i \, Thus, for pure component the mass concentration equals the density of the pure component.


Units

The SI-unit for mass concentration is kg/m3 (
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
/
cubic metre The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
). This is the same as mg/ mL and g/L. Another commonly used unit is g/(100 mL), which is identical to g/dL (
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to th ...
/
decilitre 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) ...
).


Usage in biology

In
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
, the " %" symbol is sometimes incorrectly used to denote mass concentration, also called "mass/volume percentage". A solution with 1 g of solute dissolved in a final volume of 100 mL 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 * Solutio ...
would be labeled as "1%" or "1% m/v" (mass/volume). The notation is mathematically flawed because the unit " %" can only be used for dimensionless quantities. "Percent solution" or "percentage solution" are thus terms best reserved for "mass percent solutions" (m/m = m% = mass solute/mass total solution after mixing), or "volume percent solutions" (v/v = v% = volume solute per volume of total solution after mixing). The very ambiguous terms "percent solution" and "percentage solutions" with no other qualifiers, continue to occasionally be encountered. This common usage of % to mean m/v in biology is because of many biological solutions being dilute and water-based or an
aqueous solution An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be r ...
. Liquid water has a density of approximately 1 g/cm3 (1 g/mL). Thus 100 mL of water is equal to approximately 100 g. Therefore, a solution with 1 g of solute dissolved in final volume of 100 mL aqueous solution may also be considered 1% m/m (1 g solute in 99 g water). This approximation breaks down as the solute concentration is increased (for example, in water–NaCl mixtures). High solute concentrations are often not physiologically relevant, but are occasionally encountered in pharmacology, where the mass per volume notation is still sometimes encountered. An extreme example is saturated solution of
potassium iodide Potassium iodide is a chemical compound, medication, and dietary supplement. It is a medication used for treating hyperthyroidism, in radiation emergencies, and for protecting the thyroid gland when certain types of radiopharmaceuticals are u ...
(SSKI) which attains 100 "%" m/v potassium iodide mass concentration (1 gram KI per 1 mL solution) only because the solubility of the dense salt KI is extremely high in water, and the resulting solution is very dense (1.72 times as dense as water). Although there are examples to the contrary, it should be stressed that the commonly used "units" of % w/v are grams per millilitre (g/mL). 1% m/v solutions are sometimes thought of as being gram/100 mL but this detracts from the fact that % m/v is g/mL; 1g of water has a volume of approximately 1 mL (at standard temperature and pressure) and the mass concentration is said to be 100%. To make 10 mL of an aqueous 1% cholate solution, 0.1 grams of cholate are dissolved in 10mL of water. Volumetric flasks are the most appropriate piece of glassware for this procedure as deviations from ideal solution behavior can occur with high solute concentrations. In solutions, mass concentration is commonly encountered as the ratio of mass/ olume solution or m/v. In water solutions containing relatively small quantities of dissolved solute (as in biology), such figures may be "percentivized" by multiplying by 100 a ratio of grams solute per mL solution. The result is given as "mass/volume percentage". Such a convention expresses mass concentration of 1 gram of solute in 100 mL of solution, as "1 m/v %".


Related quantities


Density of pure component

The relation between mass concentration and density of a pure component (mass concentration of single component mixtures) is: :\rho_i = \rho_i^* \frac\, where is the density of the pure component, the volume of the pure component before mixing.


Specific volume (or mass-specific volume)

Specific volume is the inverse of mass concentration only in the case of pure substances, for which mass concentration is the same as the density of the pure-substance: : \nu = \frac\ = \frac


Molar concentration

The conversion to
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 sol ...
is given by: :c_i = \frac where is the molar mass of constituent .


Mass fraction

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


Mole fraction

The conversion to mole fraction is given by: : x_i = \frac \frac where is the average molar mass of the mixture.


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 ...
is given by: :b_i = \frac


Spatial variation and gradient

The values of (mass and molar) concentration different in space triggers the phenomenon of
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
.


References

{{Chemical solutions Chemical properties Density