Definitions

# concentration

[kon-suhn-trey-shuhn]
concentration, in chemistry, measure of the relative proportions of two or more quantities in a mixture. The concentration of a solute is very important in studying chemical reactions because it determines how often molecules collide in solution and thus indirectly determines the rates of reactions and the conditions at equilibrium (see chemical equilibrium).

Concentration may be expressed in a number of ways. The simplest statement of the concentrations of the components of a mixture is in terms of their percentages by weight or volume. Mixtures of solids or liquids are frequently specified by weight percentage concentrations, such as alloys of metals or mixtures used in cooking, whereas mixtures of gases are usually specified by volume percentages. Very low concentrations may be expressed in parts per million (ppm), as in specifying the relative presence of various substances in the atmosphere.

In addition to these means of expressing concentration, several others are defined especially for describing solutions: molarity, molality, mole fraction, formality, and normality. Some of these define the concentration of the solute in reference to the amount of solvent, others in reference to the total amount of solution. The molarity of a solution is the number of moles of solute per liter of solution; e.g., a solution of glucose in water containing 180.16 grams (1 gram-molecular weight, or mole) of glucose per liter of solution is referred to as one molar (1 M). The molality of a solution is the number of moles of solute per 1,000 grams of solvent; a solution prepared by dissolving 180.16 grams of glucose in 1,000 grams of water is one molal (1 m). The mole fraction of a solution is the ratio of moles of solute to the total number of moles in the solution. Since ionic compounds, such as sodium chloride, NaCl, do not occur as molecules, their concentrations cannot be expressed in terms of molarity, molality, or mole fraction. Instead, the concentration of an ionic compound in solution may be given by its formality, the number of gram-formula weights of the compound per liter of solution; e.g., a solution containing 58.44 grams (one gram-formula weight) of NaCl per liter of solution is one formal (1 F). In considering the reactions of certain solutions in combination, for example the neutralization of acids and bases, a useful expression of the concentration is the normality of each solution, the number of gram-equivalent weights of solute per liter of solution (see equivalent weight); e.g., a solution containing 49.04 grams (one gram-equivalent weight) of sulfuric acid, H2SO4, per liter of solution is one normal (1 N). Concentrations of solutions may also frequently be given in terms of the weight of solute in a given volume of solvent or solution.

Internment centre established by a government to confine political prisoners or members of national or minority groups for reasons of state security, exploitation, or punishment. The prisoners are usually selected by executive decree or military order. Camps are usually built to house many people, typically in highly crowded conditions. Countries that have used such camps include Britain during the South African War, the Soviet Union (see Gulag), the U.S. (see Manzanar Relocation Center), and Japan, which interned Dutch civilians in the Dutch East Indies during World War II. A variation, called a “reeducation camp,” was used in Vietnam after 1975 and in Cambodia under the Khmer Rouge. Most notorious were the death camps of Nazi Germany, including Auschwitz, Bergen-Belsen, Buchenwald, Dachau, and Treblinka.

formerly hyperactivity

Behavioral syndrome in children, whose major symptoms are inattention and distractibility, restlessness, inability to sit still, and difficulty concentrating on one thing for any period of time. It occurs in about 5percnt of all schoolchildren, and it is three times more common in boys than in girls. It can adversely affect learning, though many children with ADD can learn to control their behaviour sufficiently to perform satisfactorily in school. It appears to be caused by a combination of genetic and environmental factors. Certain aspects of the syndrome may persist into adulthood. Treatment usually entails counseling and close parental supervision, and it may also include prescription medication.

In psychology, the act or state of applying the mind to an object of sense or thought. Wilhelm Wundt was perhaps the first psychologist to study attention, distinguishing between broad and restricted fields of awareness. He was followed by William James, who emphasized active selection of stimuli, and Ivan Pavlov, who noted the role attention plays in activating conditioned reflexes. John B. Watson sought to define attention not as an “inner” process but rather as a behavioral response to specific stimuli. Psychologists today consider attention against a background of “orienting reflexes” or “preattentive processes,” whose physical correlates include changes in the voltage potential of the cerebral cortex and in the electrical activity of the skin, increased cerebral blood flow, pupil dilation, and muscular tightening. Seealso attention deficit disorder.

In chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in a substance.

To concentrate a solution, one must add more solute, or reduce the amount of solvent (for instance, by selective evaporation). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute.

Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve (except in certain circumstances, when supersaturation may occur). Instead, phase separation will occur, leading to either coexisting phases or a suspension. The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute.

Analytical concentration includes all the forms of that substance in the solution.

## Qualitative description

Often in informal, non-technical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" or "weak" for solutions of relatively low concentration and of others like "concentrated" or "strong" for solutions of relatively high concentration. Those terms relate the amount of a substance in a mixture to the observable intensity of effects or properties caused by that substance. For example, a practical rule is that the more concentrated a chromatic solution is, the more intensely colored it is.

## Quantitative notation

For scientific or technical applications, a qualitative account of concentration is almost never sufficient; therefore quantitative measures are needed to describe concentration. There are a number of different ways to quantitatively express concentration; the most common are listed below. They are based on mass, volume, or both. Depending on what they are based on it is not always trivial to convert one measure to the other, because knowledge of the density might be needed to do so. At times this information may not be available, particularly if the temperature varies.

### Mass versus volume

Some units of concentration — particularly the most popular one, molarity — require knowledge of a substance's volume, which unlike mass is variable depending on ambient temperature and pressure. In fact (partial) molar volume can even be a function of concentration itself. This is why volumes are not necessarily completely additive when two liquids are added and mixed. Volume-based measures for concentration are therefore not to be recommended for non-dilute solutions or problems where relatively large differences in temperature are encountered (e.g. for phase diagrams).

Unless otherwise stated, all the following measurements of volume are assumed to be at a standard state temperature and pressure (for example 25 degrees Celsius at 1 atmosphere or 101.325 kPa). The measurement of mass does not require such restrictions.

Mass can be determined at a precision of < 0.2 mg on a routine basis with an analytical balance and more precise instruments exist. Both solids and liquids are easily quantified by weighing.

The volume of a liquid is usually determined by calibrated glassware such as burettes and volumetric flasks. For very small volumes precision syringes are available. The use of graduated beakers and cylinders is not recommended as their indication of volume is mostly for decorative rather than quantitative purposes. The volume of solids, particularly of powders, is often difficult to measure, which is why mass is the more usual measure. For gases the opposite is true: the volume of a gas can be measured in a gas burette, if care is taken to control the pressure, but the mass is not easy to measure due to buoyancy effects.

### Molarity

Molarity (in units of mol/L, molar, or M) or molar concentration denotes the number of moles of a given substance per liter of solution. A capital letter M is used to abbreviate the units of mol/L. For instance:

$frac\left\{2.0 text\left\{ moles of dissolved particles\right\}\right\}\left\{4.0 text\left\{ liters of liquid\right\}\right\} = text\left\{ solution of 0.5 mol/L\right\}.$
The actual formula for molarity is:
$frac\left\{text\left\{ Moles of solute\right\}\right\}\left\{text\left\{ Liters of solution\right\}\right\} = text\left\{ Molarity of solution\right\}.$

Such a solution may be described as "0.50 molar." It must be emphasized that a 0.5 molar solution contains 0.5 moles of solute in 1.0 liter of solution. This is not equivalent to 1.0 liter of solvent. A 0.5 mol/L solution will contain either slightly more or slightly less than 1 liter of solvent because the process of dissolution causes the volume of the liquid to increase or decrease.

Following the SI system of units, the National Institute of Standards and Technology, the United States authority on measurement, considers the term molarity and the unit symbol M to be obsolete, and suggests instead the amount-of-substance concentration (c) with units mol/m3 or other units used alongside the SI such as mol/L. This recommendation has not been universally implemented in academia or chemistry research yet.

Preparation of a solution of known molarity involves adding an accurately weighed amount of solute to a volumetric flask, adding some solvent to dissolve it, then adding more solvent to fill to the volume mark.

When discussing the molarity of minute concentrations, such as in pharmacological research, molarity is expressed in units of millimolar (mmol/L, mM, 1 thousandth of a molar), micromolar (μmol/L, μM, 1 millionth of a molar) or nanomolar (nmol/L, nM, 1 billionth of a molar).

Although molarity is by far the most commonly used measure of concentration, particularly for dilute aqueous solutions, it does suffer from a number of disadvantages. Masses can be determined with great precision as balances are often very precise. Determining volume is often not as precise. In addition, due to a thermal expansion, the molarity of a solution changes with temperature without adding or removing any mass. For non-dilute solutions another problem is that the molar volume of a substance is itself a function of concentration so that volume is not strictly additive.

### Molality

Molality (mol/kg, molal, or m) denotes the number of moles of solute per kilogram of solvent (not solution). For instance: adding 1.0 mole of solute to 2.0 kilograms of solvent constitutes a solution with a molality of 0.50 mol/kg. Such a solution may be described as "0.50 molal". The term molal solution is used as a shorthand for a "one molal solution", i.e. a solution which contains one mole of the solute per 1000 grams of the solvent.

Following the SI system of units, the National Institute of Standards and Technology, the United States authority on measurement, considers the unit symbol m to be obsolete, and suggests instead the term 'molality of substance B' (mB) with units mol/kg or a related unit of the SI. This recommendation has not been universally implemented in academia yet.

Note that molality is sometimes represented by the symbol (m), while molarity by the symbol (M). The two symbols are not meant to be confused, and should not be used as symbols for units. The SI unit for molality is mol/kg. (The unit m means meter.)

Like other mass-based measures, the determination of molality only requires a good scale, because the masses of both solvent and solute can be obtained by weighing, and molality is independent of the physical conditions like temperature and pressure, providing advantages over molarity.

In a dilute aqueous solution near room temperature and standard atmospheric pressure, the molarity and molality will be very similar in value. This is because 1 kg of water roughly corresponds to a volume of 1 L at these conditions, and because the solution is dilute, the addition of the solute makes a negligible impact on the volume of the solution.

However, in all other conditions, this is usually not the case.

### Mole fraction

The mole fraction Χ, (also called molar fraction) denotes the number of moles of solute as a proportion of the total number of moles in a solution. For instance: 1 mole of solute dissolved in 9 moles of solvent has a mole fraction of 1/10 or 0.1. Mole fractions are dimensionless quantities. (The mole percentage or molar percentage, denoted "mol %" and equal to 100% times the mole fraction, is sometimes quoted instead of the mole fraction.)

This measure is used very frequently in the construction of phase diagrams. It has a number of advantages:

• the measure is not temperature dependent (such as molarity) and does not require knowledge of the densities of the phase(s) involved
• a mixture of known mole fraction can be prepared by weighing off the appropriate masses of the constituents
• the measure is symmetrical: in the mole fractions Χ=0.1 and Χ=0.9, the roles of 'solvent' and 'solute' are reversed.

As both mole fractions and molality are only based on the masses of the components it is easy to convert between these measures. This is not true for molarity, which requires knowledge of the density.

### Mass percentage (fraction)

Mass percentage denotes the mass of a substance in a mixture as a percentage of the mass of the entire mixture. (Mass fraction xm can be used instead of mass percentage by dividing mass percentage to 100.) For instance: if a bottle contains 40 grams of ethanol and 60 grams of water, then it contains 40% ethanol by mass or 0.4 mass fraction ethanol. Commercial concentrated aqueous reagents such as acids and bases are often labeled in concentrations of weight percentage with the specific gravity also listed. In older texts and references this is sometimes referred to as weight-weight percentage (abbreviated as w/w or wt%). In water pollution chemistry, a common term of measuring total mass percentage of dissolved solids in an aqueous medium is total dissolved solids.

### Mass-volume percentage

Mass-volume percentage, (sometimes referred to as weight-volume percentage or percent weight per volume and often abbreviated as % m/v or % w/v) describes the mass of the solute in g per 100 mL of the resulting solution. Mass-volume percentage is often used for solutions made from a solid solute dissolved in a liquid. For example, a 40% w/v sugar solution contains 40 g of sugar per 100 mL of resulting solution.

### Mass-volume ratio

Often used in medicine and pharmacology, a ratio of the weight of a drug dissolved in a volume of water, is presented as, grams of solute : mL of water. Practitioners use the term "dilution" when referring to this arcane unit. The most ubiquitous example is epinephrine solutions where a 1:100,000 solution has 1 g epinephrine in 100,000 mL water. This is equivalent to 0.01 g/L epinephrine solution.

When the volume considered is a gas, a specific approach is needed: the gas' pressure and temperature conditions must be considered. A typical use is in air pollution emission quantification. It is very common to find values such as 50 g/Nm3 or 50 g/m3N. The "N" before or after the cubic meter indicates that the gas is under the Standard conditions for temperature and pressure.

### Volume-volume percentage

Volume-volume percentage (sometimes referred to as percent volume per volume and abbreviated as % v/v) describes the volume of the solute in mL per 100 mL of the resulting solution. This is most useful when a liquid - liquid solution is being prepared, although it is used for mixtures of gases as well. For example, a 40% v/v ethanol solution contains 40 mL ethanol per 100 mL total volume. The percentages are only additive in the case of mixtures of ideal gases.

### Normality

Normality highlights the chemical nature of salts: in solution, salts dissociate into distinct reactive species (ions such as H+, Fe3+, or Cl-). Normality accounts for any discrepancy between the concentrations of the various ionic species in a solution. For example, in a salt such as MgCl2, there are two moles of Cl- for every mole of Mg2+, so the concentration of Cl- is said to be 2 N (read: "two normal"). Further examples are given below.

#### Definition

A normal is one gram equivalent of a solute per liter of solution. The definition of a gram equivalent varies depending on the type of chemical reaction that is discussed - it can refer to acids, bases, redox species, and ions that will precipitate.

#### Usage

It is critical to note that normality measures a single ion which takes part in an overall solute. For example, one could determine the normality of hydroxide or sodium in an aqueous solution of sodium hydroxide, but the normality of sodium hydroxide itself has no meaning. Nevertheless it is often used to describe solutions of acids or bases, in those cases it is implied that the normality refers to the H+ or OH ion. For example, 2 Normal sulfuric acid (H2SO4), means that the normality of H+ ions is 2, or that the molarity of the sulfuric acid is 1. Similarly for 1 Molar H3PO4 the normality is 3 as it contains three H+ ions.

#### Specific cases

As ions in solution can react through different pathways, there are three common definitions for normality as a measure of reactive species in solution:

• In acid-base chemistry, normality is used to express the concentration of protons or hydroxide ions in the solution. Here, the normality differs from the molarity by an integer value - each solute can produce n equivalents of reactive species when dissolved. For example: 1 M aqueous Ca(OH)2 is 2 N (normal) in hydroxide.
• In redox reactions, normality measures the quantity of oxidizing or reducing agent that can accept or furnish one mole of electrons. Here, the normality scales from the molarity, most commonly, by a fractional value. Calculating the normality of redox species in solution can be challenging.
• In precipitation reactions, normality measures the concentration of ions which will precipitate in a given reaction. Here, the normality scales from the molarity again by an integer value.

#### Practical uses

The measure of normality is extremely useful for titrations - given two species that are known to react with a known ratio, one simply needs to scale the volumes of solutions with known normalities to get a complete reaction with the following equation:

NaVa=NbVb

However, normality cannot reliably represent an unambiguous measure of the concentration of a solution. Since the measure of normality depends on the reaction that the solute participates in, the same concentration of solute can possess two different normalities for two different reactions. For example, Mg2+ is 2 N with respect to a Cl- ion, but it is only 1 N with respect to an O2- ion.

Accordingly, normality is no longer used to represent the concentration of a solution as such. Instead, a solution should be labeled according to its molarity, and it is then possible to calculate the normality for a particular titration using the equation above. NIST has also stipulated that this unit is obsolete and recommends discontinuing its use.

### Equivalents

Expression of concentration in equivalents per liter (or more commonly, milliequivalents per liter) is based on the same principle as normality. A normal solution is one equivalent per liter of solution (Eq/L). The use of equivalents and milliequivalents as a means of expressing concentration is loosing favor, but medical reporting of serum concentrations in mEq/L still occurs.

### Formal

The formal (F) is yet another measure of concentration similar to molarity. Formal concentrations are sometimes used when solving chemical equilibrium problems. It is calculated based on the formula weights of chemicals per liter of solution. The difference between formal and molar concentrations is that the formal concentration indicates moles of the original chemical formula in solution, without regard for the species that actually exist in solution. Molar concentration, on the other hand, is the concentration of species in solution.

For example: if one dissolves sodium carbonate (Na2CO3) in a litre of water, the compound dissociates into the Na+ and CO32- ions. Some of the CO32- reacts with the water to form HCO3- and H2CO3. If the pH of the solution is low, there is practically no Na2CO3 left in the solution. So, although we have added 1 mol of Na2CO3 to the solution, it does not contain 1 M of that substance. (Rather, it contains a molarity based on the other constituents of the solution.) However, it was once said that such solutions contain 1 F of Na2CO3.

### "Parts-per" notation

The parts-per notation is used in some areas of science and engineering because it does not require conversion from weights or volumes to more chemically relevant units such as normality or molarity. It describes the amount of one substance in another. It is the ratio of the amount of the substance of interest to the amount of that substance plus the amount of the substance it is in.

• Parts per hundred (denoted by '%' [the per cent symbol], and very rarely 'pph') - denotes the amount of a given substance in a total amount of 100 regardless of the units of measure as long as they are the same. e.g. 1 gram per 100 gram. 1 part in 102.
• Parts per thousand (denoted by '‰' [the per mille symbol], and occasionally 'ppt', though this should be avoided) denotes the amount of a given substance in a total amount of 1000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per gram, or 1 gram per kilogram. 1 part in 103.
• Parts per million ('ppm') denotes the amount of a given substance in a total amount of 1,000,000 regardless of the units of measure used as long as they are the same. e.g. 1 milligram per kilogram. 1 part in 106.
• Parts per billion ('ppb') denotes the amount of a given substance in a total amount of 1,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per tonne. 1 part in 109.
• Parts per trillion ('ppt') denotes the amount of a given substance in a total amount of 1,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per kilotonne. 1 part in 1012.
• Parts per quadrillion ('ppq') denotes the amount of a given substance in a total amount of 1,000,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per megatonne. 1 part in 1015.

#### Notes for clarity

The notation is used for convenience and the units of measure must be denoted for clarity though this is frequently not the case even in technical publications.

In atmospheric chemistry and in air pollution regulations, the parts per notation is commonly expressed with a v following, such as ppmv, to indicate parts per million by volume. This works fine for gas concentrations (e.g., ppmv of carbon dioxide in the ambient air) but, for concentrations of non-gaseous substances such as aerosols, cloud droplets, and particulate matter in the ambient air, the concentrations are commonly expressed as μg/m³ or mg/m³ (e.g., μg or mg of particulates per cubic metre of ambient air). This expression eliminates the need to take into account the impact of temperature and pressure on the density and hence weight of the gas.

The usage is generally quite fixed inside most specific branches of science, leading some researchers to believe that their own usage (mass/mass, volume/volume or others) is the only correct one. This, in turn, leads them not to specify their usage in their research, and others may therefore misinterpret their results. For example, electrochemists often use volume/volume, while chemical engineers may use mass/mass as well as volume/volume. Many academic papers of otherwise excellent level fail to specify their usage of the part-per notation. The difference between expressing concentrations as mass/mass or volume/volume is quite significant when dealing with gases and it is very important to specify which is being used. It is quite simple, for example, to distinguish ppm by volume from ppm by mass or weight by using ppmv or ppmw.

## Table of concentration measures

Frequently used standards of concentration Measurement Notation Generic formula Typical units atomic percentage (A) at.% $left \left(frac\left\{rm number~of~atoms~of~dopant times 100\right\}\left\{rm number~of~atoms~of~solution\right\} right \right)$ % atomic percentage (B) at.% $left \left(frac\left\{rm number~of~atoms~of~dopant times 100\right\}\left\{rm number~of~substitutable~atoms~of~solution\right\} right \right)$ % Mass percentage wt% $left \left(frac\left\{mathrm\left\{grams solute\right\} times 100\right\}\left\{mathrm\left\{grams solution\right\}\right\} right \right)$ % Mass-volume percentage - $left \left(frac\left\{mathrm\left\{grams solute\right\} times 100\right\}\left\{mathrm\left\{milliliters solution\right\}\right\} right \right)$ % though strictly %g/mL Volume-volume percentage - $left \left(frac\left\{mathrm\left\{milliliters solute\right\} times 100\right\}\left\{mathrm\left\{milliliters solution\right\}\right\} right \right)$ % Molarity M $left \left(frac\left\{mathrm\left\{moles solute\right\}\right\}\left\{mathrm\left\{liters solution\right\}\right\} right \right)$ mol/L (or M or mol/dm3) Molinity - $left \left(frac\left\{mathrm\left\{moles solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ mol/kg Molality m $left \left(frac\left\{mathrm\left\{moles solute\right\}\right\}\left\{mathrm\left\{kilograms solvent\right\}\right\} right \right)$ mol/kg (or m**) Molar fraction Χ (chi) $left \left(frac\left\{mathrm\left\{moles solute\right\}\right\}\left\{mathrm\left\{moles solution\right\}\right\} right \right)$ (decimal) Formal F $left \left(frac\left\{mathrm\left\{moles undissolved solute\right\}\right\}\left\{mathrm\left\{liters solution\right\}\right\} right \right)$ mol/L (or F) Normality N $left \left(frac\left\{mathrm\left\{gram equivalents\right\}\right\}\left\{mathrm\left\{liters solution\right\}\right\} right \right)$ N Parts per hundred % (or pph) $left \left(frac\left\{mathrm\left\{dekagrams solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ dg/kg Parts per thousand ‰ (or ppt*) $left \left(frac\left\{mathrm\left\{grams solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ g/kg Parts per million ppm $left \left(frac\left\{mathrm\left\{milligrams solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ mg/kg Parts per billion ppb $left \left(frac\left\{mathrm\left\{micrograms solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ µg/kg Parts per trillion ppt* $left \left(frac\left\{mathrm\left\{nanograms solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ ng/kg Parts per quadrillion ppq $left \left(frac\left\{mathrm\left\{picograms solute\right\}\right\}\left\{mathrm\left\{kilograms solution\right\}\right\} right \right)$ pg/kg * Although 'ppt' is usually used to denote 'parts per trillion', it is on occasion used for 'parts per thousand'. Sometimes 'ppt' is also used as an abbreviation for precipitate.

** Obsolete unit symbols.