# Molarity

## Molarity is defined as the moles of a solute per volume of total solution.

#### Key Points

• Molarity is a property of solutions that identifies how concentrated they are by indicating the number of moles of solute per liter of solution.

• SI prefixes can be used with molarity when dilute solutions are being dealt with, such as nanomolar or picomolar, and will often be encountered.

• There are several equations that are useful for dealing with molarity in relation to a chemical reaction or dilution of a solution. These equation are presented.

#### Terms

• The concentration of a substance in solution, expressed as the number moles of solute per litre of solution.

• the proportion of a substance in a mixture

• The International System of Units (abbreviated SI from French: Système international d'unités) is the modern form of the metric system, used extensively in the sciences.

#### Figures

1. ##### Units of molarity

When dealing with dilute solutions, it becomes more practical to talk in terms of picomolarity, rather than vanishingly small molarities, so these descriptors will often be used.

In chemistry, the molar concentration, ci is defined as the amount of a constituent ni (in moles) divided by the volume of the mixture V:

$c_{i}=\frac{n_{i}}{V}$

It is also called molarity (symbol M, in moles per liter). The volume in the definition refers to the volume of the solution, not the volume of the solvent, as one liter of a solution usually contains either slightly more or slightly less than 1 liter of solvent because the process of dissolution causes volume of liquid to increase or decrease.

### Units

The SI unit for molar concentration is mol/m3. However, more commonly the unit mol/L is used. A solution of concentration 1 mol/L is also denoted as "1 molar" (1 M).

1 mol/L = 1 mol/dm3 = 1 mol dm−3 = 1 M = 1000 mol/m3

An SI prefix is often used to denote concentrations. Commonly used units are listed in the table hereafter:

### Applications of Molarity

To determine the molarity of a solution, the number of moles of solute added must be divided by the number of liters of total solution produced. If the amount of solute is given in grams, be sure to use the molar mass of the solute to determine the number of moles in order to determine the molarity.

For example, if there are 10 grams of salt (the solute) dissolved in enough water (the solvent) to produce 2L of the solution, what is the molarity of this solution?

$10 g NaCl * (\frac {1 mol}{58.4 g}) = 0.171 mol NaCl$

$\frac {0.171 mol NaCl}{2L} = 0.086M$

When performing a chemical reaction, it is oftentimes simplifying to mix two solutions of known molarity, especially when one component is difficult to measure gravimetrically (by weighing). To determine the number of moles in a given solution of known molarity, simply multiply the molarity times the volume used, where V is the volume in liters.

For example, how many moles of potassium chloride (KCl) are in 4L of a 0.65M solution?

$0.65M = \frac{0.65moles}{liter}*4L = 2.6moles$

Using this same technique once can determine how much of an X molar solution will be required so that 1 equivalent (based on moles of atoms) of a reagent is added.

### Dilution (equation)

Dilution is a reduction in the concentration of a chemical (gas, vapor, solution). It is the process of reducing the concentration of a solute in solution, usually simply by mixing with more solvent. To dilute a solution means to add more solvent without the addition of more solute. The resulting solution is thoroughly mixed so as to ensure that all parts of the solution are identical.

Mathematically this relationship can be shown in the equation: c1V1 = c2V2 where c1 and c2 are the initial and final concentrations, respectively and V1 and V2 are the initial and final volumes of the solution.

#### Key Term Glossary

atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
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chemical reaction
A process involving the breaking or making of interatomic bonds, in which one or more substances are changed into others.
##### Appears in these related concepts:
chemistry
The branch of natural science that deals with the composition and constitution of substances and the changes that they undergo as a consequence of alterations in the constitution of their molecules.
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concentration
the proportion of a substance in a mixture
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dilution
A solution that has had additional solvent, such as water, added to it into order to make it less concentrated.
##### Appears in these related concepts:
dissolution
Dissolving, or going into solution.
##### Appears in these related concepts:
gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
##### Appears in these related concepts:
liquid
A substance that flows and keeps no definite shape, such as water. A substance whose molecules, while not tending to separate from one another like those of a gas, readily change their relative position, and which therefore retains no definite shape, except that determined by the containing receptacle; an inelastic fluid.
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liter
a non-SI metric system unit of volume equal to 1 cubic decimeter (dm^3), 1,000 cubic centimeters (cm^3) or 1/1,000 cubic meter (m^3)
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mass
The quantity of matter that a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
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mixture
Something that consists of diverse elements
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molarity
The concentration of a substance in solution, expressed as the number moles of solute per litre of solution.
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molar mass
the mass of a given substance (chemical element or chemical compound) divided by its amount of substance
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mole
In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.
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prefix
that which is prefixed; especially one or more letters or syllables added to the beginning of a word to modify its meaning; as, pre- in prefix, con- in conjure
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reduction
a reaction in which electrons are gained and valence is reduced, often by the removal of oxygen or the addition of hydrogen
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salt
An ionic compound that is composed of cations and anions The product is electrically neutral. The two ions are held together by ionic bonds, not covalent bonds.
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SI unit
The International System of Units (abbreviated SI from French: Système international d'unités) is the modern form of the metric system, used extensively in the sciences.
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solute
Any substance that is dissolved in a liquid solvent to create a solution.
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solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
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Solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
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solvent
a substance that dissolves a solute, resulting in a solution
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volume
A unit of three-dimensional measure of space that comprises a length, a width, and a height. It is measured in units of cubic centimeters in metric, or cubic inches or cubic feet in English measurement.