# Equivalent (chemistry)

An equivalent (symbol: officially equiv; unofficially but often Eq) is the amount of a substance that reacts with (or is equivalent to) an arbitrary amount (typically one mole) of another substance in a given chemical reaction. It is an archaic quantity that was used in chemistry and the biological sciences (see Equivalent weight § In history). The mass of an equivalent is called its equivalent weight.

## Formula

The formula from milligrams (mg) to milli-equivalent (mEq) and back is as follows: ${\begin{aligned}{\text{mg}}\to {\text{mEq}}&:\quad {\text{mg }}\times {\frac {V}{MW}}\\[4pt]{\text{mEq}}\to {\text{mg}}&:\quad {\text{mEq }}\times {\frac {MW}{V}}\end{aligned}}$ where V is the valence and MW is the molecular weight.
For elemental compounds: ${\text{mg}}\to {\text{mEq}}:\quad {\frac {\text{element mass [mg]}}{\text{mass fraction}}}\times {\frac {V}{MV}}$

### Common examples
#### mEq to milligram

| Compound | Chemical formula | Molecular weight (MW) | Valencies (V) | Sample | Sample | Sample |
| Compound | Chemical formula | Molecular weight (MW) | Valencies (V) | Reference | Elemental mEq | Elemental mEq to compound weight |
| Potassium (reference) | K | 39.098 g/mol | 1 (K$^+$) | | 20 mEq potassium | 20*39.098/1=782 mg |
| Potassium citrate monohydrate | C$_6$H$_7$K$_3$O$_8$ | 324.41 g/mol | 3 (K$^+$) | Liquid potassium citrate/gluconate therapy for adults and teenagers taken two to four times a day | 20 mEq potassium | 20*324/3=2160 mg |
| Potassium gluconate (anhydrous) | C$_6$H$_{11}$KO$_7$ | 234.245 g/mol | 1 (K$^+$) | Liquid potassium citrate/gluconate therapy for adults and teenagers taken two to four times a day | 20 mEq potassium | 20*234.245/1=4685 mg |

#### Milligram to mEq

| Compound | Chemical formula | Molecular weight (MW) | Elemental mass fraction | Valencies (V) | Sample | Sample | Sample |
| Compound | Chemical formula | Molecular weight (MW) | Elemental mass fraction | Valencies (V) | Reference | Weight | Compound weight to elemental mEq |
| Potassium (reference) | K | 39.098 g/mol | 100% | 1 (K$^+$) | | 3000 mg | 3000*1/39.098=77 mEq K$^+$ |
| Potassium citrate monohydrate | C$_6$H$_7$K$_3$O$_8$ | 324.41 g/mol | 36.16% | 3 (K$^+$) | Tolerable DRI for potassium dietary supplements | 8.3 g (3000/0.3616) | 8296*3/324.41=77 mEq K$^+$ |
| Potassium gluconate (anhydrous) | C$_6$H$_{11}$KO$_7$ | 234.245 g/mol | 16.69% | 1 (K$^+$) | Tolerable DRI for potassium dietary supplements | 18 g (3000/0.1669) | 17975*1/234.245=77 mEq K$^+$ |

## Formal definition

In a more formal definition, the equivalent is the amount of a substance needed to do one of the following:
* react with or supply one mole of hydrogen ions (H$^+$) in an acid–base reaction
* react with or supply one mole of electrons in a redox reaction.
The "hydrogen ion" and the "electron" in these examples are respectively called the "reaction units."
By this definition, the number of equivalents of a given ion in a solution is equal to the number of moles of that ion multiplied by its valence. For example, consider a solution of 1 mole of NaCl and 1 mole of CaCl$_2$. The solution has 1 mole or 1 equiv Na$^+$, 1 mole or 2 equiv Ca$^{2+}$, and 3 mole or 3 equiv Cl$^−$.
An earlier definition, used especially for chemical elements, holds that an equivalent is the amount of a substance that will react with 1 g (0.035 oz) of hydrogen, 8 g (0.28 oz) of oxygen, or 35.5 g (1.25 oz) of chlorine—or that will displace any of the three.

## In medicine and biochemistry

In biological systems, reactions often happen on small scales, involving small amounts of substances, so those substances are routinely described in terms of milliequivalents (symbol: officially mequiv; unofficially but often mEq or meq), the prefix milli- denoting a factor of one thousandth (10$^{−3}$). Very often, the measure is used in terms of milliequivalents of solute per litre of solution (or milliNormal, where meq/L = mN). This is especially common for measurement of compounds in biological fluids; for instance, the healthy level of potassium in the blood of a human is defined between 3.5 and 5.0 mEq/L.
A certain amount of univalent ions provides the same amount of equivalents while the same amount of divalent ions provides twice the amount of equivalents. For example, 1 mmol (0.001 mol) of Na$^+$ is equal to 1 meq, while 1 mmol of Ca$^{2+}$ is equal to 2 meq.