# Conjugate (acid-base theory)

A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid gives a proton (H$^+$) to a base—in other words, it is a base with a hydrogen ion added to it, as it loses a hydrogen ion in the reverse reaction. On the other hand, a conjugate base is what remains after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a substance formed by the removal of a proton from an acid, as it can gain a hydrogen ion in the reverse reaction. Because some acids can give multiple protons, the conjugate base of an acid may itself be acidic.
In summary, this can be represented as the following chemical reaction: ${\text{acid}}+{\text{base}}\;{\ce {<=>}}\;{\text{conjugate base}}+{\text{conjugate acid}}$
Johannes Nicolaus Brønsted and Martin Lowry introduced the Brønsted–Lowry theory, which said that any compound that can give a proton to another compound is an acid, and the compound that receives the proton is a base. A proton is a subatomic particle in the nucleus with a unit positive electrical charge. It is represented by the symbol H$^+$ because it has the nucleus of a hydrogen atom, that is, a hydrogen cation.
A cation can be a conjugate acid, and an anion can be a conjugate base, depending on which substance is involved and which acid–base theory is used. The simplest anion which can be a conjugate base is the free electron in a solution whose conjugate acid is the atomic hydrogen.

## Acid–base reactions

In an acid–base reaction, an acid and a base react to form a conjugate base and a conjugate acid respectively. The acid loses a proton and the base gains a proton. In diagrams which indicate this, the new bond formed between the base and the proton is shown by an arrow that starts on an electron pair from the base and ends at the hydrogen ion (proton) that will be transferred:
In this case, the water molecule is the conjugate acid of the basic hydroxide ion after the latter received the hydrogen ion from ammonium. On the other hand, ammonia is the conjugate base for the acidic ammonium after ammonium has donated a hydrogen ion to produce the water molecule. Also, OH$^−$ can be considered as the conjugate base of H $_2$O, since the water molecule donates a proton to give NH$^+$ $_4$ in the reverse reaction. The terms "acid", "base", "conjugate acid", and "conjugate base" are not fixed for a certain chemical substance but can be swapped if the reaction taking place is reversed.

## Strength of conjugates

The strength of a conjugate acid is proportional to its splitting constant. A stronger conjugate acid will split more easily into its products, "push" hydrogen protons away and have a higher equilibrium constant. The strength of a conjugate base can be seen as its tendency to "pull" hydrogen protons towards itself. If a conjugate base is classified as strong, it will "hold on" to the hydrogen proton when dissolved and its acid will not split.
If a chemical is a strong acid, its conjugate base will be weak. An example of this case would be the splitting of hydrochloric acid HCl in water. Since HCl is a strong acid (it splits up to a large extent), its conjugate base (Cl$^−$ ) will be weak. Therefore, in this system, most H$^+$ will be hydronium ions H $_3$O$^+$ instead of attached to Cl$^−$ anions and the conjugate bases will be weaker than water molecules.
On the other hand, if a chemical is a weak acid its conjugate base will not necessarily be strong. Consider that ethanoate, the conjugate base of ethanoic acid, has a base splitting constant (Kb) of about 5.6×10$^{−10}$, making it a weak base. In order for a species to have a strong conjugate base it has to be a very weak acid, like water.

## Identifying conjugate acid–base pairs

To identify the conjugate acid, look for the pair of compounds that are related. The acid–base reaction can be viewed in a before and after sense. The before is the reactant side of the equation, the after is the product side of the equation. The conjugate acid in the after side of an equation gains a hydrogen ion, so in the before side of the equation the compound that has one less hydrogen ion of the conjugate acid is the base. The conjugate base in the after side of the equation lost a hydrogen ion, so in the before side of the equation, the compound that has one more hydrogen ion of the conjugate base is the acid.
Consider the following acid–base reaction:
Nitric acid (HNO $_3$) is an acid because it donates a proton to the water molecule and its conjugate base is nitrate (NO$^−$ $_3$). The water molecule acts as a base because it receives the hydrogen cation (proton) and its conjugate acid is the hydronium ion (H $_3$O$^+$ ).
| Equation | Acid | Base | Conjugate base | Conjugate acid |
| HClO $_2$ + H $_2$O → ClO$^−$ $_2$ + H $_3$O$^+$ | HClO $_2$ | H $_2$O | ClO$^−$ $_2$ | H $_3$O$^+$ |
| ClO$^−$ + H $_2$O → HClO + OH$^−$ | H $_2$O | ClO$^−$ | OH$^−$ | HClO |
| HCl + H $_2$PO$^−$ $_4$ → Cl$^−$ + H $_3$PO $_4$ | HCl | H $_2$PO$^−$ $_4$ | Cl$^−$ | H $_3$PO $_4$ |

## Applications

One use of conjugate acids and bases lies in buffering systems, which include a buffer solution. In a buffer, a weak acid and its conjugate base (in the form of a salt), or a weak base and its conjugate acid, are used in order to limit the pH change during a titration process. Buffers have both organic and non-organic chemical applications. For example, besides buffers being used in lab processes, human blood acts as a buffer to maintain pH. The most important buffer in our bloodstream is the carbonic acid-bicarbonate buffer, which prevents drastic pH changes when CO $_2$ is introduced. This functions as such: ${\ce {CO2 + H2O <=> H2CO3 <=> HCO3^- + H+}}$
Furthermore, here is a table of common buffers.
| Buffering agent | pK$_a$ | Useful pH range |
| Citric acid | 3.13, 4.76, 6.40 | 2.1 - 7.4 |
| Acetic acid | 4.8 | 3.8 - 5.8 |
| KH$_2$PO$_4$ | 7.2 | 6.2 - 8.2 |
| CHES | 9.3 | 8.3–10.3 |
| Borate | 9.24 | 8.25 - 10.25 |
A second common application with an organic compound would be the production of a buffer with acetic acid. If acetic acid, a weak acid with the formula CH $_3$COOH, was made into a buffer solution, it would need to be combined with its conjugate base CH $_3$COO$^−$ in the form of a salt. The resulting mixture is called an acetate buffer, consisting of aqueous CH $_3$COOH and aqueous CH $_3$COONa. Acetic acid, along with many other weak acids, serve as useful components of buffers in different lab settings, each useful within their own pH range.
Ringer's lactate solution is an example where the conjugate base of an organic acid, lactic acid, CH $_3$CH(OH)CO$^−$ $_2$ is combined with sodium, calcium and potassium cations and chloride anions in distilled water which together form a fluid which is isotonic in relation to human blood and is used for fluid resuscitation after blood loss due to trauma, surgery, or a burn injury.

## Table of acids and their conjugate bases

Below are several examples of acids and their corresponding conjugate bases; note how they differ by just one proton (H$^+$ ion). Acid strength decreases and conjugate base strength increases down the table.
| Acid | Conjugate base |
| H $_2$F$^+$ Fluoronium ion | HF Hydrogen fluoride |
| HCl Hydrochloric acid | Cl$^−$ Chloride ion |
| H$_2$SO$_4$ Sulfuric acid | HSO$^−$ $_4$ Hydrogen sulfate ion (bisulfate ion) |
| HNO$_3$ Nitric acid | NO$^−$ $_3$ Nitrate ion |
| H$_3$O$^+$ Hydronium ion | H$_2$O Water |
| HSO$^−$ $_4$ Hydrogen sulfate ion | SO$^{2−}$ $_4$ Sulfate ion |
| H$_3$PO$_4$ Phosphoric acid | H$_2$PO$^−$ $_4$ Dihydrogen phosphate ion |
| CH$_3$COOH Acetic acid | CH$_3$COO$^−$ Acetate ion |
| HF Hydrofluoric acid | F$^−$ Fluoride ion |
| H$_2$CO$_3$ Carbonic acid | HCO$^−$ $_3$ Hydrogen carbonate ion |
| H$_2$S Hydrosulfuric acid | HS$^−$ Hydrosulfide ion |
| H$_2$PO$^−$ $_4$ Dihydrogen phosphate ion | HPO$^{2−}$ $_4$ Hydrogen phosphate ion |
| NH$^+$ $_4$ Ammonium ion | NH$_3$ Ammonia |
| H$_2$O Water (pH=7) | OH$^−$ Hydroxide ion |
| HCO$^−$ $_3$ Hydrogencarbonate (bicarbonate) ion | CO$^{2−}$ $_3$ Carbonate ion |

## Table of bases and their conjugate acids

In contrast, here is a table of bases and their conjugate acids. Similarly, base strength decreases and conjugate acid strength increases down the table.
| Base | Conjugate acid |
| C $_2$H $_5$NH $_2$ Ethylamine | C $_2$H $_5$NH$^+$ $_3$ Ethylammonium ion |
| CH $_3$NH $_2$ Methylamine | CH $_3$NH$^+$ $_3$ Methylammonium ion |
| NH $_3$ Ammonia | NH$^+$ $_4$ Ammonium ion |
| C $_5$H $_5$N Pyridine | C $_5$H $_6$N$^+$ Pyridinium |
| C $_6$H $_5$NH $_2$ Aniline | C $_6$H $_5$NH$^+$ $_3$ Phenylammonium ion |
| C $_6$H $_5$CO$^−$ $_2$ Benzoate ion | C $_6$H $_6$CO $_2$ Benzoic acid |
| F$^−$ Fluoride ion | HF Hydrogen fluoride |
| PO$^{3−}$ $_4$ Phosphate ion | HPO$^{2−}$ $_4$ Hydrogen phosphate ion |
| OH$^−$ Hydroxide ion | H$_2$O Water (neutral, pH 7) |
| HCO$^−$ $_3$ Bicarbonate | H $_2$CO $_3$ Carbonic acid |
| CO$^{2−}$ $_3$ Carbonate ion | HCO$^−$ $_3$ Bicarbonate |
| Br$^−$ Bromide ion | HBr Hydrogen bromide |
| HPO$^{2−}$ $_4$ Hydrogen phosphate | H $_2$PO$^−$ $_4$ Dihydrogen phosphate ion |
| Cl$^−$ Chloride ion | HCl Hydrogen chloride |
| H $_2$O Water | H $_3$O$^+$ Hydronium ion |
| NO$^−$ $_2$ Nitrite ion | HNO $_2$ Nitrous acid |