# Acids and Bases

### Brønsted-Lowry Acid-Base

The Brønsted-Lowry acid-base theory states that upon reacting an acid with a base, the acid acts as a proton ($H^{+}$) donor, while the base acts as a proton acceptor.

## Acid-Base Dissociation

When an acid is added to water, the acid dissociates releasing $H^{+}$ ions into the solution. For example, when hydrogen chloride ($HCl_{(g)}$) is added to an aqueous solution, it dissociates into $H^{+}_{(aq)}$ and $Cl^{-}_{(aq)}$ ions:

$$HCl_{(g)} + aq \rightarrow H^{+}_{(aq)} + Cl^{-}_{(aq)}$$

Acids can release multiple protons into the solution, equal to the number of hydrogen atoms in the acid.

• Monoprotic acids: Shown by the reaction below, $HCl_{(aq)}$ is a monoprotic acid as it is only able to release one proton into the solution.
$$HCl_{(g)} + aq \rightleftharpoons H^{+}_{(aq)} + Cl^{-}_{(aq)}$$
• Diprotic acids: These acids are able to release two protons into the solution, through two stages.
\eqalign{ H_{2}SO_{4(aq)} &\rightleftharpoons H^{+}_{(aq)} + HSO_{4(aq)}^{-} \\ HSO_{4(aq)}^{-} &\rightleftharpoons H^{+}_{(aq)} + SO_{4(aq)}^{2-} }
• Triprotic acids: These acids are able to release three protons into the solution, through three stages.
\eqalign{ H_{3}PO_{4(aq)} &\rightleftharpoons H^{+}_{(aq)} + H_{2}PO_{4(aq)}^{-} \\ H_{2}PO_{4(aq)}^{-} &\rightleftharpoons H^{+}_{(aq)} + HPO_{4(aq)}^{2-} \\ HPO_{4(aq)}^{2-} &\rightleftharpoons H^{+}_{(aq)} + PO_{4(aq)}^{3-} }

## Acid-Base Reactions

Aqueous acids can take part in reactions with bases, carbonates and alkalis. In these reactions, the acid is neutralised forming a salt and water. In writing ionic equations it is important to know that:

• Ions are only dissociated in aqueous solutions. Solid ionic compounds are shown undissociated.
• Species that are unchanged in both chemical composition and physical state are cancelled out of the equation. These are known as spectator ions.
• Covalent compounds are not shown as dissociated ions in the ionic equation. Examples of such compounds include gaseous molecules such as $CO_{2}$, simple molecules and water ($H_{2}O$).

#### Reaction with Carbonates

Aqueous acids react with solid carbonates forming a salt, carbon dioxide and water.
$$2HCl_{(aq)} + CaCO_{3(s)} \rightarrow CaCl_{2(aq)} + CO_{2(g)} + H_{2}O_{(l)} \\ 2H^{+}_{(aq)} + CaCO_{3(s)} \rightarrow Ca^{2+}_{(aq)} + CO_{2(g)} + H_{2}O_{(l)}$$

If the carbonate is in solution the carbonate dissociates, so the ionic equation can be further simplified.

$$2HCl_{(aq)} + Na_{2}CO_{3(aq)} \rightarrow 2NaCl_{(aq)} + CO_{2(g)} + H_{2}O_{(l)} \\ 2H^{+}_{(aq)} + CO_{3(aq)}^{~2-} \rightarrow CO_{2(g)} + H_{2}O_{(l)}$$

#### Reaction with Bases

Aqueous acids react with bases to form a salt and water.
$$2HNO_{3(aq)} + MgO_{(s)} \rightarrow Mg(NO_{3})_{2(aq)} + H_{2}O_{(l)} \\ 2H^{+}_{(aq)} + MgO_{(s)} \rightarrow Mg_{(aq)}^{~2+} + H_{2}O_{(l)}$$

#### Reactions with Alkalis

Aqueous acids react with alkalis to form a salt and water.
$$H_{2}SO_{4(aq)} + 2KOH_{(aq)} \rightarrow K_{2}SO_{4(aq)} + 2H_{2}O_{(l)} \\ H^{+}_{(aq)} + OH^{-}_{(aq)} \rightarrow H_{2}O_{(l)}$$

#### Redox Reactions of Acids with Metals

Aqueous acids react with metals to form a salt and hydrogen gas.
$$2HCl_{(aq)} + Mg_{(s)} \rightarrow MgCl_{2(aq)} + H_{2(g)} \\ 2H^{+}_{(aq)} + Mg_{(s)} \rightarrow Mg^{~2+}_{(aq)} + H_{2(g)}$$

## Conjugate Acid-Base Pairs

An acid is a proton donor while a base is a proton acceptor. In order for an acid to release a proton, a base must be able to accept a proton. A conjugate pair is a set of two species that transform into each other with the loss or gain of a proton.

Below is the equilibrium reaction showing the dissociation of nitrous acid ($HNO_{2}$) in water.

$$HNO_{2(aq)} + H_{2}O_{(l)} \rightleftharpoons H_{3}O^{+}_{(aq)} + NO_{2(aq)}^{-}$$

In the forwards reaction:

• The acid $HNO_{2(aq)}$ releases a proton to form its conjugate base, $NO_{2(aq)}^{-}$. Therefore $HNO_{2(aq)}$ and $NO_{2(aq)}^{-}$ are a conjugate acid-base pair.
• The base $H_{2}O_{(l)}$ gains one proton to form its conjugate acid, $H_{3}O^{+}_{(aq)}$. Therefore $H_{2}O_{(l)}$ and $H_{3}O^{+}_{(aq)}$ are a conjugate acid-base pair.

\eqalign{ &HNO_{2(aq)} + &H_{2}O_{(l)} \rightleftharpoons &H_{3}O^{+}_{(aq)} + &NO_{2(aq)}^{-} \\ &\text{acid 1} &\text{base 2} &\text{acid 2} &\text{base 1} }

## $pH$ Scale

The $pH$ scale is an indicator of how acidic or basic a substance is. A substance with a $pH$ less than $7$ is acidic while a substance with a $pH$ more than $7$ is basic. The $pH$ scale shows the concentration of $H^{+}_{(aq)}$ ions in the substance. Due to the large range of possible values for $pH$, a logarithmic scale can be used to make the figures more manageable:

$$pH = -\log_{10} [H^{+}_{(aq)}] \\ [H^{+}_{(aq)}] = 10^{-pH}$$

A small value of $pH$ means a high concentration of $H^{+}_{(aq)}$ ions, while a high value of $pH$ means a low concentration of $H^{+}_{(aq)}$ ions.

### Acid Dissociation Constant

The acid dissociation constant ($K_{a}$) is a measure of the strength of an acid in a solution. For the dissociation of the acid $HA_{(aq)}$:
$$HA_{(aq)} \rightleftharpoons H^{+}_{(aq)} + A^{-}_{(aq)}$$
The equation for the acid dissociation constant is:
$$K_{a} = \frac{[H^{+}][A^{-}]}{[HA]}$$
A large value of $K_{a}$ indicates a large extent of dissociation therefore a strong acid. A small value of $K_{a}$ indicates a small extent of dissociation therefore a weaker acid.

A logarithmic scale can be used in order to make the values of $K_{a}$ more manageable. The smaller the value of $pK_{a}$, the stronger the acid.
\eqalign{pK_{a} &= -\log_{10} K_{a} \\ K_{a} &= 10^{-pK_{a}}}

## Calculating $pH$ for Strong and Weak Acids

For an acid-base equilibrium set up in aqueous solution:
$$HA_{(aq)} \rightleftharpoons H^{+}_{(aq)} + A^{-}_{(aq)}$$
The strength of the acid $HA_{(aq)}$ is determined by the extent of the dissociation of the $H^{+}_{(aq)}$ and $A^{-}_{(aq)}$ ions.

### Strong Acids

Strong acids dissociate completely in aqueous solutions. These typically have a $pH \leq 1$. This means that for:

• Monoprotic acids, $[H^{+}_{(aq)}] = [HA_{(aq)}]$.
• Diprotic acids, $[H^{+}_{(aq)}] = 2 \times [HA_{(aq)}]$
• Triprotic acids, $[H^{+}_{(aq)}] = 3 \times [HA_{(aq)}]$.

Once the $[H^{+}_{(aq)}]$ has been calculated, the $pH$ can be calculated directly with $pH = -\log_{10} [H^{+}_{(aq)}]$.

### Weak Acids

In the dissociation of weak acids:

• The assumption that the $[H^{+}] = [A^{-}]$ can be made therefore in the acid dissociation constant equation, $[H^{+}][A^{-}] = [H^{+}]^{2}$.
• As very few $HA$ molecules dissociate, the assumption is made that the concentration of undissociated $HA$ is equal to the concentration of dissociated $HA$.

From these assumptions, the acid dissociation equation can be shown as below. This equation can be used to calculate the $[H^{+}]$ from known values of $K_{a}$ and $[HA]$.
$$K_{a} = \frac{[H^{+}]^{2}}{[HA]} \\ [H^{+}] = \sqrt{K_{a} \times [HA]}$$

## Ionisation of Water

Pure water dissociates into $H^{+}_{(aq)}$ and $OH^{-}_{(aq)}$ ions in an endothermic reaction. For the dissociation of water, the equation for $K_{a}$ is:
$$K_{a} = \frac{[H^{+}_{(aq)}][OH^{-}_{(aq)}]}{[H_{2}O_{(l)}]}$$
As $[H_{2}O_{(l)}]$ and $K_{a}$ are both constants, these two values can be combined to give the ionic product of water, $K_{w}$.

$$K_{w} = [H^{+}_{(aq)}][OH^{-}_{(aq)}]$$

$K_{w}$ controls the balance between $[H^{+}_{(aq)}]$ and $[OH^{-}_{(aq)}]$ in all aqueous solutions. At $25°$, the value of $K_{w}$ is $1.00 \times 10^{-14}~mol^{2}dm^{-6}$.

### Bases

A base is a proton acceptor. An alkali is a soluble base that releases hydroxide ions ($OH^{-}$) when dissolved in water. The strength of a base is its ability to dissociate to generate $OH^{-}$ ions.
$$NaOH_{(aq)} + aq \rightarrow Na^{+}_{(aq)} + OH^{-}_{(aq)}$$

### Calculating $pH$ of Bases

In order to find the $pH$, the $[H^{+}_{(aq)}]$ must be determined. This can be done by using the ionic product of water.

$$[H^{+}_{(aq)}] = \frac{K_{w}}{[OH^{-}_{(aq)}]}$$

A strong alkali completely dissociates in aqueous solutions. This means that the $[OH^{-}_{(aq)}]$ is equal to the concentration of the base for monobasic bases such as $NaOH$ or $KOH$.