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.

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:

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:

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

$pH$ 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:

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:

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 $KOH$.

© Andrew Deniszczyc, 2018