The pH scale

1. Definition of $pH$

• pH is a measure of the acidity or basicity of a solution.
• It is calculated using the formula: $\text{pH} = -\log [H_3O^+]$

where $[H_3O^+]$ is the hydronium ion concentration in $mol·dm⁻³.$

2. Relationship Between $pH$ and $K_w$

• From the auto-ionisation of water, we know: $K_w = [H_3O^+][OH^-] = :highlight[1.0 \times 10^{-14}] \text{ at } :highlight[25^\circ C]$

• In neutral solutions:

$[H_3O^+] = [OH^-] = :highlight[1.0 \times 10^{-7}]$ $mol·dm^{-3}$ which gives:

$\text{pH} = :highlight[7]$

3. Classification of Solutions

Type of Solution	[H₃O⁺]	[OH⁻]	pH Range
Acidic	$[H_3O^+] > [OH^-]$	$[H_3O^+] > :highlight[10^{-7}] mol·dm⁻³$	$pH < :highlight[7]$
Neutral	$[H_3O^+] = [OH^-]$	$:highlight[1.0 \times 10^{-7}] mol·dm⁻³$	$pH = :highlight[7]$
Basic	$[H_3O^+] < [OH^-]$	$[H_3O^+] < :highlight[10^{-7}] mol·dm⁻³$	$pH > :highlight[7]$

5. Key Takeaways

• Lower $pH$ $(pH < 7)$ = More acidic (higher $[H_3O^+]$ ).
• Higher $pH$ $(pH > 7)$ = More basic (higher $[OH^-]$ ).
• The $pH$ scale ranges from 0 to 14, where $pH$ 7 is neutral.
• The $pH$ of a solution can be used to classify acids and bases in different chemical and biological systems.