The pH Scale (HSC SSCE Chemistry): Revision Notes

The pH Scale

Introduction to the pH scale

Scientists need a precise way to measure how acidic or alkaline a solution is. The pH scale provides this quantitative measurement. The term 'pH' stands for 'hydrogen power' or 'power of hydrogen', reflecting the fact that the scale is based on the concentration of hydrogen ions in a solution.

Danish biochemist Soren Sorensen developed this scale to make expressing hydrogen ion concentrations more manageable. Remember that in aqueous solutions, hydrogen ions ($\text{H}^+$) attach to water molecules to form hydronium ions ($\text{H}_3\text{O}^+$). Therefore, the pH scale measures the concentration of hydronium ions in solution.

The pH scale directly relates to the Brønsted-Lowry definition of acids as proton donors. This is because pH measures the number of hydronium ions present - in other words, the number of $\text{H}^+$ ions that the acid has donated to water. For example:

$\text{HCl(aq)} + \text{H}_2\text{O(l)} \rightarrow \text{H}_3\text{O}^+\text{(aq)} + \text{Cl}^-\text{(aq)}$

Understanding the pH scale

The pH scale typically ranges from $0$ to $14$, although values outside this range are possible. The scale works as follows:

• Lower pH values = more acidic solution
• Higher pH values = more basic (alkaline) solution
• pH = 7 = neutral solution (at $25°\text{C}$)

Therefore:

• Acids have pH $< 7$
• Bases have pH $> 7$
• Neutral substances have pH $= 7$

Relationship between pH and hydrogen ion concentration

The table below shows how pH values relate to hydrogen ion concentration:

pH	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$
$[\text{H}^+]$ or $[\text{H}_3\text{O}^+]$ (mol L$^{-1}$)	$1$	$1 \times 10^{-1}$	$1 \times 10^{-2}$	$1 \times 10^{-3}$	$1 \times 10^{-4}$	$1 \times 10^{-5}$	$1 \times 10^{-6}$	$1 \times 10^{-7}$	$1 \times 10^{-8}$	$1 \times 10^{-9}$	$1 \times 10^{-10}$	$1 \times 10^{-11}$	$1 \times 10^{-12}$	$1 \times 10^{-13}$	$1 \times 10^{-14}$

Notice the relationship between the pH value and the exponent (ignoring the negative sign) in the hydrogen ion concentration - they are the same number. This is because pH is mathematically defined as:

$\text{pH} = -\log_{10}[\text{H}^+]$

The relationship between hydrogen and hydroxide ions

While the pH scale is based on hydrogen ion concentration, it can also tell us about hydroxide ion ($\text{OH}^-$) concentration. At pH $7$ (neutral), both $[\text{H}^+]$ and $[\text{OH}^-]$ equal $10^{-7}$ mol L$^{-1}$.

pH	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$
$[\text{H}^+]$ (mol L$^{-1}$)	$10^0$	$10^{-1}$	$10^{-2}$	$10^{-3}$	$10^{-4}$	$10^{-5}$	$10^{-6}$	$10^{-7}$	$10^{-8}$	$10^{-9}$	$10^{-10}$	$10^{-11}$	$10^{-12}$	$10^{-13}$	$10^{-14}$
$[\text{OH}^-]$ (mol L$^{-1}$)	$10^{-14}$	$10^{-13}$	$10^{-12}$	$10^{-11}$	$10^{-10}$	$10^{-9}$	$10^{-8}$	$10^{-7}$	$10^{-6}$	$10^{-5}$	$10^{-4}$	$10^{-3}$	$10^{-2}$	$10^{-1}$	$10^0$

Key observations from this table:

• As $[\text{H}^+]$ decreases, $[\text{OH}^-]$ increases by the corresponding amount
• Adding the exponents (ignoring the negative signs) of $[\text{H}^+]$ and $[\text{OH}^-]$ always equals 14

Measuring pH

There are several methods for measuring pH, ranging from simple indicators to sophisticated electronic instruments.

Indicators

Indicators are substances that change colour depending on the pH of a solution. There are two main types:

Natural indicators: These were covered in earlier chapters and include substances like red cabbage juice.

Synthetic indicators: These provide more precise information about the degree of acidity. Common synthetic indicators include:

• Methyl violet
• Methyl orange
• Litmus
• Bromothymol blue
• Phenolphthalein

Each indicator changes colour over a specific pH range:

Universal indicator

Universal indicator is a mixture of several indicators that produces multiple colour changes across the entire pH range. This makes it very useful for getting an approximate pH value.

pH meters and pH probes

For more accurate measurements, scientists use pH meters with pH probes. These instruments provide a digital readout of the pH value.

Advantages of pH meters:

• Don't require adding additional substances to the solution
• Provide greater accuracy (when properly calibrated)
• Give a numerical readout rather than requiring colour comparison

Common substances and their pH

The table below shows the pH values of everyday substances, demonstrating the practical applications of the pH scale:

pH	$[\text{H}_3\text{O}^+]$	Substance	Type
$-1$	$10$	Concentrated hydrochloric acid	ACID
$0$	$1$	Car battery acid, $1$ mol L$^{-1}$ HCl
$1$	$10^{-1}$	$0.1$ mol L$^{-1}$ hydrochloric acid
$2$	$10^{-2}$	Stomach acid
$3$	$10^{-3}$	Vinegar, lemon juice
$4$	$10^{-4}$	Soft drinks, soda water
$5$	$10^{-5}$	Wine, black coffee
$6$	$10^{-6}$	Rain water, milk, saliva
$7$	$10^{-7}$	Very pure water	NEUTRAL
$8$	$10^{-8}$	Blood, sea water	ALKALINE
$9$	$10^{-9}$	Bore water, baking soda solution
$10$	$10^{-10}$	Toilet soap
$11$	$10^{-11}$	Laundry detergents
$12$	$10^{-12}$	Household ammonia, dishwashing machine powders
$13$	$10^{-13}$	Chlorine bleach solutions
$14$	$10^{-14}$	Oven cleaners, $1.0$ mol L$^{-1}$ NaOH

Calculating pH

The pH formula

The pH of a solution is mathematically defined as:

$\text{pH} = -\log_{10}[\text{H}^+]$

Where the square brackets $[\text{H}^+]$ represent the molar concentration of hydrogen ions in mol L$^{-1}$.

Calculating pH from concentration

For simple concentrations that are powers of $10$, the calculation is straightforward:

• If $[\text{H}^+] = 0.1$ M (or $1 \times 10^{-1}$), then pH $= 1.0$
• If $[\text{H}^+] = 0.01$ M (or $1 \times 10^{-2}$), then pH $= 2.0$
• If $[\text{H}^+] = 0.0000001$ M (or $1 \times 10^{-7}$), then pH $= 7.0$

For more complex concentrations, use a calculator.

Calculating concentration from pH

To find the hydrogen ion concentration from pH, use:

$[\text{H}^+] = 10^{-\text{pH}}$

Worked examples

Important note on significant figures

Remember!