R3.1.4 pH and the hydrogen ion concentration

The pH Scale: A Measure of Acidity and Basicity

What is pH?

Definition

pH scale

The pH scale is a logarithmic measure of the concentration of hydrogen ions ( $[H^{+}]$ ) in an aqueous solution.

It is defined mathematically as:

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

Here:

$[H^{+}]$ represents the concentration of hydrogen ions in moles per cubic decimeter ( ${mol dm}^{- 3}$ ).
The negative logarithm ensures that pH values are positive, as $[H^{+}]$ in aqueous solutions typically ranges from $1 {mol dm}^{- 3}$ to $10^{- 14} {mol dm}^{- 3}$ .

Example

Calculating pH from $[H^{+}]$

If the $[H^{+}]$ of a solution is $1.0 \times 10^{- 3} {mol dm}^{- 3}$ at 298 K, its pH is:
$pH = - \log_{10} [H^{+}] = - \log_{10} (1.0 \times 10^{- 3}) = 3.00$
This indicates the solution is acidic.

Hint

If you know the pH, you can reverse the process to calculate the $[H^{+}]$ concentration using the equation:

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

Example

Calculating $[H^{+}]$ from pH

If the pH of a solution is $5.0$ at 298 K, the $[H^{+}]$ is:
$[H^{+}] = 10^{- pH} = 10^{- 5} = 1.0 \times 10^{- 5} {mol dm}^{- 3}$

Note

pH is temperature-dependent and is typically quoted at 298 K (25°C).
Changes in temperature can affect the ionization of water, altering the $[H^{+}]$ concentration and thus shifting the neutral pH value slightly from 7 at standard conditions.

The pH Scale: Ranges and Interpretations

The pH scale generally ranges from $0$ to $14$ , though values outside this range are possible for very strong acids or bases.
Here’s how to interpret pH values:
- Acidic solutions: $p H < 7$ ( $[H^{+}] > [O H^{-}]$ )
- Neutral solutions: $p H = 7$ ( $[H^{+}] = [O H^{-}]$ )
- Basic (alkaline) solutions: $p H > 7$ ( $[H^{+}] < [O H^{-}]$ )

Measuring pH: Indicators and Probes

1. Using Indicators

Acid–base indicators are substances that change color based on the pH of the solution. For example:

Litmus paper: Turns red in acidic solutions and blue in basic solutions.
Universal indicator: A mixture of indicators that shows a spectrum of colors across the pH scale (e.g., red for pH 1, green for pH 7, violet for pH 14).

Example

If a solution turns the universal indicator orange, its pH is approximately $4$ , indicating it is weakly acidic.

2. Using a pH Probe

For precise measurements, digital pH meters are used.
These devices consist of an electrode that measures $[H^{+}]$ concentration and converts it into a pH value.
Calibration with standard buffer solutions (e.g., pH $4.00$ , $7.00$ , and $10.00$ ) is necessary for accurate readings.

Tip

Always calibrate your pH probe before use, particularly when working with solutions at extreme pH values or when high precision is required.

Common Mistakes and How to Avoid Them

Common Mistake

Students often forget that the pH scale is logarithmic.
A decrease of 1 unit in pH corresponds to a tenfold increase in $[H^{+}]$ .
For example, a solution with pH $3$ is $10$ times more acidic than one with pH $4$ , not $1$ time more.

Common Mistake

Another common error is failing to convert concentrations to ${mol dm}^{- 3}$ before calculating pH. Always ensure your units are consistent.

Practice Questions

Self review

Calculate the pH of a solution with $[H^{+}] = 2.5 \times 10^{- 4} {mol dm}^{- 3}$ at 298 K.
A solution has a pH of $8.5$ at 298K. What is the $[H^{+}]$ concentration?
Compare the $[H^{+}]$ concentrations of solutions with pH $3$ and pH $6$ at 298 K. How many times more acidic is the first solution?
Why might a pH probe provide more accurate readings than a universal indicator?

Theory of Knowledge

Logarithmic scales are used in fields beyond chemistry, such as the decibel scale in sound intensity or the Richter scale for earthquakes.

How do these tools shape our interpretation of natural phenomena?

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R3.1.4 pH and the hydrogen ion concentration

The pH Scale: A Measure of Acidity and Basicity

What is pH?

Calculating pH from [H+]

Calculating [H+] from pH

The pH Scale: Ranges and Interpretations

Measuring pH: Indicators and Probes

1. Using Indicators

2. Using a pH Probe

Common Mistakes and How to Avoid Them

Practice Questions

You've read 2/2 free chapters this week.

Introduction to pH and Hydrogen Ion Concentration

Calculating pH from $[H^{+}]$

Calculating $[H^{+}]$ from pH