Acid-Base Indicators and the pH Scale

The pH scale measures the acidity of a solution as pH = −log₁₀[H⁺], and an acid-base indicator is a weak acid or base whose color changes over a specific pH range, which allows pH to be estimated by color. In brief: a solution with [H⁺] = 1 × 10⁻³ mol/L has a pH of 3; each unit of pH is a tenfold change in hydrogen ion concentration, so a solution of pH 3 is 1,000 times more acidic than a solution of pH 6; phenolphthalein changes from colorless to pink between pH 8.2 and 10.0.

The pH scale is used in medicine, agriculture, environmental science and cooking. Indicators provide a quick, inexpensive way to measure pH and to detect the end point of titrations. This article defines pH, shows the pH of common substances, explains how indicators work, tabulates common indicators with their colors and ranges, describes pH paper and meters, works through calculations and gives the history of the concept.

What is pH?

pH is the negative base-10 logarithm of the hydrogen ion concentration (more exactly, the activity) in mol/L: pH = −log[H⁺], and conversely [H⁺] = 10^−pH. At 25 °C, pure water has [H⁺] = 1.0 × 10⁻⁷ mol/L, so its pH is 7.00, which is neutral. A pH below 7 means acidic ([H⁺] larger), and above 7 basic ([H⁺] smaller). Because the scale is logarithmic, a change of one pH unit corresponds to a tenfold change in [H⁺]. The pH scale usually runs from 0 to 14 but values below 0 and above 14 are possible for very concentrated solutions.

What is the pH of common substances?

How do indicators work?

An indicator is a weak acid (written HIn) in which the acid form and its conjugate base have different colors: HIn ⇌ H⁺ + In⁻. In acidic solution the equilibrium shifts toward the acid form HIn, and in basic solution toward the ion In⁻. The color changes gradually over a range of about two pH units around the pK_a of the indicator, which is where the concentrations of the two forms are comparable. The human eye sees the color of the acid form when it is about 10 times more concentrated than the base form, and the color of the base form when it is 10 times more concentrated, so the visible transition occurs for pH = pK_a ± 1.

Common indicators

Universal indicator is a mixture of several indicators that gives a range of colors: approximately red (pH 1 to 3), orange and yellow (4 to 6), green (7), blue (8 to 10) and violet (11 to 14). Natural indicators include the juice of red cabbage (anthocyanins), which is red in acid, purple near neutral, blue-green in weak base and yellow in strong base.

How is pH measured?

• Indicator solutions and paper: a quick estimate with an accuracy of about 0.5 to 1 pH unit. Compare the color with a chart.
• pH meter: a glass electrode measures the voltage that depends on the hydrogen ion activity, with an accuracy of ±0.01 to ±0.05 pH units after calibration with buffer solutions (typically pH 4.00, 7.00 and 10.00). The electrode must be kept moist and rinsed between samples.
• Titration: the pH can be deduced from the amounts of acid and base.

Worked examples

1. pH from concentration. What is the pH of 0.025 mol/L HCl? HCl is a strong acid, so [H⁺] = 0.025 mol/L. pH = −log(0.025) = 1.60.
2. pH from a small concentration. [H⁺] = 3.2 × 10⁻⁵ mol/L. pH = −log(3.2 × 10⁻⁵) = 4.49.
3. Concentration from pH. A solution has pH 8.35. [H⁺] = 10^−8.35 = 4.5 × 10⁻⁹ mol/L.
4. Comparing acidity. Cola (pH 2.5) and tomato juice (pH 4.5). The difference is 2 pH units, so cola has 10² = 100 times the hydrogen ion concentration of tomato juice.
5. Choosing an indicator. The color of methyl orange at pH 4.0 is orange (within its range of 3.1 to 4.4). Bromothymol blue at pH 5 is yellow, since 5 is below its transition range of 6.0 to 7.6. Phenolphthalein at pH 9 is pink, since it is within its range.
6. Unknown solution. A solution is yellow with methyl red, green with bromothymol blue, and colorless with phenolphthalein. Yellow methyl red means that the pH is above 6.2. Green bromothymol blue means that the pH is in the middle of its range, about 6.8 to 7.2. Colorless phenolphthalein means that the pH is below 8.2. Taken together, the pH is about 7, so the solution is close to neutral.

Why does pH matter?

• Health: blood pH is kept between 7.35 and 7.45. Values below 6.8 or above 7.8 are life-threatening.
• Agriculture: crops grow best at specific soil pH values. Most prefer pH 6 to 7, and blueberries prefer acidic soil of pH 4.5 to 5.5.
• Environment: acid rain with a pH below 5 harms lakes and forests, and the pH of seawater affects marine life (ocean acidification).
• Industry: the pH controls reaction rates, water treatment and food preservation.
• Swimming pools: pH 7.2 to 7.8 is recommended.

Who invented pH?

The Danish chemist Søren Sørensen introduced the pH scale in 1909 at the Carlsberg Laboratory in Copenhagen, while studying the effect of acidity on enzymes in brewing. The “p” is generally understood to stand for the German Potenz (power), or the Latin pondus hydrogenii (weight of hydrogen), as Sørensen did not explain the letter. The first electrode methods were developed in the early 20th century, and the glass electrode, discovered by Max Cremer in 1906 and developed by Fritz Haber and Zygmunt Klemensiewicz in 1909, was used in the first commercial pH meters in the 1930s. Indicators have been known since antiquity: Robert Boyle described the color change of syrup of violets with acids and bases in the 17th century.

Which mistakes are common?

Mistake 1: Treating pH as a linear scale

A pH of 3 is not “half as acidic” as pH 6. It has 1,000 times the hydrogen ion concentration.

Mistake 2: Thinking that pH cannot be negative or above 14

Very concentrated strong acids (for example 12 mol/L HCl, pH about −1.1) have a negative pH, and concentrated bases can have a pH above 14.

Mistake 3: Using the wrong indicator

An indicator is useful only near its transition range. Choose an indicator whose range includes the pH you want to detect.

Mistake 4: Assuming that pH 7 is neutral at all temperatures

Neutral means [H⁺] = [OH⁻]. At 100 °C, neutral water has a pH of about 6.14.