ChemistryAcids & BasesA-Level

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pH definition

Definition of pH in terms of hydrogen ion concentration.

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p H = - lo g_{10} [H^{+}]

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Core idea

Overview

The pH scale measures the acidity or alkalinity of an aqueous solution by calculating the negative base-10 logarithm of the molar concentration of hydrogen ions. It provides a manageable numerical range, typically from 0 to 14, representing the inverse relationship between hydrogen ion concentration and the degree of acidity.

When to use: Use this equation when working with dilute aqueous solutions to quantify acidity or basicity. It assumes that the molar concentration of hydrogen ions is approximately equal to their thermodynamic activity, which is most accurate for concentrations below 1.0 M.

Why it matters: This scale is crucial for chemistry, biology, and environmental science because even small shifts in H⁺ concentration can denature proteins, alter chemical reaction rates, or impact aquatic life. It simplifies exponential concentration values into a linear scale that is easier to communicate and interpret.

Symbols

Variables

[H^+] = Hydrogen Ion Concentration, pH = pH Value

[H^{+}]

Hydrogen Ion Concentration

m o l / d m^{3}

p H

pH Value

V a r iab l e

Walkthrough

Derivation

Understanding pH Definition

Defines acidity using a logarithmic scale based on hydrogen ion concentration in aqueous solution.

Solution is aqueous and $[H^{+}]$ is expressed in $mol dm^{- 3}$ .

State the Definition:

A decrease of 1 pH unit corresponds to a tenfold increase in $[H^{+}]$ .

pH = - lo g_{10} [H^{+}]

Invert to Find [H+]:

Use this to calculate concentration from a pH value.

[H^{+}] = 1 0^{- pH}

Result

[H^{+}] = 1 0^{- pH}

Source: AQA A-Level Chemistry — Acids and Bases

Free formulas

Rearrangements

Solve for $p H$

Make pH the subject

p H = - lo g_{10} [H^{+}]

pH is already the subject of the formula.

Difficulty: 1/5

Solve for $[H^{+}]$

Make [H^+] the subject

[H^{+}] = 1 0^{- p H}

To make [H^+] the subject, first isolate the base-10 logarithm term, then apply the exponential function (raise 10 to the power of both sides).

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph follows a logarithmic curve where pH decreases as hydrogen ion concentration increases. This shape shows that small changes in hydrogen ion concentration result in large shifts in pH at low concentrations, while the curve flattens as concentration grows, reflecting the logarithmic nature of acidity. The most important feature is that the curve never reaches zero, meaning that even at extremely high concentrations, the pH value remains defined and positive.

Graph type: logarithmic

Why it behaves this way

Intuition

The pH scale is a numerical ruler that maps the vast range of hydrogen ion concentrations in a solution to a more compact, inverse measure of acidity, allowing for easy comparison of acidic and basic strengths.

A measure of the acidity or alkalinity of an aqueous solution.

A lower pH value indicates higher acidity (more hydrogen ions), while a higher pH value indicates lower acidity (fewer hydrogen ions, more hydroxide ions).

[H^{+}]

The molar concentration of hydrogen ions (or more accurately, hydronium ions, [H₃O⁺]) in an aqueous solution.

Directly represents the quantity of acid-contributing species per unit volume of solution. A higher concentration means a more acidic solution.

Signs and relationships

-: The negative sign is used to ensure that pH values are typically positive for most common aqueous solutions (where [H⁺] is usually less than 1 M, making log₁₀[H⁺] negative).
log₁₀: The base-10 logarithm is used to compress the very wide range of possible hydrogen ion concentrations (e.g., from 10⁻¹⁴ M to 1 M) into a more manageable and convenient numerical scale (e.g., 0 to 14).

Free study cues

Insight

Canonical usage

Converts the molar concentration of hydrogen ions (typically in mol/L) into a dimensionless pH value.

Common confusion

Students often attempt to assign units to pH or confuse molarity (mol/L) with other concentration units when performing calculations.

Dimension note

The pH value itself is dimensionless, representing a logarithmic scale. While the hydrogen ion concentration `[H+]` has units of molar concentration (mol/L), the logarithm is mathematically applied to the numerical value

Unit systems

$p H$ dimensionless · A logarithmic scale value, representing the acidity or alkalinity of a solution. It is a pure number without physical units.

$[H +]$ mol/L · Represents the molar concentration of hydrogen ions. In practice, the numerical value of the concentration in mol/L is used, implicitly assuming division by a standard concentration of 1 mol/L to make the argument of the

Ballpark figures

Quantity:

One free problem

Practice Problem

A sample of hydrochloric acid has [H+] = 0.04 mol/ $d m^{3}$ . Calculate the pH of this solution to 2 decimal places.

Hydrogen Ion Concentration0.04 mol/dm^3

Solve for: $p H$

Hint: pH = -log10[H+]. Use a scientific calculator.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Converting measured [H⁺] to a pH reading.

Study smarter

Tips

A change of 1 pH unit represents a 10-fold change in H⁺ concentration.
Low pH values (< 7) indicate acidic solutions, while high values (> 7) indicate basic solutions.
To find the concentration from pH, use the inverse log: [H⁺] = 10 to the power of negative pH.
Pure water at 25°C has a pH of exactly 7.0.

Avoid these traps

Common Mistakes

Forgetting the negative sign.
Using ln instead of log10.

Common questions

Frequently Asked Questions

Defines acidity using a logarithmic scale based on hydrogen ion concentration in aqueous solution.

Use this equation when working with dilute aqueous solutions to quantify acidity or basicity. It assumes that the molar concentration of hydrogen ions is approximately equal to their thermodynamic activity, which is most accurate for concentrations below 1.0 M.

This scale is crucial for chemistry, biology, and environmental science because even small shifts in H⁺ concentration can denature proteins, alter chemical reaction rates, or impact aquatic life. It simplifies exponential concentration values into a linear scale that is easier to communicate and interpret.

Forgetting the negative sign. Using ln instead of log10.