By Rosann Kozlowski | Updated Aug 30, 2022

Photo: Photongpix/iStock/GettyImages

In chemistry, the concept of equivalent units—or equivalents—helps quantify the reactive capacity of species such as electrons or ions. An equivalent represents the number of electrons or ions that a substance can donate or accept in a given reaction.

What Are Equivalents?

The reactive capacity of a species depends on what is transferred during a chemical reaction. In acid–base chemistry, an equivalent equals the amount of a substance that reacts with one mole of hydrogen ions (H⁺). In redox reactions, it is one mole of electrons.

Linking Oxidation State to Equivalents

The oxidation (or valence) state of an element indicates how many electrons are involved in its interactions. Therefore, the number of equivalents often equals the absolute value of the oxidation state.

• Calcium ion (Ca²⁺) – 2 equivalents
• Aluminum ion (Al³⁺) – 3 equivalents

Equivalents in Acids and Bases

For acids, an equivalent corresponds to the number of hydrogen ions a molecule can donate. This number is simply the coefficient of hydrogen in the molecular formula.

• Hydrochloric acid (HCl) – 1 equivalent
• Sulfuric acid (H₂SO₄) – 2 equivalents
• Phosphoric acid (H₃PO₄) – 3 equivalents
• Nitric acid (HNO₃) – 1 equivalent

For bases, the equivalent is the count of hydroxide ions (OH⁻) they provide:

• Sodium hydroxide (NaOH) – 1 equivalent
• Barium hydroxide (Ba(OH)₂) – 2 equivalents

Assessing Acid–Base Strength with Equivalents

One equivalent of an acid reacts with one equivalent of a base. Thus, equal equivalents of an acid and a base produce a neutral solution. For instance, 1 equivalent of HCl neutralizes 1 equivalent of NaOH, while 2 equivalents of H₂SO₄ require twice the amount of NaOH.

Practical Applications of Equivalents

Although modern laboratories rarely use equivalents for routine calculations, they remain essential for determining gram‑equivalent weight and normality, especially in titrations.

Gram‑Equivalent Weight Calculations

The gram‑equivalent weight of an acid or base is calculated as:

Equivalent weight = Molecular weight ÷ number of equivalents

Example: Find the gram‑equivalent weight of phosphoric acid (H₃PO₄).

1. Calculate its molecular weight: 3(1.01) + 30.97 + 4(16.00) = 127 g mol⁻¹.
2. Number of equivalents (n) = 3.
3. Equivalent weight = 127 ÷ 3 = 42.3 g eq⁻¹.

Normality Calculations

Normality (N) is defined as equivalents per liter of solution. The formula is:

N = (mass of solute in g ÷ equivalent weight) ÷ volume in L

Example: Prepare a 2 N solution of H₃PO₄.

1. Normality desired: N = 2 eq L⁻¹.
2. Volume: V = 1 L.
3. Equivalent weight: 42.3 g eq⁻¹.
4. Mass required: m = N × V × equivalent weight = 2 × 1 × 42.3 = 84.6 g.

Thus, dissolve 84.6 g of phosphoric acid in enough water to reach 1 L to obtain a 2 N solution.

Key Takeaways

• Equivalents provide a convenient way to relate stoichiometry to reactive capacity.
• They are essential for calculating gram‑equivalent weight and normality in titration work.
• Understanding equivalents bridges concepts in acid–base and redox chemistry.