Polyvalance and Normality

Not every acid or base reacts one proton or hydroxide ion at a time. This subtopic covers polyvalence — an acid or base's capacity to donate or accept more than one H⁺ or OH⁻ per molecule — the equivalent, the reactive-unit measure polyvalence is built on, and normality, the concentration unit that tracks that reactive capacity directly. Normality is especially important for titrations and other quantitative acid-base calculations.

Key Takeaways

• Polyvalence is an acid or base's capacity to donate/accept more than one H⁺ or OH⁻ per molecule.

• An equivalent: for an acid, the amount that donates one mole of H⁺; for a base, the amount that accepts one mole of H⁺ or donates one mole of OH⁻.

• A polyprotic acid donates more than one H⁺ per molecule — e.g., diprotic H₂SO₄ (2 H⁺) or triprotic H₃PO₄ (3 H⁺). A polyvalent base accepts/donates more than one H⁺/OH⁻ per molecule — e.g., Ca(OH)₂ (2 OH⁻).

• Normality (N) = equivalents of solute / L solution = M × n, where n is the number of equivalents per mole (the valence factor).

• Normality is especially useful for titrations and other quantitative acid-base analyses, since it tracks reactive capacity directly rather than just moles present.

Polyvalence and Equivalents

Polyvalence refers to an acid or base's capacity to donate or accept more than one proton (H⁺) or hydroxide ion (OH⁻) per molecule.

This capacity is measured using the equivalent:

• For an acid, one equivalent is the amount of acid that can donate one mole of H⁺ ions.

• For a base, one equivalent is the amount of base that can accept one mole of H⁺ ions, or donate one mole of OH⁻ ions.

A monoprotic acid or monovalent base — one that can only donate/accept a single H⁺ or OH⁻ per molecule — has one equivalent per mole. A polyvalent acid or base has more than one equivalent per mole, since each molecule can react more than once.

Polyprotic Acids and Polyvalent Bases

An acid capable of donating more than one proton per molecule is a polyprotic acid. Sulfuric acid (H₂SO₄) is a classic example: it's diprotic, donating two H⁺ ions per molecule.

H₂SO₄ → 2H⁺ + SO₄²⁻

A supplied example, independently verified, illustrating that polyvalence isn't limited to two: phosphoric acid (H₃PO₄) is triprotic, donating three H⁺ ions per molecule across three successive dissociation steps:

H₃PO₄ → 3H⁺ + PO₄³⁻

A base capable of accepting more than one proton, or donating more than one OH⁻, per molecule is a polyvalent base. Calcium hydroxide (Ca(OH)₂) is a classic example, donating two OH⁻ ions per molecule:

Ca(OH)₂ → Ca²⁺ + 2OH⁻

Normality — Concentration by Equivalents

Normality (N) is a measure of concentration defined as the number of equivalents of solute per liter of solution:

N = Equivalents of Solute / Volume of Solution (L)

Because normality counts equivalents rather than moles, it directly tracks a solute's reactive capacity — which is exactly what matters in an acid-base reaction. This makes normality especially useful for titrations and other quantitative acid-base analyses, where the reaction depends on how many H⁺ or OH⁻ ions are actually available, not just how many moles of acid or base are present.

As established when concentration units were first introduced, normality also relates directly to molarity through the number of equivalents each mole of solute supplies: N = M × n, where n is the number of equivalents per mole (1 for a monoprotic acid or monovalent base, 2 for a diprotic acid like H₂SO₄, and so on).

Calculating Normality — Worked Examples

The following three examples are original, independently verified, and not sourced from the transcript, which states the normality formula but provides no numeric application.

Example 1 — Diprotic acid. What is the normality of a 0.250 M H₂SO₄ solution?

H₂SO₄ is diprotic, so n = 2 equivalents per mole:

N = M × n = 0.250 mol/L × 2 = 0.500 N

Example 2 — Triprotic acid. What is the normality of a 0.100 M H₃PO₄ solution?

H₃PO₄ is triprotic, so n = 3 equivalents per mole:

N = M × n = 0.100 mol/L × 3 = 0.300 N

Example 3 — Polyvalent base. What is the normality of a 0.150 M Ca(OH)₂ solution?

Ca(OH)₂ donates two OH⁻ per formula unit, so n = 2 equivalents per mole:

N = M × n = 0.150 mol/L × 2 = 0.300 N

Common MCAT Mistakes

• Treating molarity and normality as interchangeable. They're only equal when n = 1 (a monoprotic acid or monovalent base). For anything polyvalent, normality is always a multiple of molarity — N = M × n.

• Forgetting that "equivalent" is defined differently for acids vs. bases. For an acid, an equivalent is tied to H⁺ donated; for a base, it's tied to H⁺ accepted or OH⁻ donated — but both ultimately measure the same reactive capacity in an acid-base reaction.

• Assuming H₂SO₄ always reacts as 1 mole = 1 reactive unit. Because it's diprotic, one mole of H₂SO₄ supplies 2 equivalents — this matters directly for titration and stoichiometry calculations.

• Mixing up "diprotic" and "triprotic" with charge instead of proton count. Diprotic/triprotic refers to the number of donatable protons (H⁺), not the ion's final charge — though for H₂SO₄ and H₃PO₄ here, the two happen to match.

MCAT-Style Concept Check

Question: What is the normality of a 0.200 M solution of H₃PO₄?

• A) 0.200 N

• B) 0.400 N

• C) 0.600 N

• D) 0.800 N

Answer: C

Explanation: H₃PO₄ is triprotic, donating 3 H⁺ per molecule, so n = 3. Normality = M × n = 0.200 mol/L × 3 = 0.600 N. Choosing (A) mistakenly treats normality as equal to molarity, ignoring the acid's polyprotic character.

FAQ

What is the difference between molarity and normality?

Molarity measures moles of solute per liter of solution. Normality measures equivalents of solute per liter — where each equivalent corresponds to one mole of H⁺ (or OH⁻) that a substance can donate or accept. For a monoprotic acid or monovalent base they're numerically equal; for a polyvalent species, normality is a multiple of molarity (N = M × n).

What does "diprotic" mean, and how is it different from "triprotic"?

Diprotic means an acid can donate two protons (H⁺) per molecule, like H₂SO₄. Triprotic means it can donate three, like H₃PO₄. Both are types of polyprotic acids — the prefix just tells you how many ionizable protons the molecule has.

How do you calculate the number of equivalents per mole (n) for a base?

Count how many H⁺ ions the base can accept, or how many OH⁻ ions it can donate, per formula unit. Ca(OH)₂, for example, donates two OH⁻ per formula unit, so n = 2 and its normality is twice its molarity.

Why is normality especially useful for titrations?

Normality tracks a solute's reactive capacity directly — the actual number of H⁺ or OH⁻ ions available to react — rather than just the number of moles present. Since a titration reaction depends on that reactive capacity matching between titrant and titrand, normality simplifies the stoichiometry, especially for polyprotic/polyvalent species.