Odd-Electron Molecules and Radicals

Introduction

Most introductory Lewis examples use pairs of electrons throughout. If a species has an odd number of valence electrons, an all-paired drawing cannot possibly account for it. Nitric oxide, NO, is a useful example: N contributes five and O contributes six, giving eleven. The odd total signals an unpaired electron and a limit of the ordinary octet template.

Core explanation

A Lewis bond line represents two electrons and a lone pair represents two. Any sum made solely of such marks is even. Therefore an odd valence-electron budget requires at least one single dot somewhere in an elementary diagram. That single dot represents an unpaired electron. The budget does not by itself say which atom or orbital carries the electron in the real molecule; placement in a Lewis drawing is a simplified representation to be checked against valence and evidence.

Nitric oxide, NO, has eleven valence electrons. One useful simple drawing has an N=O double bond, two lone pairs on O, and on N one lone pair plus one single unpaired dot. Count: four electrons in the double bond, four in oxygen's lone pairs, two in nitrogen's lone pair and one unpaired electron, totaling eleven. Oxygen counts eight around it. Nitrogen counts four bonding, two lone-pair and one unpaired electron, totaling seven. Each atom has formal charge zero in this representation when the single dot is included in nitrogen's nonbonding count.

Trying to give both N and O ordinary octets by adding another line or pair would violate the eleven-electron budget or create an invalid second-period electron count. The correct conclusion is not that NO cannot exist. It is an experimentally observed gas with distinctive chemistry. The octet rule was a useful expectation for many closed-shell examples, and the odd-electron count tells us this example is outside that scope.

Nitrogen dioxide, NO₂, is another odd-electron molecule. Its neutral-atom budget is N 5 + 2(O 6) = 17. A simple set of resonance-related Lewis drawings can show an unpaired electron associated with the N-centered framework, but the real electron distribution and bond equivalence are more subtle than one fixed dot location. NO₂ should not be confused with nitrite, NO₂⁻, which has one extra electron and therefore eighteen valence electrons. A superscript charge changes the entire electronic problem.

Unpaired electrons often make radicals more reactive than related closed-shell species, but “radical” does not mean a molecule vanishes instantly. Lifetime and reaction behavior depend on structure, concentration, temperature and collision partners. Unpaired electrons also contribute to magnetic behavior: a species with such electrons may be paramagnetic. Inferring a precise magnetic response from a Lewis dot alone can be unsafe, because the simple diagram may miss electronic states, as the classic case of O₂ illustrates. The odd budget is a strong first clue, not a complete magnetic theory.

Step-by-step reasoning

1. Write the exact formula and any ionic charge. 2. Count valence electrons and identify whether the total is odd. 3. If odd, reserve at least one electron as an unpaired single dot. 4. Allocate bonds and lone pairs without exceeding the budget or second-period capacity. 5. Check the formal-charge sum and state that the drawing is a simplified model.

Visual explanation

Draw a number line with even totals divided into pairs and the eleven-electron NO total leaving one dot. Beside it, draw N=O with two O lone pairs, one N lone pair and one dot on N; label the counts 4 + 4 + 2 + 1. Put NO₂ at 17 and NO₂⁻ at 18 below to show how one charge mark changes odd to even.

Real-world analogy

Packing eleven identical cards into two-card sleeves leaves one card unpaired. Similarly, an odd electron count cannot be represented only by two-electron bond and lone-pair marks. The analogy helps with parity, not with the real spatial distribution of electrons.

Real-world example

Nitric oxide is involved in biological signaling and in atmospheric chemistry. Its unpaired-electron character affects reactions, but the biological role depends strongly on where, when and how much NO is produced. The Lewis drawing identifies a relevant electronic feature while leaving reaction mechanisms and physiological context to more detailed study.

Why?

Why does neutral NO₂ require an unpaired electron in a simple valence count while NO₂⁻ does not? Neutral NO₂ has seventeen valence electrons. Adding one for the negative charge gives nitrite eighteen, which can be allocated into pairs in its ordinary resonance diagrams.

Common misconception

“A molecule with one unpaired electron is impossible because not every atom has an octet.” The odd budget itself proves that a universal paired-octet demand cannot apply. Many radical species exist and can be detected, even though their reactivity varies.

Worked example

Audit the described NO drawing. N 5 + O 6 = 11 available electrons. A double bond uses four. Two oxygen lone pairs use four more, leaving three. Put a nitrogen lone pair and one nitrogen single dot, using the final three. Oxygen has four nonbonding plus four bonding electrons around it; nitrogen has two nonbonding in a pair, one unpaired and four bonding, for seven. Formal-charge bookkeeping gives N: 5 − 3 nonbonding − 2 bond-line share = 0, and O: 6 − 4 − 2 = 0. The drawing matches formula, budget and neutral net charge while openly showing the octet exception.

Quick check

1. What does an odd total of valence electrons prove about an all-paired Lewis drawing? Answer: It cannot be complete; at least one electron must remain unpaired in the simple representation.

Exam focus

Check charge before deciding parity. Show the full electron ledger, including a single dot, and avoid “repairing” an odd count by inventing an electron. Describe radical reactivity with qualifications rather than claiming all radicals behave identically.

Advanced insight

Electron spin underlies paramagnetic behavior, and molecular orbital theory can describe unpaired electrons spread over a molecule. Even an even-electron total does not guarantee every electron is paired in the true ground state; O₂ is an important example. Thus odd count guarantees at least one unpaired electron in a simple pairing model, while even count does not guarantee none.

Summary

Odd valence-electron totals cannot be represented solely by two-electron bonds and lone pairs. NO has eleven and NO₂ has seventeen, so their Lewis descriptions need an unpaired electron. The dot is a useful accounting signal, while actual spin and electron distribution need deeper models.

Practice questions

1. How many valence electrons does neutral NO have? Answer: Eleven, five from nitrogen and six from oxygen. 2. How many does NO₂⁻ have? Answer: Eighteen, including one extra electron for its negative charge. 3. Does an even electron total always imply a diamagnetic molecule? Answer: No. Electron arrangement can leave unpaired electrons despite an even total. 4. Why is a single dot included in an odd-electron Lewis drawing? Answer: It represents an electron that cannot be placed in a two-electron pair.