Electron gain enthalpy and electronegativity

Pull an electron away from an atom and you measure ionisation enthalpy. Now ask the opposite question: what happens when an atom gains an electron instead? Some atoms release energy doing this — they "want" the extra electron. Others resist it, or even need energy pumped in to accept it. This willingness to gain an electron is electron gain enthalpy, and it explains why halogens form salts so readily while noble gases essentially never do. A closely related but distinct idea describes atoms once they are already bonded: electronegativity, the tug-of-war an atom wins (or loses) for the shared electron pair in a covalent bond. Both properties trace back to the same two forces you have already met — effective nuclear charge and shielding — but they answer different questions about different situations: one about a lone gaseous atom, the other about an atom sitting inside a molecule. This article builds both ideas from Pass-1's definitions up to a working numerical bridge between them.

The core insight

Electron gain enthalpy measures the energy change when an isolated gaseous atom accepts an electron (generally more negative, i.e. more favourable, across a period and less negative down a group, with noble-gas, half-filled, and F-versus-Cl exceptions), while electronegativity measures how strongly an already-bonded atom pulls shared electron density toward itself, and the two are connected quantitatively by the Mulliken relation χM=12(IE1+∣ΔegH1∣)\chi_M = \tfrac{1}{2}(\text{IE}_1 + |\Delta_{eg}H_1|).

The core idea

Electron gain enthalpy (ΔegH\Delta_{eg}H) is defined for a single, isolated gaseous atom accepting one electron:

X(g)+e−→X−(g)ΔegH1\text{X(g)} + e^- \rightarrow \text{X}^-\text{(g)} \qquad \Delta_{eg}H_1

where: X(g) is the neutral gaseous atom, X−^-(g) is the resulting gaseous anion, and ΔegH1\Delta_{eg}H_1 is the first electron gain enthalpy, usually negative because most atoms release energy on gaining an electron. A second electron gain enthalpy, X−^-(g) + e−e^- →\rightarrow X2−^{2-}(g), is always positive: forcing an electron onto an ion that is already negative means fighting electron-electron repulsion, which costs energy no matter how favourable the first addition was.

Across a period, ΔegH1\Delta_{eg}H_1 becomes generally more negative (left to right), because effective nuclear charge ZeffZ_{eff} rises steadily and pulls the incoming electron in more strongly. Halogens, one electron short of a noble-gas shell, show the most negative values in every period — chlorine's ΔegH1\Delta_{eg}H_1 is about −349 kJ mol−1-349\ \text{kJ mol}^{-1}, among the most exothermic of any element.

Three exceptions matter for exam answers. Noble gases have a large positive ΔegH1\Delta_{eg}H_1 because the incoming electron must start a brand-new, higher-energy shell. Group 2 (ns2ns^2) and Group 15 (np3np^3) elements resist the extra electron because it would break a stable filled or half-filled subshell, so their values are less negative than neighbouring elements. And fluorine's ΔegH1\Delta_{eg}H_1 is less negative than chlorine's despite F being smaller and more electronegative, because the extra electron crowds into fluorine's already compact 2p subshell and suffers strong electron-electron repulsion there — a size effect that works in the opposite direction to the usual "smaller means stronger pull" intuition.

Down a group, ΔegH1\Delta_{eg}H_1 generally becomes less negative (F-to-Cl being the flagged exception), since the incoming electron lands in a larger, more shielded orbital farther from the nucleus, so the net attraction weakens.

Electronegativity is different in kind: it is not a measurable enthalpy but a relative, qualitative number describing an atom that is already bonded in a molecule and its pull on the shared electron pair. The Pauling scale is the standard reference, running from about 0.7 (caesium, the least electronegative common element) up to 4.0 for fluorine, the most electronegative element of all. Because ZeffZ_{eff} rises across a period, electronegativity increases left to right; because the bonding electrons sit progressively farther out and more shielded down a group, electronegativity decreases top to bottom — the same two trends, ZeffZ_{eff} and shielding, doing the same job they always do in periodicity.

Figure
Two periodic trend arrows showing electron gain enthalpy becoming more negative and electronegativity increasing from left to right across a period, and both weakening down a group
Electron gain enthalpy and electronegativity across the periodic grid halogen: most negative EA, high EN noble gas: positive EA across a period: Zeff rises, EA more negative, electronegativity increases down a group: shielding grows, both weaken

The two properties feel similar because they share a cause, but they are not measuring the same event.

Electron gain enthalpy is one-atom, one-electron energy bookkeeping. Picture the incoming electron approaching a bare, isolated atom. Two forces act: the attraction of ZeffZ_{eff} pulling it in, and the repulsion of the electrons already present, especially if packed into a small shell. Across a period, ZeffZ_{eff} climbs steadily, so attraction strengthens and ΔegH1\Delta_{eg}H_1 trends more negative — until a filled or half-filled subshell makes the repulsion term suddenly dominate. This is why Group 2, Group 15, and Group 18 break the smooth period trend, and why fluorine's compact 2p shell makes its electron gain enthalpy anomalously less negative than chlorine's, even though fluorine's ZeffZ_{eff} is higher.

Electronegativity, in contrast, is a relative pulling power exercised inside an existing bond, not the energy of a single reaction. Chemists compare how much electron density shifts toward each bonded atom. This pull comes from the same ZeffZ_{eff}-versus-distance competition, so the trends run in step with electron gain enthalpy's general direction, but electronegativity has no equivalent of the noble-gas spike, since noble gases essentially do not form ordinary covalent bonds. Electron gain enthalpy is measured in kJ mol−1\text{kJ mol}^{-1} for a specific isolated-atom reaction with two exceptions rooted in subshell stability; electronegativity is a unitless, bonded-atom ranking with no reaction of its own.

Derivation AMulliken's electronegativity bridges electron gain enthalpy and ionisation enthalpy into one number

Show that an atom's electronegativity can be estimated directly from two quantities already in your toolkit — ionisation enthalpy (how hard it is to remove an electron) and electron gain enthalpy (how much energy is released gaining one) — without appealing to bond energies at all, by averaging the two on a per-electron basis to capture how strongly an atom resists losing electron density and how strongly it seeks to gain it.

Step 1. An atom that is strongly electronegative should do two things simultaneously: hold onto its own electrons tightly (high ionisation enthalpy, IE1_1) and pull additional electron density toward itself readily (large negative ΔegH1\Delta_{eg}H_1, i.e. large magnitude ∣ΔegH1∣|\Delta_{eg}H_1|). Robert Mulliken proposed combining exactly these two quantities, both already defined for isolated gaseous atoms, into a single index.

Step 2. Mulliken's electronegativity is defined as the arithmetic mean of the ionisation enthalpy and the magnitude of the electron gain enthalpy, both expressed in electron-volts (eV) per atom:

χM=IE1+∣ΔegH1∣2\chi_M = \frac{\text{IE}_1 + |\Delta_{eg}H_1|}{2}

where: χM\chi_M is the Mulliken electronegativity (eV), IE1_1 is the first ionisation enthalpy of the atom (eV), and ∣ΔegH1∣|\Delta_{eg}H_1| is the magnitude of its first electron gain enthalpy (eV).

Step 3. Physically, the average makes sense: an atom that is both hard to ionise and eager to gain an electron scores high on both terms, so their average is high — exactly the profile of a strongly electronegative atom like fluorine or oxygen. An atom that is easy to ionise and reluctant to gain an electron (a Group 1 metal) scores low on both terms, matching its low electronegativity.

Step 4. Because IE1_1 and ∣ΔegH1∣|\Delta_{eg}H_1| both increase across a period (rising ZeffZ_{eff}) and both decrease down a group (growing shielding and atomic size, subject to the same exceptions already discussed), χM\chi_M inherits the same period and group trends as the Pauling electronegativity scale, even though the two scales are built from entirely different raw data — one from measured bond and ionisation energies, the other purely from single-atom IE and EA values.

Worked example

Question: Using standard reference values, IE1_1(F) = 1681 kJ mol−1^{-1}, ΔegH1\Delta_{eg}H_1(F) = −328-328 kJ mol−1^{-1}, IE1_1(Cl) = 1251 kJ mol−1^{-1}, and ΔegH1\Delta_{eg}H_1(Cl) = −349-349 kJ mol−1^{-1}, compute the Mulliken electronegativity of fluorine and chlorine and check whether the ordering matches the known Pauling values (F: 3.98, Cl: 3.16), consistent with the F-versus-Cl electron gain enthalpy anomaly from Pass-1.

Step 1. Convert every energy from kJ mol−1^{-1} to eV per atom using 1 eV=96.485 kJ mol−11\ \text{eV} = 96.485\ \text{kJ mol}^{-1}. Fluorine: IE1_1 = 17.42 eV17.42\ \text{eV}, ∣ΔegH1∣|\Delta_{eg}H_1| = 3.40 eV3.40\ \text{eV}. Chlorine: IE1_1 = 12.96 eV12.96\ \text{eV}, ∣ΔegH1∣|\Delta_{eg}H_1| = 3.62 eV3.62\ \text{eV}.

Step 2. Apply χM=(IE1+∣ΔegH1∣)/2\chi_M = (\text{IE}_1 + |\Delta_{eg}H_1|)/2 to fluorine: χM(F)=(17.42+3.40)/2=10.41 eV\chi_M(\text{F}) = (17.42 + 3.40)/2 = 10.41\ \text{eV}.

Step 3. Apply the same formula to chlorine: χM(Cl)=(12.96+3.62)/2=8.29 eV\chi_M(\text{Cl}) = (12.96 + 3.62)/2 = 8.29\ \text{eV}.

Step 4. Compare: χM(F)=10.41 eV>χM(Cl)=8.29 eV\chi_M(\text{F}) = 10.41\ \text{eV} > \chi_M(\text{Cl}) = 8.29\ \text{eV}, the same ordering as the Pauling values (3.98 versus 3.16). Notice why chlorine's larger ∣ΔegH1∣|\Delta_{eg}H_1| does not flip the result — fluorine's much larger IE1_1 dominates the average, so fluorine remains more electronegative than chlorine even though chlorine has the more favourable (more negative) electron gain enthalpy, exactly the distinction Pass-1 flagged between the two properties.

Common traps

  • Treating "more negative electron gain enthalpy" and "higher electronegativity" as interchangeable — chlorine beats fluorine on electron gain enthalpy magnitude but loses to it on electronegativity, as the worked example shows numerically.
  • Forgetting that ΔegH\Delta_{eg}H is measured for one specific reaction on an isolated gaseous atom (units kJ mol−1\text{kJ mol}^{-1}), while electronegativity has no reaction and no fixed unit of its own — it is a relative ranking.
  • Missing the noble-gas, Group 2, and Group 15 exceptions when asked to explain a period-wise electron gain enthalpy trend, or missing that electronegativity has no equivalent noble-gas spike because noble gases rarely form ordinary bonds.
  • Sign errors: a negative ΔegH\Delta_{eg}H means energy is released and the process is favourable — students sometimes read "more negative" as "less favourable" and reverse period-trend answers.

Ask the tutor: if the Mulliken-versus-Pauling electronegativity comparison or the F-versus-Cl electron gain enthalpy anomaly still feels shaky, ask the AI tutor to walk through the unit conversions and the repulsion argument step by step.

Why does chlorine have a more negative electron gain enthalpy than fluorine, but fluorine is still more electronegative

These are two different measurements. Electron gain enthalpy asks how much energy is released when one isolated gaseous atom grabs one electron — and fluorine's very small 2p subshell makes that specific addition less favourable due to electron-electron repulsion. Electronegativity asks how strongly an atom already sitting in a bond pulls the shared pair toward itself, a broader pull that also reflects fluorine's very high ionisation enthalpy and small size. The Mulliken formula makes this explicit: it averages ionisation enthalpy with electron gain enthalpy, and fluorine's much larger ionisation enthalpy wins out even though its electron gain enthalpy alone is smaller in magnitude than chlorine's.

Is electron gain enthalpy the same thing as electron affinity

They describe the same underlying tendency but are defined with opposite sign conventions in many older textbooks. Electron affinity was traditionally reported as a positive number for a favourable (energy-releasing) addition, while electron gain enthalpy, the IUPAC-preferred term used in your syllabus, follows standard thermodynamic convention: energy released is negative. Numerically the magnitudes usually match; only the sign differs. Always use the electron gain enthalpy convention, negative means favourable, unless a question explicitly asks about the older electron affinity convention.

Why does second electron gain enthalpy always come out positive, even for an atom that badly wants a full octet, like oxygen

Because the ion accepting the second electron is already negatively charged. Even though O2−^{2-} is the thermodynamically desirable end state for forming ionic oxides, the immediate step, O−^-(g) + e−e^- to O2−^{2-}(g), forces an electron onto a particle that is already repelling extra negative charge. That electron-electron repulsion costs more energy than the nuclear attraction releases, so ΔegH2\Delta_{eg}H_2 is positive on its own. The overall formation of an ionic solid like MgO is still favourable once you add in the large negative lattice enthalpy released when the ions pack into a crystal — but that is a separate step, not part of ΔegH2\Delta_{eg}H_2 itself.

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