Sigma & Pi Bonds, Polarity, Ionic Character, Bond Energy

Sigma (σ) Bonds

A Sigma Bond is formed by the head-on (axial) overlap of two partially filled atomic orbitals along the internuclear axis. The electron density is concentrated symmetrically around the line joining the two nuclei, with maximum probability of finding the bonding electrons directly between them. This type of overlap can occur between any combination of orbitals: s-s (as in H₂), s-p (as in HF), p-p (as in F₂), or between hybrid orbitals such as sp³-s (as in CH₄). Every covalent bond contains at least one Sigma Bond — it is always the first bond formed between two atoms, and it determines the direction of the bond.
Formation: Head-on (axial) overlap of atomic orbitals along the line joining two nuclei
Electron Density: Maximum along the internuclear axis — concentrated directly between the two nuclei
Strength: Stronger than a pi bond due to greater extent of orbital overlap
Rotation: Free rotation about the sigma bond axis is possible in single bonds
Orbital Combinations: s-s, s-p, p-p, sp³-s, sp²-sp², sp-sp overlaps all produce sigma bonds

Examples of Sigma Bond Formation

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H₂ — 1s–1s (s-s overlap)
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HF — 1s–2p (s-p overlap)
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F₂ — 2p–2p (p-p head-on overlap)
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CH₄ — sp³–1s (four C-H sigma bonds)
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H₂O — sp³–1s (two O-H sigma bonds)
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C₂H₄ — sp²–sp² (one C-C sigma bond)

Pi (π) Bonds

A Pi Bond is formed by the sideways (lateral) overlap of two parallel, unhybridized p orbitals. Unlike a sigma bond, the electron density in a pi bond is concentrated above and below the internuclear axis, with a nodal plane (zero electron density) along the axis itself. A pi bond can only form between two atoms that already share a sigma bond — it is always the second or third bond in a multiple bond. In ethene (C₂H₄), each carbon undergoes sp² hybridization leaving one unhybridized p orbital perpendicular to the molecular plane. The sideways overlap of these p orbitals forms one pi bond. In ethyne (C₂H₂), each carbon is sp hybridized with two unhybridized p orbitals, producing two pi bonds in perpendicular planes. In N₂, one sigma bond (p-p head-on) and two pi bonds (p-p sideways) together form the triple bond with a Bond Energy of 941 kJ/mol.
Formation: Sideways (lateral) overlap of two parallel, unhybridized p orbitals
Electron Density: Maximum above and below the internuclear axis; zero on the axis (nodal plane)
Prerequisite: Can only form after a sigma bond already exists between the same two atoms
Strength: Weaker than sigma bonds due to less effective sideways overlap
Rotation: Prevents free rotation about the bond axis — creates rigidity in double and triple bonds

Multiple Bond Composition

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Single bond (C—C) = 1 sigma bond
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Double bond (C=C) = 1 sigma + 1 pi bond
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Triple bond (C≡C) = 1 sigma + 2 pi bonds
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O=O double bond = 1 sigma + 1 pi bond
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N≡N triple bond = 1 sigma + 2 pi bonds
The fundamental difference between sigma and pi bonds lies in their orbital overlap geometry and resulting Bond Energy. For carbon-carbon bonds, the Bond Energy values are: C—C (single, sigma only) = 348 kJ/mol, C=C (one sigma + one pi) = 614 kJ/mol, and C≡C (one sigma + two pi) = 839 kJ/mol. A double bond is not twice as strong as a single bond (614 ≠ 2 × 348 = 696), and a triple bond is not three times as strong (839 ≠ 3 × 348 = 1044). This confirms that the pi bond contributes less energy than the sigma bond. Similarly, Bond Length values follow the reverse order: C—C = 154 pm, C=C = 133 pm, C≡C = 120 pm — multiple bonds are shorter and stronger, but the pi component adds less strength per bond than the sigma component.
Overlap Direction: Sigma — head-on along the axis; Pi — sideways, perpendicular to the axis
Electron Density: Sigma — along the internuclear axis; Pi — above and below the axis with a nodal plane on the axis
Bond Strength: Sigma bond is always stronger than pi bond
Energy Trend: C—C (348 kJ/mol) < C=C (614 kJ/mol) < C≡C (839 kJ/mol) — but not in simple multiples
Length Trend: C—C (154 pm) > C=C (133 pm) > C≡C (120 pm) — shorter bonds are stronger
Formation Order: Sigma bond always forms first; pi bond forms only after sigma

Bond Polarity and Molecular Polarity

When two identical atoms share electrons equally, the bond is a Non-Polar Covalent Bond. Examples include H₂, Cl₂, F₂, Br₂, and I₂, where both atoms have the same Electronegativity and the bonding electron pair is equally shared. When two different atoms are bonded, the more electronegative atom attracts the shared electron pair more strongly, creating a Polar Covalent Bond. This unequal sharing produces partial charges: the less electronegative atom carries a partial positive charge (δ⁺) and the more electronegative atom carries a partial negative charge (δ⁻). In HF, fluorine is more electronegative than hydrogen, so the bond is polar with H(δ⁺)—F(δ⁻). In H₂O, oxygen is more electronegative than hydrogen, giving O(δ⁻) and each H(δ⁺). The greater the electronegativity difference, the more polar the bond becomes, until the character becomes predominantly ionic (ΔEN ≥ 1.7).
Non-Polar Bond: Equal sharing between identical atoms (same electronegativity) — no charge separation
Polar Bond: Unequal sharing — electron pair displaced towards the more electronegative atom
Partial Charges: δ⁺ on the less electronegative atom, δ⁻ on the more electronegative atom
Electronegativity Trend: Larger difference → greater polarity → more ionic character

Examples of Polar Covalent Bonds

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H—F: fluorine more electronegative → H(δ⁺)—F(δ⁻)
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H—O: oxygen more electronegative → H(δ⁺)—O(δ⁻)
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C—Cl: chlorine more electronegative → C(δ⁺)—Cl(δ⁻)
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C—O: oxygen more electronegative → C(δ⁺)—O(δ⁻)
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N—H: nitrogen more electronegative → N(δ⁻)—H(δ⁺)
A molecule may have polar bonds but still be non-polar overall if its geometry causes the individual bond dipoles to cancel out by vector addition. Molecular polarity depends on both the polarity of individual bonds and the three-dimensional shape of the molecule. To predict whether a molecule is polar, identify all bond dipoles and determine whether their vector sum equals zero (non-polar) or is non-zero (polar). Symmetric molecules like CO₂ (linear), BF₃ (trigonal planar), CH₄ (tetrahedral), and CCl₄ (tetrahedral) have zero net Dipole Moment despite having polar bonds, because symmetry causes perfect cancellation. Asymmetric or bent molecules like H₂O (angular, 104.5°), NH₃ (trigonal pyramidal, 107.5°), and SO₂ (angular) have non-zero net dipole moments because the bond dipoles do not cancel.
The net molecular dipole moment is the vector sum of all individual bond dipole moments in the molecule. If bond dipoles cancel, the net is zero (non-polar). If they do not cancel, the molecule is polar.
=Net molecular dipole moment(Debye (D))
=Individual bond dipole moment (points from δ⁺ to δ⁻)(Debye (D))
Key Principle: Net molecular polarity equals the vector sum of all bond dipole moments
Non-Polar Molecules: Symmetric geometry causes all bond dipoles to cancel → net μ = 0
Polar Molecules: Asymmetric or bent geometry → bond dipoles do not fully cancel → net μ ≠ 0
Geometry Matters: Same bonds can give polar or non-polar molecules depending on shape

Non-Polar Molecules (Zero Net Dipole Despite Polar Bonds)

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CO₂ — linear (O=C=O), dipoles cancel exactly
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CS₂ — linear, dipoles cancel
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BF₃ — trigonal planar, dipoles cancel
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CH₄ — tetrahedral, dipoles cancel
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CCl₄ — tetrahedral, dipoles cancel
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SiCl₄ — tetrahedral, dipoles cancel

Polar Molecules (Non-Zero Net Dipole)

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H₂O — angular (104.5°), μ = 1.85 D
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H₂S — angular, μ = 0.95 D
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NH₃ — trigonal pyramidal (107.5°), μ = 1.49 D
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SO₂ — angular, μ = 1.61 D
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HF — μ = 1.90 D
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HCl — μ = 1.03 D

Ionic Character of Covalent Bonds

No covalent bond is purely covalent — every bond has some degree of Ionic Character due to the electronegativity difference between bonded atoms. The greater the electronegativity difference, the greater the ionic character. As a general rule, if the electronegativity difference is 1.7 or more, the bond is considered predominantly ionic. NaCl has 72% ionic character and CsF has 92% ionic character, but calculations confirm that no bond is 100% ionic. The Ionic Character can also be estimated from Bond Energy data — the difference between the experimentally observed bond energy and the value calculated assuming equal sharing reveals the extra stability contributed by ionic attraction. In H-X compounds, this difference is largest for HF (274 kJ/mol) and smallest for HI (8 kJ/mol), reflecting the trend of decreasing electronegativity and ionic character from F to I.
Electronegativity Rule: ΔEN ≥ 1.7 → predominantly ionic; ΔEN < 1.7 → predominantly covalent
Examples: NaCl — 72% ionic; CsF — 92% ionic (highest known, but still not 100%)
Effect on Bond Energy: Ionic character increases bond energy beyond the pure covalent value because partial ionic attraction adds extra binding force
Trend in H-X: HF (567 kJ/mol, Δ = 274) > HCl (431, Δ = 95) > HBr (366, Δ = 55) > HI (299, Δ = 8)

Ionic Character Reflected in Bond Energy (H-X Compounds)

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H—F: observed 567 kJ/mol, covalent estimate 293, extra 274 kJ/mol (highest ionic character)
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H—Cl: observed 431 kJ/mol, covalent estimate 336, extra 95 kJ/mol
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H—Br: observed 366 kJ/mol, covalent estimate 311, extra 55 kJ/mol
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H—I: observed 299 kJ/mol, covalent estimate 291, extra 8 kJ/mol (least ionic character)

Bond Energy (Bond Enthalpy)

Bond Energy is the average amount of energy required to break all bonds of a particular type in one mole of a substance in the gaseous state. It is expressed in kJ/mol and is also called bond enthalpy, as it represents the enthalpy change at 298 K. When a bond forms between two atoms, the same amount of energy is released. Bond energy is determined experimentally by measuring the heat absorbed or released in chemical reactions. The enthalpy change involved in splitting a molecule into its component atoms is called the enthalpy of atomization. Bond energy values are averaged over many compounds since the exact energy of a specific bond type varies slightly depending on the molecular environment.
Definition: Average energy to break one mole of a particular bond type in the gaseous state
Units: kJ/mol — energy to break 6.02 × 10²³ bonds of that type
Reversibility: The same amount of energy is released when an equal number of bonds are formed
Measurement: Determined experimentally from thermochemical data (enthalpy of atomization)

Selected Average Bond Enthalpies (kJ/mol)

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H—H: 436
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C—C: 348
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C=C: 614
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C≡C: 839
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C—H: 413
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C—F: 485
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C—Cl: 328
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N—H: 391
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O—H: 463
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N≡N: 941
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O=O: 495
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F—F: 155
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Cl—Cl: 242
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Br—Br: 193
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I—I: 151
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H—F: 567
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H—Cl: 431
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H—Br: 366
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H—I: 299
The strength of a bond — and hence its Bond Energy — depends on three main factors: the electronegativity difference between the bonded atoms, the sizes (atomic radii) of the atoms, and the Bond Length. A polar covalent bond is stronger than a non-polar covalent bond of similar length because the partial ionic attraction adds extra binding force. Bonds with shorter lengths have higher bond energies. For C—C bonds: C≡C (120 pm, 839 kJ/mol) is stronger than C=C (133 pm, 614 kJ/mol), which is stronger than C—C (154 pm, 348 kJ/mol). However, a double bond is not twice as strong as a single bond (614 ≠ 2 × 348 = 696), and a triple bond is not three times as strong (839 ≠ 3 × 348 = 1044). This confirms that the Sigma Bond is always the strongest component and the Pi Bond is weaker. A polar covalent bond is also stronger than a non-polar covalent bond of the same bond length because of the additional electrostatic attraction between the partial charges.
Electronegativity Difference: Greater difference → more ionic character → stronger bond (H—F 567 > H—I 299 kJ/mol)
Bond Length: Shorter bond → higher bond energy (inversely related)
Bond Order: Triple > double > single, but the increase is not linear — pi bonds contribute less than sigma bonds
Sigma vs Pi: Within any multiple bond, the sigma component is stronger than the pi component

Bond Energy and Bond Length — Carbon-Carbon Series

1
C—C single: 348 kJ/mol, 154 pm (1 sigma only)
2
C=C double: 614 kJ/mol, 133 pm (1 sigma + 1 pi; not 2 × 348)
3
C≡C triple: 839 kJ/mol, 120 pm (1 sigma + 2 pi; not 3 × 348)

Bond Length

The Bond Length is the distance between the nuclei of two bonded atoms, measured in picometres (pm). It is determined experimentally using electron diffraction, X-ray diffraction, or spectroscopic methods. The Covalent Radius of an atom is approximately half the bond length in a homonuclear diatomic molecule — carbon has a covalent radius of 77 pm (half of C—C = 154 pm), and chlorine has a covalent radius of 99 pm (half of Cl—Cl = 198 pm). Covalent radii are approximately additive, meaning the bond length of a heteronuclear bond can be estimated by summing the individual covalent radii. For example, the estimated C—Cl bond length is 77 + 99 = 176 pm, which is very close to the experimental value.
The bond length between two atoms is approximately equal to the sum of their individual covalent radii. This additivity works well for non-polar bonds but underestimates the actual length when ionic character is significant.
=Covalent radius of the first atom(pm)
=Covalent radius of the second atom(pm)
significant electronegativity difference exists
→
the ionic character shortens the actual bond length below the sum of covalent radii
Definition: Internuclear distance between two bonded atoms, measured in picometres (pm)
Covalent Radius: Half the bond length in a homonuclear diatomic molecule (r_C = 77 pm, r_Cl = 99 pm)
Additivity: Bond length is approximately equal to the sum of the covalent radii of the two atoms
Measurement: Electron diffraction, X-ray diffraction, or spectroscopic methods

Selected Bond Lengths and Hybridization

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C—C in ethane (sp³): 154 pm
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C=C in ethene (sp²): 133 pm
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C≡C in ethyne (sp): 120 pm
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C=O in acetone (sp²): 122 pm
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B—F in BF₃ (sp²): 130 pm
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Si—H in SiH₄ (sp³): 148 pm
Several factors affect the Bond Length. Hybridization plays a key role: as the s-character of the hybrid orbital increases, the bond becomes shorter because s orbitals have a smaller mean radius than p orbitals. In carbon compounds, s-character increases from sp³ (25% s) to sp² (33% s) to sp (50% s), producing progressively shorter C—C bonds: 154, 133, and 120 pm respectively. Ionic Character also shortens bonds — the electrostatic attraction between partial charges pulls the atoms closer together. For example, the Si—F bond length is 154–159 pm, much shorter than the sum of covalent radii (117 + 64 = 181 pm). Periodic trends also apply: bond lengths increase down a group as atomic radii increase (Si—Si > C—C), and decrease across a period as effective nuclear charge increases (C—C > N—N).
Hybridization Effect: Greater s-character → shorter bond (sp: 50% s, sp²: 33% s, sp³: 25% s)
Ionic Character: Electrostatic attraction between partial charges shortens the bond below the sum of covalent radii
Group Trend: Bond length increases down a group as atomic radii increase (Si—Si > C—C, P—P > N—N)
Period Trend: Bond length decreases across a period as effective nuclear charge increases with the same principal quantum number

Dipole Moment

When bonded atoms in a heteronuclear molecule have different electronegativities, the unequal electron sharing creates a separation of partial charges called a dipole. The Dipole Moment quantifies this charge separation as a vector quantity — it has both magnitude and direction. It is defined as the product of the magnitude of partial charge (q) and the distance between the centres of positive and negative charge (r). The vector points from the positive end to the negative end of the molecule. Dipole moments are measured in Debye (D), where . As a reference, a unit electronic charge ( C) separated by 100 pm (1 Å) gives a dipole moment of 4.8 D.
The dipole moment measures the magnitude of charge separation in a polar bond or molecule. A larger partial charge or greater separation distance produces a larger dipole moment.
=Dipole moment(Debye (D) or mC (milliCoulomb·metres))
=Magnitude of the partial charge(Coulombs (C))
=Distance between centres of positive and negative charge (approximately the bond length)(metres (m))
Vector Quantity: Has both magnitude and direction — the vector points from δ⁺ to δ⁻
Unit Conversion:
Reference Value: A full electronic charge separated by 100 pm produces μ = 4.8 D
The Dipole Moment provides two types of structural information: the percentage ionic character of a bond, and the geometry (bond angles) of molecules. For a polyatomic molecule, the net dipole moment is the vector sum of all individual bond dipole moments. In CO₂ (linear, O=C=O), the two C=O bond dipoles are equal in magnitude and exactly opposite in direction, so they cancel to give zero net dipole moment. In H₂O (angular, 104.5°), the two O—H bond dipoles add up to give a net dipole moment of 1.85 D. The fact that water has a non-zero dipole moment rules out a linear structure — if H₂O were linear, its net dipole would be zero. Similarly, NH₃ has a net dipole of 1.49 D confirming trigonal pyramidal geometry, while CH₄ has zero dipole confirming perfect tetrahedral symmetry.
The percentage ionic character is calculated by comparing the observed dipole moment of a bond with the dipole moment it would have if the bond were fully ionic (complete electron transfer).
=Experimentally observed dipole moment of the molecule or bond(Debye (D))
=Dipole moment if the bond were 100% ionic (full charge × bond length)(Debye (D))
→
Multiply the full electronic charge (1.6022 × 10⁻¹⁹ C) by the bond length, then convert to Debye
Vector Addition: Net molecular dipole = vector sum of all individual bond dipole moments
Geometry Determination: Dipole moment data confirms or rules out molecular geometries
Zero Dipole Examples: CO₂ (linear), BF₃ (trigonal planar), CH₄ (tetrahedral), CCl₄ (tetrahedral)
Non-Zero Examples: H₂O (angular, 1.85 D), NH₃ (pyramidal, 1.49 D), SO₂ (angular, 1.61 D)
Ionic Character: Can be calculated from dipole moment data using the % ionic character formula

Dipole Moments of Selected Substances (Debye)

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HF: 1.90
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H₂O: 1.85
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NH₃: 1.49
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SO₂: 1.61
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H₂O₂: 2.20
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CH₃F: 1.81
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C₂H₅OH: 1.69
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CH₃Br: 1.85
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HCl: 1.03
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HBr: 0.78
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HI: 0.38
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H₂S: 0.95
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CH₃Cl: 1.45
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CH₃I: 1.35
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CO: 0.12
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NO: 0.16
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H₂: 0.00
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CO₂: 0.00
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CH₄: 0.00