Worked example 1
What is the hybridization of the nitrogen atom in ammonia, and what bond angle does it imply?
Try it first: Count nitrogen domains, including lone pairs.
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BondingHybridizationContent level: Core 16 min
Hybrid Orbitals from Domain Count
What you'll be able to do: Assign sp, sp² or sp³ hybridization to a central atom directly from its electron domain count.
Best after: Counting Electron Domains
Introduction
Hybridization is not extra work: if you already counted domains for VSEPR, the label is immediate.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- State why hybrid orbitals are needed to explain observed geometry
- Assign sp, sp² and sp³ from domain counts
- Connect each hybridization to its ideal bond angle
- Explain orbital conservation in hybridization
- Assign hybridization to atoms with lone pairs
Lesson
Why mix orbitals at all
Carbon has two 2s electrons and two 2p electrons, which would predict two bonds at 90 degrees. Methane instead has four identical bonds at 109.5 degrees. Mixing one s orbital with three p orbitals produces four equivalent sp³ hybrid orbitals aimed at the corners of a tetrahedron, which matches the measured structure.
The counting rule
Count electron domains, then use two domains for sp, three for sp² and four for sp³. Lone pairs count, so the oxygen in water and the nitrogen in ammonia are both sp³ even though neither has four bonded atoms. Orbitals are conserved: mixing three orbitals must produce exactly three hybrids.
Hybridization and electron geometry carry the same information: sp is linear, sp² is trigonal planar, sp³ is tetrahedral.
Leftover p orbitals
An sp² atom keeps one unhybridized p orbital perpendicular to the plane, and an sp atom keeps two. Those leftover p orbitals are exactly what form pi bonds, which is why sp² carbon appears in double bonds and sp carbon in triple bonds.
Link domains to remaining p orbitals
For common second-period centers, two electron domains correspond to sp hybridization, three to sp², and four to sp³. Forming sp leaves two unhybridized p orbitals, which can participate in two π bonds; sp² leaves one. This is a useful local bonding model, not a separate count for each line of a multiple bond.
A triple bond counts as one domain but uses two unhybridized p orbitals for its π bonds.
Key ideas
Rule
Domain to hybridization
2 domains is sp, 3 domains is sp², 4 domains is sp³.
Rule
Orbital conservation
The number of hybrid orbitals formed equals the number of atomic orbitals mixed.
Definition
Hybrid orbital
A blended orbital with mixed s and p character that points along a bonding direction.
Key concept
CO₂ carbon
Two domains means sp hybridization, two leftover p orbitals and a 180 degree bond angle.
Equation
Hybridization index
number of hybrid orbitals = number of electron domains
Equation
Leftover p orbitals
unhybridized p = 3 - (number of p orbitals used)
Worked examples
Worked example 2
Assign the carbon hybridization in H-C≡N and explain its two C-N π bonds.
Try it first: Count directions of electron density around carbon.
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Common mistakes
Ignoring lone pairs when assigning hybridization.
Why it's wrong: Lone pairs occupy hybrid orbitals just as bonds do.
Check instead: Use the same domain count you used for VSEPR.
Counting a double bond as two domains and calling the atom sp³.
Why it's wrong: A double bond is one domain, so a carbon with one double bond and two single bonds is sp².
Check instead: Count attached atoms plus lone pairs.
Saying an sp² atom has no p orbitals left.
Why it's wrong: Only two of the three p orbitals are used in sp² hybridization.
Check instead: Subtract the p orbitals used from three.
After the lesson · Question bank
Independent practice
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What you should now know
Atomic orbitals mix to form an equal number of degenerate hybrid orbitals that point toward the electron domains. Two domains give sp, three give sp² and four give sp³. The number of hybrid orbitals always equals the number of atomic orbitals mixed, which equals the domain count.
- Hybrid orbitals explain the geometries that pure atomic orbitals cannot
- Domain count sets the hybridization: 2 is sp, 3 is sp², 4 is sp³
- Lone pairs occupy hybrid orbitals and must be counted
- Orbitals are conserved when they mix
- Unused p orbitals remain available for pi bonding
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.