How to determine bond angles?

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how to determine bond angles?

Surfed all over the internet and couldn’t find a reasonable method to determine bond angles in chemical molecules? Well, you have reached the right spot because in this article we have tried to address all your questions regarding bond angles in covalently bonded molecules.

So, without any further delay, let’s start reading.

What is a bond angle?

A bond angle is simply defined as the geometric angle formed between two adjacent covalent bonds that share a common atom at the center.

According to the Valence Shell Electron Pair Repulsion (VSEPR) theory of chemical bonding, covalently bonded molecules consist of two different types of electron pairs i.e., a bond pair and a lone pair of electrons.

The electron pairs stay furthest away from each other to minimize their repulsive effect. This controls the shape of the molecule which in turn controls the bond angles present in this molecule.

what is bond angle

So, now we know that the bond angle in a molecule can be determined using the VSEPR theory. Let’s see how.

What is the VSEPR theory?

The Lewis structure is a very useful way of representing the structure of covalently bonded molecules. However, it does not give any information about the geometry and shape of a molecule. This information can be obtained from the VSEPR theory.

Also check –

A molecule consists of two different geometries i.e., an electronic geometry and a molecular geometry. The electronic geometry represents the 3-dimensional structure of the molecule. It depends on the total number of electron pairs present around the central atom in the molecule.

The molecular geometry on the other hand determines the shape of the molecule. It takes into account the different numbers of bond pairs and lone pairs around the central atom. Bond angles help molecules maintain their specific shapes and molecular geometries.

The VSEPR notation uses an alphabet A to represent the central atom to which other atoms X are covalently bonded while E denotes a lone pair present on the central atom.

axe method to find bond angle

Determining bond angles using VSEPR theory (AXE method)       

Linear geometry

If the central atom (A) in a molecule is bonded to two other atoms (X) and there is no lone pair (E) present on it then the molecule occupies a linear geometry and shape.

It is represented by the VSEPR notation AX2. The central atom is sp hybridized. Its linear shape signifies that all the bonded atoms lie on a straight line thus they form a mutual bond angle of 180°.

how to find bond angle of linear geometry

Trigonal planar geometry

If the central atom (A) is bonded to three other atoms (X) and there is no lone pair on the central atom, then the molecule occupies a trigonal planar geometry and shape.

The VSEPR notation for this molecule is AX3.  The central atom is sp2 hybridized. Three X around the central A atom form an equilateral triangle. A complete circle is made up of 360°, when it is divided into three equal parts (360/3 = 120) then each A-X  bond angle in a trigonal planar shape has a 120° bond angle.

how to determine bond angle in trigonal planar geometry

In AX2E type molecules, one of the three bonded atoms in the trigonal planar molecule gets replaced by a lone pair of electrons (E). This leads to lone-pair bond-pair repulsions which in turn decreases the X-A-X bond angle. The lone-pair bond-pair repulsions are significantly greater than bond-pair bond-pair repulsions.

Thus, although the molecule has a trigonal planar electronic geometry, but its molecular geometry changes and it occupies a bent shape to minimize the repulsive effect.

The bond angle decreases from the ideal 120° to approximately 119 or 118°.

bond angle in AX2E VSEPR model

As a general rule of thumb, for each X replaced by a lone pair (E), the bond angle gets reduced by 2°. So, you need to subtract 2° from the ideal bond angle to obtain the bond angle for a specific shape.

Tetrahedral geometry

 AX4-type molecules have a tetrahedral geometry and shape. Four atoms (X) are bonded to the central atom (A) like the four vertices of a tetrahedron. The central atom is sp3 hybridized. It has an X-A-X bond angle of 109.5°.

how to determine bond angle in tetrahedral geometryYou should also note that a greater p character in the hybrid orbitals is another factor contributing to a reduced bond angle.

 Bond angle decreases in the order : linear (sp)> trigonal planar (sp2) > tetrahedral (sp3).

If one X atom gets replaced by a lone pair (E), it forms AX3E-type molecules. The lone pair is placed at the apex of the molecule to minimize lone-pair bond-pair repulsions.

The X-A-X bond angle decreases (109.5°- 2° = 107.5° ). The molecule occupies a trigonal pyramidal shape and molecular geometry. It has a triangular base and a pyramid at the top of it.

bond angle in AX3E vsepr modelIf two X atoms get replaced by two lone pairs, AX2E2-type molecules are formed. The repulsive effect is further increased as lone-pair lone-pair repulsions > lone-pair bond-pair repulsions > bond-pair bond-pair repulsions.

To accommodate the strong electronic repulsions, both the lone pairs are placed as far apart from each other as possible. Thus, the molecule occupies a bent shape, and the X-A-X bond angle decreases further to 104.5°.

  bond angle in AX2E2 VSEPR model

Trigonal bipyramidal geometry

AX5-type molecules have a trigonal bipyramidal electronic geometry. The central atom is sp3d hybridized. The central atom (A) is surrounded by five X atoms on the sides. It forms a triangular base and two pyramids above and below the triangle.

The bonded atoms form three different bond angles i.e., 120° at the triangular base, 180° along the X-A-X straight line, and 90° where the X-A atoms lie at a right angle to each other.

how to find bond angle in trigonal bipyramidal geometryIn the trigonal bipyramidal geometry, the two axial X atoms are held fixed while equatorial X atoms can be removed and replaced with lone pairs. One X atom replaced by an E forms an AX4E-type molecule. Such molecules occupy an irregular seesaw shape to minimize their electronic repulsions.

So, they do not really have definite bond angle values. Different types of bond angles can be present at different positions in the seesaw shape. The bond angles are usually > 90° and <180°.

bond angle in seesaw shape

Two equatorial X replaced with E in AX3E2-type molecules makes the molecule occupy a T-shape with a bond angle < 180° while all three equatorial X replaced by lone pairs forms linear AX2E3-type molecules with a bond angle =180°.

bond angle in ax3e2 VSEPR model

bond angle in ax2e3 vsepr model                                                                                                                               

Octahedral geometry

AX6-type molecules possess an octahedral electronic geometry and shape. The central atom is sp3d2 hybridized. The six X atoms lie around the central A atom in an eight vertices arrangement i.e., an octahedron.

It forms two different bond angles i.e.,  180° at the center while the peripheral X-A-X atoms lie at right angles (90°) to each other.

bond angle in octahedral geometryThe four X atoms forming a square base are held fixed while the atom at the top and bottom of the octahedron can be removed and replaced with lone pairs. The top X atom removed and replaced with a lone pair (AX5E) lends the molecule a square pyramidal shape and geometry.

The X-A-X bond forms a 90° bond angle at the square base while the bond angles at other positions on the molecule are < 90°.

how to find bond angle in square pyramidal shape

Both the top and bottom X atoms replaced with lone pairs make the molecule occupy a square planar shape and a 90° bond angle. The lone pairs are placed opposite each other to minimize their repulsive effect.

how to find bond angle in square planar shape

What factors affect bond angles?

Overall, we have identified four main factors that affect the bond angles present in a molecule namely:

  • Molecular geometry or shape.
  • Lone-pair lone-pair and lone-pair bond-pair repulsions are present in the molecule.
  • Hybridization of the central atom. The bond angle decreases as the p character increases.
  • Electronegativity of the central atom. The bond angle decreases by decreasing the electronegativity of the central atom.

Chart of bond angles

The bond angles chart will help you in determining the ideal bond angles for different molecules having varying shapes/molecular geometries according to the VSEPR concept.

bond angle chart

Also check – AXE notation in details

FAQ

What is the Bond angle?

A bond angle is simply defined as the geometric angle formed between two adjacent covalent bonds that share a common atom at the center.

How can you find the bond angle?

The bond angle can easily find by using the VSEPR theory –

  • Write the Lewis dot structure for the molecule.
  • Use the steric number and VSEPR theory to determine the electron domain geometry of the molecule.
  • Use the VSEPR shape to determine the angles between the electron domains.

Check also-

What is the molecular geometry and bond angle of the water (H2O)?

According to the VSEPR theory, H2O is an AX2E2-type molecule. The central oxygen (O) atom belongs to Group VI A of the Periodic Table. It has a total of 6 valence electrons.

2 bond pairs and 2 lone pairs around oxygen make the H2O molecule occupy a bent molecular geometry and shape with a bond angle of 104.5°.

Why is the bond angle of H2S less than that of H2O although both have bent shapes?

Both H2S and H2O are AX2E2-type molecules with 2 bond pairs and 2 lone pairs around the central atom. Both molecules have a bent molecular shape and geometry.

The H-O-H bond angle in H2O is 104.5° while the H-S-H bond angle in H2S is 92.1° because the sulfur (S) atom is less electronegative as compared to oxygen.

The bond-pair bond-pair repulsions between H-S bonds are reduced so bonds come closer, consequently, the bond angle decreases.

factor affecting bond angle

Why is the bond angle in NF3 less than that in NH3?

The bond angle in NF3 is 101.9° while that in NH3 is 107.5° although both have a trigonal pyramidal shape with 3 bond pairs and 1 lone pair around the central nitrogen (N) atom.

This is because the F atoms in NF3 are highly electronegative.

The bonded electron pairs are furthest away from the central N atom in NF3. Consequently, there is less distortion present in the molecule.

The bond-pair bond-pair repulsions between N-F atoms decrease which leads to a reduced bond angle.

Why do bond angles in CH4, NH3, and H2O differ?

The bond angles in these four molecules differ based on their different molecular geometries/shapes.

CH4 has an ideal tetrahedral electronic geometry. There are 4 bond pairs and no lone pair around the central carbon atom. The H atoms arrange symmetrically around the central atom and form a mutual bond angle of 109.5°.

The ideal tetrahedral geometry gets distorted when a bond pair is replaced by a lone pair as in NH3, so it occupies a trigonal pyramidal geometry with a bond angle of 107.5°.

Two bond pairs replaced by lone pairs further distort the shape. Lone-pair lone-pair repulsions exist which makes H2O occupy a bent shape and molecular geometry with a bond angle of 104.5°.

 Short tricks for bond angle comparison between different molecules?

The bond angle is:

  • inversely proportional to lone pairs on central atoms.
  • inversely proportional to the p-character in the hybridization of the central atom.
  • directly proportional to the size of atoms surrounding the central atom.
  • directly proportional to the electronegativity of the central atom.

Summary

  • A bond angle is the geometric angle between two adjacent bonds joined to a mutual atom at the center.
  • Bond angles contribute to the overall shape of the molecule.
  • A molecule may have a different molecular geometry or shape from its ideal electronic geometry as per VSEPR theory.
  • The molecule occupies a shape that demonstrates minimum repulsive effect between its different electronic regions.
  • An ideal bond angle is the maximum angle at which the electronic repulsions are minimized.
  • The bond angles help differentiate between linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral electronic and molecular geometries.
  • Greater the distortion present in a molecule, the lower the bond angle between its covalently bonded atoms.

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Welcome to Topblogtenz, My name is Vishal Goyal. I am an engineer, chemistry tutor, blogger, and founder of topblogtenz.com. I'm a science geek with a passion for life sciences and chemistry. Being a chemistry tutor and having a degree in Engineering, I know how hard it is to learn by yourself, that is why I created a site where you can find help related to science and chemistry before everyone else.

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