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# Linear Geometry

The lewis structure can be drawn only in two dimensions. The shapes of very few molecules can be adequately represented using two dimensions and hence it is necessary to look beyond the lewis structure to provide an idea of the shapes of molecules.

The valence shell electron pair repulsion model helps us in this regard. According to this model the valence electrons which are represented in a lewis dot structure are the main instrument to predict the geometry of molecule. The valence shell electrons repel each other and this repulsion leads to various geometries. These geometries are arrived at only after the repulsion in between the electrons are found to have minimum effect or geometries which are considered the most stable. The geometry shows the electrons around a central atom are as far away from each other as possible but at the same time maintain the association with the central atom.

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## Linear Geometry Definition

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For any molecular geometry it is not necessary to have only one central atom and more than one atom may be considered as central atom, but in case of linear form the presence of only one central atom is evident as the repulsion in between the electrons create a perfect geometry on either side of the central atom.
• The differing balloons of identical attached to a central point and if each of the balloons have identical electrostatic charges they repel each other.
• The inter repulsion between the electrons gives a final geometry with the balloons adopting either of the following.
• If the balloons are 180$^{\circ}$ apart then we get to see a linear geometry while the balloons apart by 120$^{\circ}$ shows a triangular planar geometry.
• The difference between the respective four balloons showing 109.5$^{\circ}$ apart define a tetrahedral geometry.
• When we compare the molecular geometry in H2O or BeH2 we can see that both molecules have a B-A-B connectivity and access to same valence orbitals.
In case of $BeH_{2}$ only four valence electrons are available and this results in filling of orbitals 1 and 2. In case of water molecule, $H_{2}O$, it has eight electrons which helps in filling in orbital 1 and 4 for ground state electron configuration. The orbitals 1 and 3 are most stable in a bent geometry and orbital 2 showing the most stable form in a linear geometry.

We observe that the molecule will be bent at an angle that results from a balance of the destabilisation of orbital 2 as compared to the stabilisation of orbitals 1 and 3. The presence of a single electron in orbital 3 causes the most stable bent geometry of the molecule whereas the occupation of orbital 4 by electrons has little or no effect on the geometry as this orbital does not contribute to bonding and the energy depends only to a small extent on angle. The regions of high electron density can be defined by looking at the lewis dot structure and these are either bonds to another atom (single, double or triple) or unshared pairs of electrons. The geometry that we get to see when these regions of high electron density are as far as possible is called electron pair geometry.

When all the regions of high density are bonds then the electron pair geometry is exactly same as molecular geometry. One of the strengths of valence shell electron pair repulsion theory is that it can predict correctly the molecular geometries of small molecules but even molecular orbital theory is also capable of predicting the same.

## Linear Geometry Examples

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The best examples for linear form of molecular geometry are Beryllium hydride BeH2, Carbon di oxide CO2, Hydrogen cyanide HCN, Acetylene C2H2.

Carbon di oxide:
In its ground state CO2 is linear and non-polar in nature. Although it contains two polar C-O bonds the direction of polarity is associated with the separation of charge in the C-O bonds and equal in intensity as well as opposite in direction.

CO2 maintains all the characteristics of a species containing polar bonds with sites on either side of central atom that behave quite differently. The carbon atom is electrophilic while the oxygen atoms are nucleophilic.

Any distortion of the molecule from linearity cause variation of the molecular energy and C-O bond length, due to the repulsion force activity gathered around among the electrons. The energy involved in the molecular orbitals changes as per the plane along which the molecules display the bending.

Any type of molecular excitation or interaction with electron donors that causes the crowding of lowest unoccupied molecular orbital will cause distortion of CO2 linear form.

Hydrogen cyanide:
In this molecule the central atom is carbon with no lone pair electrons. The carbon and nitrogen are bonded with triple bond while on other side the bond with hydrogen is single bond and hence these both are considered as bonded pairs. With the presence of two electron pairs the shape is considered as linear.

Beryllium hydride:
At normal temperature and pressure BeH2 uses its empty valence orbitals to form a larger molecular aggregates and hydrogen atoms share electrons with the next adjacent ‘Be’ atoms in bridge bonds.

## Linear Geometry Bond Angle

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Molecular geometry describes the shape of a molecule and the arrangement of atoms around a central atom. The bond angle is the angle between two bonds formed by the same central atom. When all the electron pairs around a central atom are bonding pairs, with no lone pairs, the bond angles are the same as the electron pair angles.

The molecular geometries are the same as the electron pair geometry which helps in describing the shapes of the molecules. The molecular geometry is very simple for linear shape. There are two bonding pairs in all; one between carbon and hydrogen on one side while the second bonding pair is between carbon and nitrogen. The number of electron groups in linear molecular geometry is 2. The angle of linear molecular geometry is 180 degree.

In some cases we get to see partial linear geometry. In molecules involving Boron, the borates have stable monomeric molecule in vapour phase at a very high temperature with a linear AX2 geometry at Boron. The two BO bonds have length of 131 pm which basically consist of MO-B=O. In case of metaboric acid, HOBO, we get to a similar structure. The same linear –B= geometry is found in the oxides as well as sulphides which overall has a V shape in gaseous phase.

Molecules like Chloro (oxo) boron, Chloro (sulphido) boron, and thioborine are also linear. ## Non-Linear Geometry

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The non-linear molecular geometry is nothing but the description given for bent form. If the molecular shape is not linear then they are clubbed under non-linear form.

Comparative chart:

 No. of electrons Hybridisation Electron domain geometry VSEPR lone pairs Molecular geometry Example Bond Angles Polarity 4 sp$^3$ Tetrahedral Two unshared pairs Bent $H_{2}O$ Greater than 90$^{\circ}$ Polar 3 sp$^2$ Trigonal planar One unshared pair Bent $NO_{2}$ Greater than 90$^{\circ}$ Polar 2 sp Linear No unshared pair Linear $CO_{2}$, $HN$ 180$^{\circ}$ Non - Polar

The salient features of non-linear molecules and their determining factors:
• Number of hybrid orbitals determines the number of electron domains around a central atom, which determines the electron domain geometry and molecular geometry
• The electron domain geometry and molecular geometry may or may not be same and this depends upon the presence of unshared electron pairs
• An unshared electron pair is counted as one electron domain
• The unshared electron pair is very important in determining the molecular geometry
• Water molecule has a bent or non-linear molecular geometry and the bond angle close to tetrahedral angle 109.5$^{\circ}$
• The number of electron domains around an atom equals the sum of the super scripts in hybridisation state
• A polar covalent bond containing molecule need not be polar and it’s the geometry which decides the polarisation
• Molecular geometry does not decide the polar character of bent or non-linear form and hence not all polar bond containing molecules are polar in nature.
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