Question

Which of the following species has tetrahedral geometry?
(A)- $B{{H}_{4}}^{-}$
(B)- $N{{H}_{2}}^{-}$
(C)- $C{{O}_{3}}^{2-}$
(D)- ${{H}_{3}}{{O}^{+}}$

Answer 1

A model which is used to predict the geometry of chemical molecules from the number of electron pairs surrounding their central atoms is known as Valence shell electron pair repulsion theory (abbreviated as VSEPR theory).

Complete answer:
-The theory of VSEPR theory is that the valence electron pairs surrounding an atom tend to repel each other and arrange in a way that they minimize the repulsion, which in turn decreases the molecule’s energy and increases its stability and hence determines the molecular geometry.
-VSEPR theory is based on observable electron density rather than depending on mathematical wave function and hence unrelated to orbital hybridization, although both address the molecular shape.
-Following are the postulates of VSEPR theory-
(i) In polyatomic molecules, one atom among constituents is identified as a central atom which has all other atoms linked to it.
(ii) The shape of the molecule is decided by the total number of valence shell electron pairs.
(iii) The electron pairs tend to arrange themselves in a way that they minimize the electron-electron repulsion between them by maximizing the distance between them.
(iv) The valence shell can be considered as a sphere in which the electron pairs are localized on the surface in such a way that the distance is maximized.
(v) If the centre is surrounded by lone pairs and electrons both, then the asymmetrically shaped molecule can be expected.
(vi) The presence of lone pairs and bond pairs both can tend to make a distorted shape of the molecule.
(vii) The VSEPR theory can be applied to each of the resonance structures formed of the molecule.
(viii) The strength of the bond is strongest in two lone pairs and weakest in two bond pairs.
(ix) If the electron pairs around the central atoms are much closer to each other, they will repel each other which in turn increases the energy of the molecules.
(x) If the electron pairs around the central atoms are far from each other, they will have the least repulsion between them which will eventually decrease the energy of the molecules.
-Following the above concepts for predicting the shapes of molecules, we will follow the following steps to decide the shape of the molecule-
(i) The least electronegative atom is selected as the central atom since it has the highest ability to share its electrons with the other atoms belonging to the molecule.
(ii) The total number of electrons belonging to the outermost shell of central must be counted for calculation.
(iii) The total number of electrons belonging to other atoms which are used to bond with the central atom must be counted.
(iv) These two values must be added to obtain the electron pair number or the VSEP number.
-The VSEP number is the number obtained after calculation which determines the shape of the molecules. Total number of electron pairs around the central atom$=\dfrac{1}{2}\left( \text{Number of valence electrons of central atom + Number of atoms linked to central atom by single bonds} \right)$. For negative ions, add the number of electrons equal to the units of negative charge on the ions to the valence electrons of the central atom and for positive ions, subtract the number of electrons equal to the units of positive charge on the ion from the valence electrons of the central atom.
-The number of bond pairs is equal to the total number of atoms linked to the central atom by single bonds.
-The number of lone pairs is equal to the total number of electrons subtracted by the number of shared pairs.
-The VSEP number describes the number of the molecule according to the as the described table-

VSEP Number	The shape of the molecule
2	Linear
3	Trigonal planar
4	Tetrahedral
5	Trigonal bipyramidal
6	Octahedral
7	Tetragonal bipyramidal

-Let us now calculate the VSEP number for the compounds given to us in option.
-In option A, tetrafluoroborate ($B{{H}_{4}}^{-}$) has a boron atom as a central atom with 3 electrons on its outermost shell. While fluorine atoms have 7 non paired electrons with a net charge as -1, hence an extra electron is combined.
VSEPR $\begin{aligned} & =\dfrac{[3+1+(1\times 4)}{2}=4 \\\ & \Rightarrow Tetrahedral \\\ \end{aligned}$
-In option B, $N{{H}_{2}}^{-}$ the VSEP number is 4, hence the geometry should be tetragonal. But the nitrogen has two lone pairs which distort the geometry and makes the molecule of bent shape.
-In option C, carbonate ($C{{O}_{3}}^{2-}$) molecule has 3 electron pairs hence trigonal planar geometry.
-In option D, hydronium ion (${{H}_{3}}{{O}^{+}}$) has three bond pairs and one lone pair, therefore the geometry is tetrahedral.

Therefore, the correct answers are options A and D.

Note: VSEPR theory does have some limitations which are-
(i) VSEPR model is not a theory as it does not explain or attempt to explain any observation or predictions; rather it is an algorithm that accurately predicts the structures of a large number of compounds.
(ii) The VSEPR model does not work for all chemical species.
(iii) The idealized bond angle does not always match the measured bond angle values.
(iv) VSEPR model also predicts that group 2 halides will form linear structure although they have bent shape in reality.