Answer the quesiton according to this example: The water molecule has an H-O-H b

Question

Answer the quesiton according to this example:

The water molecule has an H-O-H bond angle of 104.5degree. Formulate the hybrid orbital description for the oxygen atom in water, i.e., Derive an expression for the dependence of % s (and p) character on the bond angle theta. Calculate the % contribution of the 2s and 2p atomic orbitals. Mathematically p-orbitals behave like vectors, so we can express the amount of px and py in each hybrid by using simple vector geometry, i.e., h1 = a s + b p1 h1 = a s + b [ cos(theta/2) py + sin(theta/2) px ] h2 = a s +b p2 h2 = a s +b [ cos(theta/2) py - sin(theta/2) px ] h1 = a s + b [cos(theta/2) py + sin(theta/2) px ] h2 = a s + b [ cos(theta/2) py - sin(theta/2) px ] Orthogonality requires h1h2 d tau = 0 = a2 + b2 [cos2 (theta/2) - sin = a2 + b2 cos theta hence cos theta = a2/b2 Normalization of either h., or h2 yields a2 + b2 = 1, hence b2 = 1-a2. Putting 1 and 2 together gives: where a2 =(% s-character) What about the rabbit ears in H2O? How big is phi Given that two O-H bonds have 20 % s-character (see above Table), the two lone pairs must share the remainder, i.e., 30 % each, thus a2 = 0.30 For the lone pairs cos phi = - a2/ (1 - a2) (with a2 = 0.30), and hence phi = 115.5degree phi > theta: Lone pairs are more separated than bond pairs. This is a result of greater electron repulsion between lone pairs than between bond pairs (cf. VSEPR).

Explanation / Answer

According to experimental evidence from microwave spectroscopy, ozone is a bent molecule, with C2v symmetry (similar to the water molecule). The O

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