Nitrogen of ammonia has one lone pair while oxygen of water has 2 lone pairs. There is repulsion between lone pair and bond pairs in both the cases. But there is also repulsion between 2 lone pairs in the case of water. This leads to lesser bond angle in water.
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As we know that the valence electron of Nitrogen is 5 and valence electron of Oxygen is 6.
In NH3 , Nitrogen share 3 electron with 3 Hydrogen, leaving behind 2 electron unshared ( 1 lone pair), called Lone pair. Similarly, in H2O , Oxygen share 2 electron with 2 hydrogen, leaving behind 4 electron ( 2 lone pair).
A lone pair takes up more space (according to VSEPR theory) than a bonded hydrogen. NH3 has one pair, H2O has two, so the remaining hydrogens have to squeeze closer together. So, NH3 has greater bond angle than H2O.
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