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Question

Why is there no charge on carbene, even though the carbon atom has a lone pair?

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Solution

lone pair does n't imply it has a charge,
For example ,Consider a single C atom ,it has 2 lone pairs(Z=6).Does it mean carbon should have charge?No,
Now I will tell you why Carbene is neutral
According to the electronic theory of bonding, bonds between atoms are formed by a sharing of electrons. In terms of this theory, then, a carbene is a compound in which only two of the four valence, or bonding, electrons of a carbon atom are actually engaged in bonding with other atoms. By contrast, in multiple bonded compounds, such as hydrogen cyanide, all four of the valence electrons of the atoms are involved in bonds with other atoms. Because there is no excess or deficiency of electrons in the molecules of carbenes, they are electrically neutral (nonionic).

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