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If you have a molecular model kit, or a computer simulation that plays a similar role, use it to build both molecules. You discover that neither (2) nor (4) is entirely planar: (4) is not planar because the internal methylene group is out of plane (the only way to get realistic bond angles at the central carbon), and you find (2) is not planar because of ...


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As Ivan Neretin pointed out in the comments, $\pi$ bonds will remain same whether or not in resonance. However, if you have trouble counting the double bond equvalent, you can directly use the formula for it given as $$\ce{DU=\dfrac{2C+2-H+N-X}{2}}$$ so here number of carbons are C=23, H=21, N=1 which also gives 14 as the answer.


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