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The reason is that carbon is tetravalent. A normal (straight chain) alkane has a formula of CnH2n+2.
When you make a cycloalkane (one ring only), you will tether two ends of a straight chain to close it into a loop. You have to lose TWO hydrogens in order to “open up” both ends, so that you can close the loop.
So, if you look at the formula for a cycloalkane, it is the formula of a normal alkane, minus two hydrogens. Therefore, the formula of a cycloalkane is CnH2n (i.e. CnH2n+2 minus 2).
When you make an normal (straight chain) alkene [actually, a mono-alkene with only one double bond], you have to create a double bond between two carbon atoms in the chain. In order to do this, you have to lose TWO hydrogen atoms from adjacent carbon atoms, so that the two carbons can then get together and make a double bond. Therefore, the formula for a straight chain mono-alkene is CnH2n (CnH2n+2 minus 2).
This is why cycloalkanes and alkenes have the same formula CnH2n.
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