Why do some alkenes have geometric (cis-trans) isomers?

Answer 1

Why? Well, simply because they can.

Take a simple olefin, #"2-butene"#. Clearly its formula is #C_4H_8# or #H_3C-CH=CH-CH_3#. Because the double bond extends above and below the plane of the molecule, the pendant methyl groups cannot rotate with respect to each other.
Thus this simple formula generates a pair of geometric isomers, compounds that have identical connectivity (i.e. #C_1# connects #C_2......# to #C_4#, but have different geometry.
Just to illustrate that this does make a difference, the melting point of #"cis-2-butene"# is #-138.9# #""^@C# versus #"trans-2-butene"# is #-105.5# #""^@C#. These are certainly different compounds with different physical and chemical properties even though their formulae are identical.
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Answer 2

Some alkenes have geometric (cis-trans) isomers due to the restricted rotation around the carbon-carbon double bond. This restricted rotation prevents the groups attached to the carbons of the double bond from freely rotating, leading to different spatial arrangements of these groups. Depending on the relative positions of the substituent groups, geometric isomers can form, where the groups are either on the same side of the double bond (cis) or on opposite sides (trans).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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