Question

Why does 2-butene exists as a pair of cis-trans isomers and 2-hydroxybutanoic acid exists as a pair of optical isomers?

Answer 1

Why? Because geometric isomerism is the inevitable outcome of a 4 carbon structure with an internal double bond, and optical isomerism is the result of a carbon with 4 different substituents.

Explanation:

We have the symmetric olefin, 2-butene. Note that in terms of connectivity we can generate 2 isomers from a structure where methyl `C1` is joined to unsaturated `C2` is joined to unsaturated `C3` is joined to `C4`. That is for the given structure `H_3C(H)C=CHCH_3`, a specific CONNECTIVITY with respect to carbon, two geometric isomers can be generated: cis and trans 2-butene. Here connectivity is the same in each isomer but the spatial geometry is different.

Connectivity is identical for both antipodes (sorry, using that word makes me feel scientific!) of 2-hydroxybutanoic acid. Nevertheless the optical isomers are non-superposable as `C2` is a chiral centre that generates 2 optical isomers. Connectivity is the same, but chirality, handedness, about `C2` MAY be different.

I would try to get a model set out and establish this isomerism for yourself. I would also practise representing this isomerism on the printed page.