Question

How would we identify `Bu^(t)CO_2H` by its IR spectrum?

Answer 1

You have probably got `D`.

Explanation:

Now I cannot even see the scale of your IR spectrum, but there is a VERY broad peak around about `3000*cm^-1`, which is consistent with the presence of `-O-H` bonds. Further, there is (I think) a strong peak at `1650-1750*cm^-1` that is probably due to `C=O`.

So `C` and `B` are non-starters, and the choice is between `A` and `D`. Because `A` is an alcohol, and DOES not possess a carbonyl, this choice is contraindicated, and we choose `D`.

IR spectroscopy is a very poor discriminant of organic structure. If you really want to identify the stuff as `Bu^tC(=O)OH` you would have to make a few derivatives and take melting points.