a pure compound is put in a polarimeter and the optical activity is measured to be 0 º. what do you know about the compound?

I may not be optically active.

If it is optically active, the sample is a racemic mixture.

You have not stated the wavelength. It is quite possible that the compound is optically active but the rotation is zero at the wavelength used. Google 'optical rotatory dispersion'.

As DrBob says the compound may not be optically active, but don't assume that it does not have any chiral centres. For an example of a compound with zero optical rotation and two chiral centres google 'mesotartaric acid'.

The question assumes that the compound is a liquid?

In a polarimeter, the optical activity measures the ability of a substance to rotate the plane of polarized light. If the optical activity is measured to be 0º, it indicates that the compound is optically inactive or has no effect on the polarization of light passing through it. This suggests that the compound is either achiral (lacks chirality) or exists in a racemic mixture.

To determine more about the compound, you could perform additional tests. One important test is to check if the compound is chiral or achiral.

To determine chirality, you can look for the presence of chiral centers or asymmetric carbon atoms in the compound's molecular structure. If the compound contains an internal plane of symmetry or has a center of symmetry, it will be achiral.

Another test that could be conducted is a racemization experiment. A racemic mixture contains equal amounts of two enantiomers (mirror image isomers) that rotate polarized light in opposite directions. By subjecting the compound to racemization conditions, such as heating in the presence of a catalytic agent, if it forms an equal mixture of both enantiomers (racemization), it confirms that the compound is optically inactive.

Overall, to fully understand the compound and its optical activity, additional structural and chemical information is required.