Final answer:
1,3-dibromo-2,4-dichlorocyclobutane is achiral due to its symmetrical 'trans' arrangement, leading to a meso compound with an internal plane of symmetry. Therefore, it has zero chiral centers.
Step-by-step explanation:
The student asked about the number of chiral centers in the compound 1,3-dibromo-2,4-dichlorocyclobutane. A chiral center, or stereocenter, is a carbon atom with four different groups attached to it, allowing for non-superimposable mirror images, or enantiomers. In the compound 1,3-dibromo-2,4-dichlorocyclobutane, each of the four carbon atoms has two different halogens attached, along with two other carbon atoms. When the halogen substituents are arranged such that no two identical substituents are on the same carbon, it has potential chiral centers; however, this compound has a planar structure due to the cyclobutane ring, which can lead to an internal plane of symmetry, negating chirality if the substituents are opposite to each other. Therefore, to determine the presence of chiral centers, we must consider the specific 3D arrangement of the substituents.
Since the compound is given as a 'trans' arrangement (1,3-dibromo and 2,4-dichloro), we have a symmetrical molecule on either side of the cyclobutane plane, leading to a meso compound, which is achiral. Hence, despite having two carbon atoms with four different groups attached, due to the molecule's symmetry, there are no chiral centers. The answer, in this case, is A. 0.