Which of the following molecules is expected to rotate the plane of plane polarized light?

Optical activity is shown only by chiral molecules, i.e. molecules whose mirror images are non-superimposable. In ordinary organic compounds chirality normally arises when an $$sp^{3}$$ carbon (called a stereogenic or chiral centre) is bonded to four different substituents. A molecule that contains such a carbon and possesses no element of internal symmetry will exist as a pair of enantiomers and will rotate the plane of plane-polarised light.

Option A : 2-chlorobutane, $$CH_3-CH(Cl)-CH_2-CH_3$$
The second carbon is $$sp^{3}$$ and is attached to four different groups:
  • $$CH_3-$$ (methyl)
  • $$Cl-$$ (chlorine)
  • $$CH_2CH_3-$$ (ethyl)
  • $$H-$$ (hydrogen)
Because all four substituents differ, this carbon is a true chiral centre. The molecule has no plane of symmetry, so the two mirror-image forms are non-superimposable enantiomers. Hence 2-chlorobutane is optically active and will rotate plane-polarised light.

Option B : 1-chlorobutane, $$CH_3-CH_2-CH_2-CH_2Cl$$
Every carbon is either $$sp^{3}$$ with two identical hydrogens or is attached to two identical groups (e.g. the terminal $$CH_3$$ group). No carbon bears four different substituents, so the molecule is achiral and optically inactive.

Option C : meso-2,3-dichlorobutane, $$CH_3-CH(Cl)-CH(Cl)-CH_3$$ (meso form)
Each of C-2 and C-3 is attached to four different groups and is individually chiral; however, the molecule possesses an internal plane of symmetry that relates the two centres. The optical rotations of the two halves cancel internally, so the meso form is achiral and does not rotate plane-polarised light.

Option D : trans-1,2-dichloroethene, $$ClCH=CHCl$$ (trans)
The carbon-carbon double bond makes each carbon $$sp^{2}$$ hybridised (trigonal planar). An $$sp^{2}$$ carbon cannot be a chiral centre, and the molecule has a plane of symmetry passing through the double bond. Therefore it is achiral and optically inactive.

Among the four choices, only Option A (2-chlorobutane) lacks any element of symmetry and contains a stereogenic carbon with four different substituents. It is therefore the only compound expected to rotate the plane of plane-polarised light.

Hence, the correct answer is:
Option A which is: 2-chlorobutane.