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How does an internal plane of symmetry make a meso compound achiral?

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Two diagrams show the three-dimensional structure of a methane molecule: panel A uses a ball-and-stick model with a central carbon atom connected to four hydrogen atoms in a tetrahedral arrangement, while panel B illustrates the bond angle of 109.5 degrees and bond length of 1.09 angstroms between carbon and hydrogen atoms. — isomerism Tetrahedral geometry of methane: (A) stick-and-ball model and (B) diagram showing bond angles and distances. (Plain bonds represent bonds in the plane of the image; wedge and dashed bonds represent those directed toward and away from the viewer, respectively.)

A meso compound is an achiral molecule that contains stereogenic atoms but remains achiral due to its internal symmetry.

The presence of an internal plane of symmetry means that the molecule can be divided into two halves that are mirror images of each other. Because of this structural arrangement, the molecule is superimposable on its own mirror image. In chemistry, chirality is defined by the lack of superimposability between a molecule and its mirror image; therefore, when a molecule possesses an internal plane of symmetry, it cannot be chiral, regardless of whether it contains individual stereogenic atoms.

For example, in 2,3-dichlorobutane, the internal plane of symmetry causes the SR combination to be identical to its mirror image, resulting in an achiral meso compound rather than a pair of enantiomers.12