What is the specific rotation of the product mixture from an SN1 reaction that produces a racemic mixture?

In an S$_{\text{N}}$1 reaction, the leaving group departs first, forming a planar carbocation intermediate. Because the carbocation is planar, the nucleophile can attack from either face with equal probability.

This leads to the formation of a racemic mixture, which is an equimolar mixture of two enantiomers. Enantiomers rotate plane-polarized light in equal but opposite directions.

Therefore, the specific rotation of the product mixture from an S$_{\text{N}}$1 reaction, if it produces a racemic mixture, is:

$$\text{Zero}$$