H₂ reacts much faster with Cl₂ than D₂ because

The minimum energy required for atoms or molecules to undergo a successful chemical transformation in a reaction is known as activation energy. Hydrogen reacts more rapidly than D₂ with Cl₂ because the activation energy of D₂ is lower than H₂. 

As deuterium slows down the reaction, this property is utilized for understanding the reaction by replacing H₂ with D₂. The slow down of a reaction by substituting D₂ in place of H₂ is known as the deuterium isotope effect