Could the mechanism for the reaction of crystal violet with sodium hydroxide consist of one elementary step? Explain.

Yes

Explanation:

Let's write the reaction as

CV⁺ + OH⁻ ⟶ CVOH

The reaction is first order in [CV⁺] and in [OH⁻], so the rate law is

rate = k[CV⁺][OH⁻]

A bimolecular collision between a crystal violet ion and a hydroxide ion as an elementary step would predict the observed rate law.

However, other plausible mechanisms may predict the same rate law.