The reaction depends ONLY on the concentration of the alcohol, which is why we would call this reaction unimolecular (SN1)
Is that the answer to this question?
Almost. It is not quite an experiment yet. Let me ask you a question. If you double the concentration of R-X, does the rate double for the S
N1 case? For the S
N2 case?
If you write the two rate equations side-by-side or on two adjacent lines of text, you will see one difference between them that suggests a second experiment. Two final points. One I interpreted the initial question to be, "How do you discriminate (decide) between the possibility that the reaction proceeds by the S
N1 versus the S
N2 mechanism" A related question is "Does this particular set of conditions favor one mechanism over the other" I would answer the two questions differently. Two, I think it is better to say that the nucleophile is bromide ion, Br
1-, than to say it is bromine.