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Answer:
To determine the rate law for the reaction:
[tex][ \text{CH}_3\text{CH}_2\text{CH}_2\text{CHBrCH}_3 + \text{OH}^- \rightarrow \text{CH}_3\text{CH}_2\text{CH}_2\text{CHOHCH}_3 + \text{Br}^- ][/tex]
we need to understand the mechanism of the reaction and the rate-determining step. This reaction is likely an S_N2 (bimolecular nucleophilic substitution) mechanism because it involves a primary or secondary alkyl halide reacting with a strong nucleophile (OH^-).
In an S_N2 mechanism, the rate of reaction depends on the concentration of both the alkyl halide (RBr) and the nucleophile (OH^-). The rate law for an S_N2 reaction can be expressed as:
[tex][ \text{Rate} = k[\text{RBr}][\text{OH}^-] ][/tex]
where:
Thus, the rate law for the given reaction would be:
[tex][ \text{Rate} = k[\text{CH}_3\text{CH}_2\text{CH}_2\text{CHBrCH}_3][\text{OH}^-] ][/tex]
This rate law indicates that the reaction rate is directly proportional to the concentrations of both the alkyl halide and the hydroxide ion.