Let's analyze the given rate law step-by-step to determine the overall order of the reaction.
The rate law expression is:
[tex]\[ R = k \left[(CH_3)_3CBr\right]^1 \left[H_2O\right]^0 \][/tex]
Here, the rate [tex]\( R \)[/tex] is dependent on the concentrations of the reactants [tex]\((CH_3)_3CBr\)[/tex] and water [tex]\( H_2O \)[/tex], each raised to specific exponents which represent the order with respect to each reactant.
1. Identify the exponents:
- The exponent for [tex]\((CH_3)_3CBr\)[/tex] is [tex]\(1\)[/tex].
- The exponent for [tex]\(H_2O\)[/tex] is [tex]\(0\)[/tex].
2. Determine the individual orders:
- The reaction order with respect to [tex]\((CH_3)_3CBr\)[/tex] is [tex]\(1\)[/tex], because the concentration term is raised to the power of [tex]\(1\)[/tex].
- The reaction order with respect to [tex]\(H_2O\)[/tex] is [tex]\(0\)[/tex], because the concentration term is raised to the power of [tex]\(0\)[/tex], which means that changes in the concentration of [tex]\( H_2O\)[/tex] do not affect the rate of the reaction.
3. Calculate the overall order:
- The overall order of the reaction is obtained by summing the individual orders of the reactants.
- Therefore, we add the exponents: [tex]\(1\)[/tex] (from [tex]\((CH_3)_3CBr\)[/tex]) and [tex]\(0\)[/tex] (from [tex]\(H_2O\)[/tex]).
[tex]\[ \text{Overall order} = 1 + 0 = 1 \][/tex]
Thus, the overall order of the reactants in this reaction is [tex]\(1\)[/tex].
