We're being asked to determine the rate law of the reaction.
A + B → C
Recall that the rate law only focuses on the reactant concentrations and has a general form of:
k = rate constant
A & B = reactants
x & y = reactant orders
To calculate the order of the reaction with respect to each reactant, we will use the experimental data given:
For the reaction A + B -> C at a fixed concentration of A and [B] at the start is 0.10 M, the initial rate was measured. Another reaction was done at the same [A] but [B] was 0.20 M. The initial rate went up 4-fold. The rate law for this reaction is
A. rate = k
B. rate = k[B]
C. rate = k[B]2
D. rate = k[B]3
E. cannot determine
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