Final answer:
Based on the reaction rates given when concentrations of A and B are changed, the relationship of the rates of disappearance is that A's disappearance is twice as fast as B. Thus, the correct answer is -{4d[A]/dt} = -{d[B]/dt}. option C is correct answer.
Step-by-step explanation:
When considering the reaction rate involving reactants A and B (aA + bB → Products), and the rate of reaction is expressed as dx/dt = k[A]^a[B]^b, we need to use the given information to deduce the orders of the reaction with respect to each reactant and the relationship between their rates of disappearance.
According to the problem, doubling the concentration of A quadruples the rate, indicating that the reaction is second order with respect to A (a = 2). If quadrupling the concentration of B only doubles the rate, the reaction is first order with respect to B (b = 1).
The rate of disappearance of reactants in a balanced chemical equation is related to the stoichiometry of the reaction and the respective orders of the reactants. In this case, since the order with respect to A is 2 and with respect to B is 1, there must be a stoichiometric factor relating the rate of disappearance of A to that of B. Given the orders of reaction, this relationship can help us find the correct option.
Considering the stoichiometry of aA and bB, we can set up a proportionality between the rates of disappearance; -d[A]/dt = a × (-d[B]/dt) or -d[B]/dt = b × (-d[A]/dt). Since 'a' is 2 and 'b' is 1, the disappearance rate of A is twice as fast as that of B. Therefore, option C is correct: -{4d[A]/dt} = -{d[B]/dt}.