J.R. S. answered 09/16/20
Ph.D. University Professor with 10+ years Tutoring Experience
The rate of change for [B] will depend on the order of the reaction with respect to [B], and unless this is an elementary step, the order cannot be determined from the equation.
Rate = k[A]m[B]n where k is the rate constant and m and n are the order with respect to A and B, respectively.
This hold for initial rates.
Now, since the question asks for the MAGNITUDE of the rate of change for [B], we can approach the problem as follows:
-dA/dt = -1/2 dB/dt = 1//3 dC/dt = dD/dt
so -1/2 dB/dt = 1/3 dC/dt
1/2 dB/dt = 1/3 x 4.6 M/s = 1.53
dB/dt = 3.1 M/s