# What is the relation between Rate of reaction and rate of consumption of reactants?

The rate of the following reaction is 0.300M/s. What is the relative rate of change of each species in the reaction?$$\ce{A + 3B -> 2C}$$

1. We are supposed to find A and B and I understand that we have to use $\frac{ [\delta]A}{[\delta]t}$ and then use a negative for the coefficient. But what I don't understand is, why for B we had to multiply -3 but not -1/3? And is it the same for A?

2. Also, I am confused on how I can differentiate between using these two equations of rates. The Delta of reactants/delta of time, versus the rate $v(nu)=k[A]m[B]n$ equation.

For your first part you're supposed to multiply it by -3 instead if $\frac{-1}{3}$ as the rate of reaction is given for one mole. That is if $R$ is the rate of reaction it is defined as . $$\frac{-d[A]}{dt} = \frac{-d[B]}{3dt} = \frac{d[C]}{2dt} = R$$ So the rate of consumption of B is $-3R$.