# 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.

## 1 Answer

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 $-3R$.

As for your second part it's a tad unclear for me if you could further edit your question.I could take a shot at answering your second part as well

• Thank you very much! I have another question. I hope you can answer it please. How did you find that the rate of the reaction is given for one mole? For the second question I meant that are we treating [A] the same way we are treating the coefficient of [B]? – WEA Feb 1 '18 at 4:08
• @WEA I didn't find out that the rate of reaction is for one mole. It is defined like that only. Also we are not treating the rate of consumption of [A] the same as that of [B]. There rate of consumption of B is thrice of that of A. – Avnish Kabaj Feb 1 '18 at 4:31
• Your help was very helpful and clear. I have one more question if you don't mind. So if the coefficient of A is always one does it mean that we have to multiply by the original coefficient with a negative sign? – WEA Feb 1 '18 at 4:46
• If the reaction is balanced, then yes. In general Reactants are multiplied with a negative sign to show that they are being consumed in the reaction i.e their concentration is decreasing with the passage of time. – Avnish Kabaj Feb 1 '18 at 4:54