# Rate determining step for parallel reaction?

I have always read that the rate determining step is the slowest step in a reaction (source: Wikipedia).

In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS) or rate-limiting step.

However on this website (source), it says that the rate determining step for a parallel reaction is the fastest step. I was quite confused about this statement.

For a parallel reaction $$\ce{B <- A -> C}$$, where $$\ce{A -> B}$$ has rate constant $$k_1$$ and $$\ce{A -> C}$$ has rate constant $$k_2$$, the equations (from solving the first-order linear differential equations for A, B, and C, give: $$A = A_oe^{-(k_1+k_2)t}$$, $$B = \frac{k_1*A_o}{k_1+k_2}*(1-e^{-(k_1+k_2)*t})$$, and $$C = \frac{k_2*A_o}{k_1+k_2}*(1-e^{-(k_1+k_2)*t})$$.

But I do not know how to proceed from there.

## 1 Answer

Let's suppose that $$\ce{A -> C}$$ is the fast step in the parallel reaction scheme. This implies that $$k_2 \gg k_1$$. Thus, $$k_1 + k_2 \approx k_2$$, it is therefore (approximately) true to write the rate of consumption of $$\ce{A}$$ as $$A_0 e^{-k_2t}$$. This is what is meant by the fast reaction "controlling" rate for parallel reactions.