# Reaction rate coefficient constant multiplier for equation with multiple atoms consumed?

For the elementary reaction $$\ce{2O -> O2}$$, when calculating the rate of concentration change of atomic oxygen as $$\frac{d[O]}{dt}$$, would I use the standard rate coefficient $$k_f$$ or would I have to multiply by 2 since 2 oxygen molecules are being consumed?

$$\ce{O + O -> O2}$$ with $$\frac{d[O]}{dt} = -2 \cdot k_f \cdot [O] \cdot [O]$$

or

$$\ce{O + O -> O2}$$ with $$\frac{d[O]}{dt} = -k_f \cdot [O] \cdot [O]$$

Or would the rate constant define the dependency on atomic oxygen?

• Given that equation, the rate is for production of $\ce{O2}$. So you do need to factor for the stoichiometry of $\ce{O}$ relative to $\ce{O2}$. – Zhe Oct 16 '18 at 17:43

In general if the reaction is $$\ce{aA + bB \to cC +dD}$$ the the rate is written as $$r=\displaystyle -\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}$$.
$$\ce{\frac{d[O]}{dt} = - k \cdot [O]^2}=2 \cdot{\ce{\frac{d[O2]}{dt}}}$$