# Rate and order of a reaction

The rate of reaction can be measured from a concentration vs time graph of a particular reactant in a reaction.

But, if in your reaction you have different reactants of different orders surely they will each give a different concentration vs time graph and so different rate at any time t. This implies that the rate of reaction can have multiple values depending on which reactant you follow.

The rate of reaction is defined in IUPAC's Gold Book as:

$$r = - \frac{1}{a} \frac{\mathrm d[\ce{A}]}{\mathrm dt} = - \frac{1}{b} \frac{\mathrm d[\ce{B}]}{\mathrm dt} = \frac{1}{p} \frac{\mathrm d[\ce{P}]}{\mathrm dt} = \frac{1}{q} \frac{\mathrm d[\ce{Q}]}{\mathrm dt}$$

where $[\ce{X}]$ denotes the concentration of the substance $\ce{X}$, and the lower case letters represent the coefficients of those substances in the balanced equation. The rates for $\ce{P}$ and $\ce{Q}$ are positive, as these are products in the reaction.

You are right in that you can determine the reaction rate by studying the change in concentration of a particular reactant (or product) over time. But, to determine the rate r for the reaction, not just for a particular species, you must take into consideration the coefficients in the balanced equation. The stoichiometric numbers are included in the definition of the rate, $r$, so that it is independent of which reaction species you study. For example if $a = 1$ and $b = 3$ then $\ce{B}$ is consumed three times more rapidly than $\ce{A}$, but $r = -\mathrm d[\ce{A}]/\mathrm dt = -(1/3)\mathrm d[\ce{B}]/\mathrm dt$ is uniquely defined.

If I understand your question correctly, you are asking about a reaction that requires multiple steps to reach completion?

Eg. In a reaction such as Compound A --> Compound B; there are intermediates formed first?

In reactions like these, the overall reaction-rate is determined by which ever step takes the most amount of time to complete - the rate determining step. This is because, no matter how quickly the reaction takes place in steps that occur before the rate determining step, there will only be a build up of "intermediate reactants". Likewise, steps that occur following the rate determining step will not speed up the overall reaction rate, because the reactants will only be made available to later steps once they have been formed by the rate determining step.