When designing a reactor, we require an equation for the reaction rate. This is typically in terms of the concentrations of the species in the reaction. We therefore need to understand how the rate of the formation for any component is related to the rate of reaction and the overall reaction.
Consider the general reversible reaction $$aA + bB\xrightleftharpoons[k_{-1}]{k_1} cC + dD$$
We typically express the reaction rate in terms of one of the components, usually the rate of reaction is equal to the rate of formation of A in this case. The rates of the other components can be then written in terms of A. For example every mole of A consumed in this reaction gives us $c/a$ moles of C, therefore this means that
$$\frac{-r_A}{a}=\frac{-r_B}{b}=\frac{r_C}{c}=\frac{r_D}{d}$$
The rate law must be determined experimentally; however, if the rate is elementary (i.e. a simple single step reaction involving all reagents in their stoichiometric ratio) then we can express the rate of reaction of the formation of A as,
$$-r_A=k_1C_A^aC_B^b-k_{-1}C_C^cC_D^d$$
Taking this system as a simple batch reaction then $r_A=\text{d}C_A/\text{d}t$, thus,
$$-\frac{\text{d}C_A}{\text{d}t}=k_1C_A^aC_B^b-k_{-1}C_C^cC_D^d$$
This equation can either be solved numerically for the concentration of the components or analytically solved for simple systems.
The graph below shows the change in the concentration with time for the components for relative reaction rates, with initial concentration of $C_A=C_B=1$. If $k_{-1}=0$ then the reaction is not reversible and if $b$ or $d$ are equal to $0$ then they do not take part in the reaction.
Explore how the variations in the stoichiometric coefficients and the relative reaction rates affect the concentration of the components with time. This analysis can be extended to series reactions and parallel reactions.