`text(Average rate of reaction)` :

With the progress of reaction the concentration of reactants decreases while that (those) of product(s) increases. Thus, the rate of reaction is defined as the rate at which the concentration of reactant decreases or alternatively, the rate at which concentration of product increases. That is, the change in concentration of any of the substance (reactant/product) per unit time during the reaction is called rate of reaction of that substance. If `DC` is the change in concentration of any reactant or any product during the time interval `Dt` then the rate may be given as

`Rate =(Delta C)/(Delta t)`

(`-ve` sign applies in the case of reactant whose concentration goes on decreasing with time and `+ve` sign applies in the case of product whose concentration goes on increasing with time).

For Example : `PCl_5-> PCl_3 + Cl_2`

Suppose in the time interval `Delta t`, change in concentration of `PCl_5` is `Delta[PCl_5]` and change in concentration of `PCl_3` and `Cl_2` are `Delta[PCl_3]` & `Delta` `[Cl_2]` respectively.

Then, Average rate of reaction `=(-Delta[PCl_5])/(Delta t) = (Delta[PCl_5])/(Delta t)=(Delta[Cl_2])/(Delta t)`

In general, for any reaction of the type `A+B -> C+D`

Then, Average of reaction `=(-Delta [A])/(Delta t)` = `(-Delta[B])/(Delta t)` = `(Delta[C])/(Delta t)` = `(Delta[D])/(Delta t)`

`text(Instantaneous rate of reaction)` : However, the rate of reaction is not uniform (Except for zero order reaction). With the passage of time the concentration(s) of reactant(s) goes on decreasing and hence according to Law of Mass Action, the rate of reaction goes on decreasing. Intact, the rate of reaction decreases moment to moment This is shown in the rate vs time curve of a reaction.

Rate varies from moment to moment so rate of reaction has to be specified at a given instant of time. It is called instantaneous rate or rate at any time `t`. This is defined as

`r_text(inst)` or `r_t =pm (dc)/(dt)`

Rate varies from moment to moment so rate of reaction has to be specified at a given instant of time. It is called instantaneous rate or rate at any time `t`. This is defined as

`r_text(inst)` or `r_t= pm (dc)/(dt)`

Where `d_c` is the infinitesimal change in concentration during infinitesimal time interval `dt` after time `t` i.e. between `t` and `t + dt`. The time interval `dt` being infinitesimal small, the rate of reaction may be assumed to be constant during the interval. The rate of reaction expressed as `pm Delta C//Delta t` is actually the average rate with time interval considered.

For the reaction: `2N_2O_5-> 4N_O_2 + O_2`

The rate of reaction at any time `t` may be expressed by one of the following.

`(-d[N_2O_5])/(dt)` or `+(d[NO_2])/(dt)` or `+(d[O_2])/(dt)`

Where square bracket terms denote molar concentration of the species enclosed. The above three rates are not equal to one
another as is evident from the stoichiometry of the reaction. For every mole of `N_2O_5` decomposed, `2` moles of `NO_2` and `1//2` mole of `O_2` will be formed. Obviously, the rate of formation of `NO_2` will be four times that of `O_2` and it is twice the rate of consumption of `N_2O_ 5`. Thus, their three rates are interrelated as,

`+(d[NO_2])/(dt)=2{-(d[N_2O_5])/(dt)}=4{+(d[O_2])/(dt)}`

Dividing throughout by `4`,

`1/2{-(d[N_2O_5])/(dt)=1/4{+(d[NO_2])/(dt)}=+(d[O_2])/(dt)`

Thus, rate of reaction expressed in terms of the various species involved in a reaction will be equal to one another if each of them is divided by the stoichiometric coefficient of the species concerned. Thus, for a reaction represented by the general equation

`aA+bB-> cC+dD`

`1/a{-(dC_(A))/(dt)}=1/b {-(dC_(B))/(dt)}=1/c{+(dC_(c))/(dt)}=1/d{-(dC_(D))/(dt)}`