# Rate of reactions

The rate (speed or velocity) of the reaction may be defined as “The rate of change of the concentration of the reactants with time”. In other words it is measured by the amount of substance in unit volume changed in unit time and amount is measured in mole.

Thus,

$\text{Velocity of reaction} = \dfrac{\text{Amount transformed}}{\text{Time taken in transformation}} = \dfrac{\delta x}{\Delta t}$

Where $\Delta x$ is the amount of substance changed and $\Delta t$ is a interval of time.

rate of reaction

It is important to note that the concept of mechanical velocity or speed cannot be used in measuring the rates of reactions. Because rate of reaction depends upon the molar concentration of the reactants and it decreases with time. Therefore rate of reaction varies with time. In order to determine the rate of reaction at any time t, we take slope of the tangent of the graph; plotted between concentration of the reactant (or product) and time; at any time t.

The rate of change of concentration of any of the reactant or product for a very small duration of time, i.e., at any instant is called. Instantaneous Reaction Rate. It is given as

$-\dfrac{dx}{dt}$

It can be written for any of the reactant or product with stoichiometric coefficient as follows:

For a general reaction;

$aA+ bB \to cC + dD$

Rate of reaction may be given as:

$r = - \dfrac{dC_A}{dt} \times \dfrac{1}{a} = kC^a_A C^b _B$

$\text{or} \hspace{3mm} r = -\dfrac{dC_B}{dt} \times \dfrac{1}{b} = Kc^a_AC^b_B$

$\text{or} \hspace{3mm} r = + \dfrac{dC_C}{dt} \times \dfrac{1}{bc} = Kc^a_A C^b_B$

$\text{or} \hspace{3mm} r = + \dfrac{dC_D}{dt} \times \dfrac{1}{d} = kC^a_AC^b_B$

where r = rate of reaction; $C_A, C_B, C_C \text{and} C_D$ are concentrations of A, B, C and D respectively.

Evidently the various expressions for the rate of reaction are equal to one another.

I.e.

$r = -\dfrac{dC_A}{dt} \times \dfrac{1}{a} = -\dfrac{dC_B}{dt} \times \dfrac{1}{b}$

$= \dfrac{dC_C}{dt} \times \dfrac{1}{bc} = \dfrac{dC_D}{dt} \times \dfrac{1}{d}$

Let us consider the following reactions:

(i)                  $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$

$r = - \dfrac{1}{2} \dfrac{d[N_2O_5]}{dt} = \dfrac{1d [NO_2]}{4dt} = \dfrac{d[O_2]}{dt}$

(ii)                $N_2(g) + 3H_2(g) \to 2NH_3(g)$

$r = - \dfrac{d[N_2]}{dt} = - \dfrac{1}{3} \dfrac{d[H_2]}{dt} = \dfrac{1d[NH_3]}{2dt}$

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