Rate of a Reaction

Rate of reaction basically means the speed at which a chemical reaction occurs. The speed of a reaction is determined by monitoring the concentrations of the reactants or products at intervals of time. The volume of the reaction vessel is kept constant and there is no addition to or removal from the reaction vessel of any of the reactants and products. For a hypothetical reaction, A B, as the reaction proceeds the concentration of the reactant (A) decreases with time while the concentration of the product (B) increases.

fig 6.1 - Change in concentration of reactant with time

fig 6.2 - Change in concentration of Product with time

If the concentration of the reactant (A) is monitored at different times, say t₁ and t₂ then the rate of the reaction is given by

[A]₂ is the concentration of A at time t₁ while [A]₁ is the concentration A at a time t₁. Equation 1 can be written as,

D, signifies the change in concentration of A.

If the product [B] is monitored then the rate of the reaction is given by

Equations (2) and equation (4) represent the average rate of a reaction. For the hypothetical reaction A B, the rate of the reaction in the terms of appearance and disappearance of the product and reactant is given as

r = Rate of disappearance of A

r = Rate of appearance of B

The average rate of a reaction is a positive quantity, therefore a negative sign precedes in the term in the equation of the rate of reaction when it is expressed in terms of concentrations of the reactants. Average rate of a reaction does not represent the actual rate of a reaction at any instant of time. From the figures 6.1 and 6.2 it is clear that the rate of reaction actually decreases with time. This is because the rate of reaction depends on the concentration of the reactant.

Since the concentration of the reactant is continuously decreasing, it makes sense, to express the rate of a reaction at a particular instant of time. Average rate is measured over a time interval Dt. When this time interval is infinitesimally shortened, that is, Dt 0 then the average rate equation becomes the expression for instantaneous rate (r_inst). Mathematically, instantaneous rate (r_inst) is given by,

Instantaneous rate is the value of�

for the tangent at a given time t. This is actually the slope of the tangent to the concentration versus time curves of the reactants and the products.

r_inst = -slope for the reactant

= + slope for the product