. The integrated rate equation: We have just learnt that the rate of change of concentration of the reactant is directly proportional to that of concentration of the reactant. For a general reaction, product The rate law is Rate = d[A] dt k [A] x Where k is the rate constant, and x is the order of the reaction. The above equation is a differential equation, -d[A] dt , so it gives the rate at any instant.
However, using the above expression, we cannot answer questions such as how long will it take for a specific concentration of A to be used up in the reaction? What will be the concentration of reactant after a time ‘ t ’?. To answer such questions, we need the integrated form of the above rate law which contains time as a variable. .
. Integrated rate law for a first order reaction A reaction whose rate depends on the reactant concentration raised to the first power is called a first order reaction. Let us consider the following first order reaction, product Rate law can be expressed as Rate = k [A] Where, k is the first order rate constant. -d[A] dt k [A] ⇒ -d[A] [A] k dt ...( ) Integrate the above equation between the limits of time t = and time equal to t, while the concentration varies from the initial concentration [A ] to [A] at the later time.