The half-life of a zero order reaction is x second. If the reaction takes t 1 second to complete, calculate t 1 in terms of x .

In case of zero-order reactions, the reaction rate is independent of the concentration of a reactant, so that changing its concentration has no effect on the rate of the reaction. So, the concentration changes linearly with time. The integrated rate equation of a zero order reaction = [ A ] = [ A ] 0 - kt , Where, [ A ] 0 = Initial concentration of the reactant. [ A ] = Concentration of the reactant after time, t . And k = Rate constant. If, t = x , [ A ] = [ A ] 0 2 Then, [ A ] 0 2 = [ A ] 0 − kx x = [ A ] 0 2 k . . . . . . . . . . . . . . . . . . . . 1 If t 1 is the taken for the completion of reaction, Then, [ A ] = 0 and 0 = [ A ] 0 − kt 1 t 1 = [ A ] 0 k . . . . . . . . . . . . . . . . . . . . . . 2 From the equations 1 and 2 x = 1 2 × A 0 K = 1 2 t 1 Therefore, t 1 = 2 x

Show that the time required for 99 % completion of a first order reaction is twice the time required for 90 % completion of that reaction.

A chemical reaction in which the rate of reaction is directly proportional to the concentration of the reacting substance is called first order reaction. For a first order reaction, the time required for 99 % completion of reaction is, t 1 = 2 . 303 k log 100 100 - 99 = 2 . 303 k log 100 = 2 × 2 . 303 k For a first order reaction, the time required for 90 % completion of reaction is, t 2 = 2 . 303 k log 100 100 - 90 = 2 . 303 k log 100 10 = 2 . 303 k log 10 = 2 . 303 k Hence, t 1 = 2 t 2 .

What is meant by instantaneous reaction rate?

The instantaneous rate of reaction is defined as the change in concentration of an infinitely small-time interval. An instantaneous rate is a rate at some instant in time. An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate, - d Reactant dt or d Product dt We determine an instantaneous rate at time t , by calculating the negative of the slope of the curve of concentration of a reactant versus time at time, t or by calculating the slope of the curve of concentration of a product versus time at time, t .

Derive an integrated rate equation for a first order reaction.

Let us, consider a unimolecular first order reaction represented by the general equation, A → Product At t = 0 a 0 At t = t a - x x The initial concentration of A is a mole L - 1 and its concentration after time t is ( a – x ) mole L - 1 . This means during the time interval t , x mole L – 1 of A has reacted. The rate of reaction at any time t is given by the following first order kinetics. dx dt = k a - x where k is the rate constant of the reaction. dx a - x = kdt This is differential rate equation and can be solved by integration. ∫ dx a - x = k ∫ dt - ln a - x = k . t + C . . . . . ( 1 ) where C is integration constant. The constant C can be evaluated by applying the initial condition of the reaction i.e. when t = 0 , x = 0 . Putting these in equation (1), we get C = – ln a Putting the value of C in equation (1), we get – ln ( a – x ) = k . t – lna k = 1 t ln a a - x = 2 . 303 t log a a - x . . . . . ( 2 ) Equation (2) integrated rate equation for a first order reaction.

What is activation energy of a reaction?

The additional amount of energy required by reactants to form intermediate activated complexes and hence undergo chemical changes to form products is called activation energy of a reaction. Denoted by : E a . Unit of activation energy = J mol - 1