## Shaillee Kaushal is teaching live on Unacademy Plus

XII-04 KINETICS VII

First order growth kinetics:- It is used for population growth and bacteria multiplicatio Time population dt a +x Growth rate is directly proportional to present population: dx dt - k(a x dx -= kdt atx Or 2.303 loa (a a+x

1. If volume of reagents are given in volumetric analysis then we use the following equation to determine the rate constant Yo-V log 2.303, Vo volume used at zero time V volume used at time 't Voo volume used at infinite time

Case I. When vo is not given, we use 2.303 0o lo Case ll. When Vo is not given, then 2.303 V lo Vi

2. If pressure is given in gaseous reactions, then we use the following kinetic equation. log | Po Po-x Po = pressure of reactant at initial stage. Po x pressure of such a reactant at time 't' A-B C D P 0 0 0 0 Po Po Po At t = 0 pressrue after a long time Pressure at time t (P x) (Po-x) Pt= (Po _ x + x + x + x ) Pt = total pressure at time ,t,

If the number of moles of both S02Cl2 reactants and products are same as for example 2.303 Pi lo (2pi-Pt)

Second order reactions A reaction is said to be of second order if its reaction rate is determined by the variation of two concentration terms. The kinetics of second order reactions are given as follovw When concentrations of both reactants are equal or two molecules of th same reactant are involved in the change, i.e., A+B Products Or 2AProducts dx d ax)2 On solving this equation, t a(a-x) Where, a initial concentration of the reactant or reactants and x concentration of the reactant changed in time t.

When the initial concentrations of the two reactants are different, i.e. A + B Products Initial conc. 2.303 b(a-x) log10 a(b-X) (a - x)and (b -x) are the concentrations of A and B after time interval, t.

Characteristics of the second order reactions (i) The value of k(velocity constant) depends on the unit of concentration. The unit of k is expressed as (mol/litre)-1 timeor litre mol-1time-1 (ii) Half life period (t1/2)-1 0.5a1 k.ax .5a ka Thus, half life is inversely proportional to initial concentration.

(ii) Second order reaction conforms to the first order when one of the reactants is present in large excess. 2.303 log1o b(a-, if a > b then Taking, k tla-b) (a xa and (a - b) a Hence, k 2303 loq _ba log10 ta a(b-x) Or ka k'2303 10g1 2.303 log10 b (b-x) (since, 'a' very large, may be treated as constant after the change). Thus, the reaction follows first order kinetics with respect to the reactant taken relatively in small amount.