Notes On Integrated Rate Equations: First Order Gas Phase Reaction - CBSE Class 12 Chemistry
The integrated rate equation for a first order reaction, in which the reactant and the products are expressed in terms of concentration, is Integrated rate equation: k = 2.303/t . log [A]0/[A] Where k = rate constant [A]0 = Initial concentration [A] = Concentration at time't' The rate equation for a first order gaseous phase reaction by applying the integrated rate equation for the reaction can be attained by replacing the "concentration of A0" "in the rate equation                                 A(g)     →      B(g)          +              C(g)                        1 mole of A       1 mole of B               1 mole of C t = 0                  Po atm              0 atm                         0 atm At time t            Po - Patm             P atm                                 P atm k = 2.303/t . log P0/PA PA can be calculated using total pressure of the reaction mixture. The total pressure of the reaction mixture at constant volume and temperature is equal to the sum of the partial pressures of all the gaseous reactants and products involved in the reaction. Total pressure (Pt) = Partial pressures gaseous reactants (PA) + Partial pressure of gaseous products (PB +PC) Total pressure = PA + PB + PC Pt = P0- P + P + P Pt = P0 + P P = Pt - P0 PA = P0 - P PA = P0 - (Pt - P0) = 2P0 - Pt Therefore rate equation can be written as, k = 2.303/t . log P0/(2P0 - Pt)

#### Summary

The integrated rate equation for a first order reaction, in which the reactant and the products are expressed in terms of concentration, is Integrated rate equation: k = 2.303/t . log [A]0/[A] Where k = rate constant [A]0 = Initial concentration [A] = Concentration at time't' The rate equation for a first order gaseous phase reaction by applying the integrated rate equation for the reaction can be attained by replacing the "concentration of A0" "in the rate equation                                 A(g)     →      B(g)          +              C(g)                        1 mole of A       1 mole of B               1 mole of C t = 0                  Po atm              0 atm                         0 atm At time t            Po - Patm             P atm                                 P atm k = 2.303/t . log P0/PA PA can be calculated using total pressure of the reaction mixture. The total pressure of the reaction mixture at constant volume and temperature is equal to the sum of the partial pressures of all the gaseous reactants and products involved in the reaction. Total pressure (Pt) = Partial pressures gaseous reactants (PA) + Partial pressure of gaseous products (PB +PC) Total pressure = PA + PB + PC Pt = P0- P + P + P Pt = P0 + P P = Pt - P0 PA = P0 - P PA = P0 - (Pt - P0) = 2P0 - Pt Therefore rate equation can be written as, k = 2.303/t . log P0/(2P0 - Pt)

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