Notes On Integrated Rate Equations: Zero And First Order Reactions - CBSE Class 12 Chemistry
Using the differential rate equation and rate law, the rate of the reaction in terms of the rate of disappearance of reactant A is Rate = - d[A]/dt = k[A]n Zero order reactions: Reactions in which the rate of reaction doesn't depend on the concentration of the reactants are called zero order reactions. The integrated rate equation for a zero order reaction is,         - d[A]/dt = k      ∫ d[A] = - k ∫ dt          [A] = -kt + C  C = Constant of Integration Initial Concentration [A] = [A]o at t = 0                               [A] = -kt + C                               [A]o = -k x 0 + C                                C = [A]o                                   [A] = -kt + C    C =  [A]o [A] = -kt + C [A] = -kt + [A]o Ex: Photochemical reactions are zero order reactions. Certain enzymatic reactions are also zero order reactions.                       hv      H2 + Cl2      →     2HCl                          hv 6CO2 + 6H2O    → C6H12O6  +  6O2               Pt,1130 k 2NH3          →           N2 + 3H2            High Pressure        Δ 2HI →  H2  + I2       Au First order reactions: A reaction in which the rate of reaction is proportional to the first power of the concentration of the reactant is called a first order reaction. The integrated rate equation for a first order reaction is - d[A]/dt = k[A]n - d[A]/dt = k[A] ∫ d[A]/[A] = -k ∫ dt loge[A] = -kt + C [A] = [A]0, at t = 0 loge[A]0 = -k x 0 + C C = loge[A]0 loge[A] = -kt + loge[A]0 k = 1/t . loge([A]0/[A]) loge = 2.303 log10 k = 2.303/t log10 ([A]0/[A])

#### Summary

Using the differential rate equation and rate law, the rate of the reaction in terms of the rate of disappearance of reactant A is Rate = - d[A]/dt = k[A]n Zero order reactions: Reactions in which the rate of reaction doesn't depend on the concentration of the reactants are called zero order reactions. The integrated rate equation for a zero order reaction is,         - d[A]/dt = k      ∫ d[A] = - k ∫ dt          [A] = -kt + C  C = Constant of Integration Initial Concentration [A] = [A]o at t = 0                               [A] = -kt + C                               [A]o = -k x 0 + C                                C = [A]o                                   [A] = -kt + C    C =  [A]o [A] = -kt + C [A] = -kt + [A]o Ex: Photochemical reactions are zero order reactions. Certain enzymatic reactions are also zero order reactions.                       hv      H2 + Cl2      →     2HCl                          hv 6CO2 + 6H2O    → C6H12O6  +  6O2               Pt,1130 k 2NH3          →           N2 + 3H2            High Pressure        Δ 2HI →  H2  + I2       Au First order reactions: A reaction in which the rate of reaction is proportional to the first power of the concentration of the reactant is called a first order reaction. The integrated rate equation for a first order reaction is - d[A]/dt = k[A]n - d[A]/dt = k[A] ∫ d[A]/[A] = -k ∫ dt loge[A] = -kt + C [A] = [A]0, at t = 0 loge[A]0 = -k x 0 + C C = loge[A]0 loge[A] = -kt + loge[A]0 k = 1/t . loge([A]0/[A]) loge = 2.303 log10 k = 2.303/t log10 ([A]0/[A])

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