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Part of PC-08 — Chemical Kinetics

Chemical Kinetics — Quick Review

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The rate of a chemical reaction measures how rapidly concentrations of reactants decrease or products increase per unit time, always expressed as a positive value. The rate law, rate=k[A]m[B]n\text{rate} = k[A]^m[B]^n, is determined experimentally and the exponents are not necessarily equal to stoichiometric coefficients. For a zero-order reaction, concentration decreases linearly with time and the half-life is directly proportional to the initial concentration (t1/2=[A]0/2kt_{1/2} = [A]_0/2k). For a first-order reaction, the half-life t1/2=0.693/kt_{1/2} = 0.693/k is independent of concentration, making it the most NEET-tested formula in this chapter. In a second-order reaction, $1/[A]increaseslinearlywithtimeandthehalflifeisinverselyproportionaltotheinitialconcentration.Orderisanexperimentallydeterminedquantitythatcanbezero,fractional,orinteger,whilemolecularityisatheoreticalcountofmoleculesinanelementarystepandisalwaysapositiveinteger.TheArrheniusequationincreases linearly with time and the half-life is inversely proportional to the initial concentration. Order is an experimentally determined quantity that can be zero, fractional, or integer, while molecularity is a theoretical count of molecules in an elementary step and is always a positive integer. The Arrhenius equationk = Ae^{-E_a/RT}quantifieshowtherateconstantincreaseswithtemperatureasmoremoleculesacquiresufficientenergytosurpasstheactivationenergybarrier.Acatalystprovidesanalternativepathwayofloweractivationenergy,increasingquantifies how the rate constant increases with temperature as more molecules acquire sufficient energy to surpass the activation energy barrier. A catalyst provides an alternative pathway of lower activation energy, increasingkwithoutalteringthethermodynamicquantitieswithout altering the thermodynamic quantities\Delta HororK.Therelationship. The relationship E_a(\text{forward}) - E_a(\text{backward}) = \Delta Hconnectskineticstothermodynamicsthroughtheenergyprofile.Pseudofirstorderreactionsoccurwhenonereactantisinsuchlargeexcessthatitsconcentrationiseffectivelyconstant,simplifyingthekineticstoapparentfirstorderbehaviour. connects kinetics to thermodynamics through the energy profile. Pseudo first-order reactions occur when one reactant is in such large excess that its concentration is effectively constant, simplifying the kinetics to apparent first-order behaviour.

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