, Volume 40, Issue 5, pp 453–456 | Cite as

Simple integrated rate equations for reversible bimolecular reactions

  • E. A. Boeker


If the complete rate equations for reversible, one-step, bimolecular reactions are written withPeP as the concentration variable (wherePe is the equilibrium, andP is the instantaneous, product concentration), the 3 possible stoichiometries can be reduced to a single straightforward differential equation. This can be solved very economically. For each stoichiometry,

weret is time,k1 is the forward rate constant,Ke is the equilibrium constant, and ΔP isPPo. The termsPcPo andD+PcPo are the physically possible and physically impossible roots of the quadratic equation forPePo in terms of the initial concentrations andKc.D is the discriminant in this equation. All 3 quantities can be calculated if the equilibrium constant is known. A plot oft against ln{[1−ΔP/(D+PcPo)]/[1−ΔP/(PcPo)]} should be a straight line for any second order reaction. For each stoichiometry,PcPo approachesAo, the initial concentration of the first reactant, as the equilibrium constant increases. When a second reactant is present,D+PeP o approachesBo. The limiting equation is then that of an irreversible bimolecular reaction. For A⇌P+Q,D approaches −Ke as the equilibrium constant becomes large, and the value of the second logarithmic term in the integrated equation approaches zero. The limiting equation is that of an irreversible, unimolecular reaction.


Differential Equation Equilibrium Constant Rate Equation Order Reaction Quadratic Equation 
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Copyright information

© Birkhäuser Verlag 1984

Authors and Affiliations

  • E. A. Boeker
    • 1
    • 2
  1. 1.Department of Chemistry and BiochemistryUtah State UniversityLoganUSA
  2. 2.Department of BiochemistryUniversity of BirminghamBirmingham(England)

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