An Alternate Form of the Integrated First-Order Rate Equation

Abstract

Derivation of the Alternate Form Radioactive processes and many chemical processes follow first order kinetics. The usual equations found in general chemistry textbooks are: a. ln / Ao A kt = , Where, Ao is the original amount of the sample, A is the amount at time t and k is the rate constant. b. Changing the rate constant to half-life, 1/2 2 ln kt = , where t1/2 is the half-life. c. Solving equation 2 for k and substituting into equation 1 the result is ( ) 1/2 / 2 / lnAo A ln t t = . d. Rearranging equation 3 gives ( ) 1/2 2 / / ln t t o A A e = as indicated in [1]. e. Since 2 2 ln e = , substitution into equation 4 yields 1/2 / / 2 t o A A = the Alternate Form of the Integrated first-order rate equation Our students have found equation 5 to be relatively easier to use than equations 1 and 2. In equation 5, by dividing the time by the half-life, they get a number. On their calculators, they enter the number 2, yx, the number and press=The result is divided into Ao, giving the value for A. For radioactive processes, the values of Ao and A may be in mass, such as grams, or activity in Becquerel’s (counts/second). For chemical processes, units for Ao and A may be written as rates, such as molarity/second. References 1. Kenneth AC (1991) Chemical kinetics, the study of reaction rates in solution. VCH Publishers, USA, p. 496. Crimson Publishers Wings to the Research Opinion