Frank E Stary*
Department of Chemistry, USA
*Corresponding author:Frank E Stary, Department of Chemistry, USA
Submission: June 11, 2019; Published: June 25, 2019
ISSN 2637-8078Volume3 Issue3
Derivation of a first-order equation suitable for use in beginning energy science and chemistry courses is shown to be
A = Ao/ 2t /t1/2
Ao is the original amount of the sample
A is the amount
T is time t and
t1/2 is the half-life
Ao is larger than A
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, ln2 = kt1/2 , where t1/2 is the half-life.
c. Solving equation 2 for k and substituting into equation 1 the result is lnAo / A = (ln2)t/t1/2 .
d. Rearranging equation 3 gives / (ln2)t /t1/2 o A = A e as indicated in .
e. Since eln2 = 2 , substitution into equation 4 yields / 2t /t1/2 o A = A the Alternate Form of the
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.
© 2019 Frank E Stary. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and build upon your work non-commercially.