• Submissions # An Alternate Form of the Integrated First-Order Rate Equation

Frank E Stary*

Department of Chemistry, USA

*Corresponding author:Frank E Stary, Department of Chemistry, USA

Submission: June 11, 2019; Published: June 25, 2019

DOI: 10.31031/SBB.2019.03.000564 ISSN 2637-8078
Volume3 Issue3

#### Abstract

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

Where,

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

#### 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, 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

### 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.

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