JOHN J. ALEXANDER University of Cincinnati Cincinnati. 45221
The Brevity of a Million Years: Approximates in Kinetics Problems H. Graden Kirksey Memphis State University Memphis, Tennessee 38152 T h e ability to make an appropriate approximation in solving problems requires cognitive behavior a t the level of synthesis for general chemistry students. Unlike the approximation made for the calculation of concentrations in solutions of weak electrolytes, the approximation used here is not normally discussed in general chemistry textbooks. 792 / Journal of Chemical Education
Furthermore. most first-order reaction rate ~ r o b l e m sin textbooks require that students use the integrated form of the ratr exnwssion: this one dues not. Puttinr-uauestion like this . on an out-of-class exam gives students time to contemplate their answers. Question The age of Earth has been estimated by one method to be 4.5 X 109 years, which is also the half-life for the alpha decay of 238U to 234Th. For a sample of 2Wwith an initial mass of 1.0 g, how many atoms will he decaying per second when the sample is one million years old?
Answer The half-liieofZWUisover threeordenot'magnitude (lo3)greater than one-million yrors. Rrcouw rhedornstated in rhisquesrion haw bur two significant figures, the numhrr otoromr ol ""11 rrmaming. after one-million years can be approximated as being equal to the number of atoms in the original 1.0 g sample. In 2 k = -= 5.0 X 10-l8 sec-I t l-.i-l
A
=
(1.0 g) (6.0 X
loz3atoms mole-')
238 a mole-' = -1.3 X
= 2.5 X
loz1 atoms
lo4 atoms see-'
Volume 55, Number 12, December 1978 / 793
