-
Edited by GEORGEWIGER
textbook forum Derivation of the Ideal Gas Law
California State University Carson. CA 90747
Since it has been established that in the limit of low pressure the (PV) product of a gas goes to zero a t the temperature of absolute zero, eqn. (4) has been derived.
S. Levine
Saginaw Valley State College Universiv Center. MI 48710 The equation (eqn. (4) below) for the behavior of a mole of gas in the ideal state that is obtained by the extrapolation of the properties of real gases has been based upon three wellknown phenomenological laws. These may be formulated as eqs. (l), (2), and (3). T=AP at constant volume (1)
A Comment on "The Order of CHBCHO Decomposition"
T = CV
at constant pressure
(2)
P = BIV
at constant temperature
(3)
Mlchael T. H. Llu
per mole of ideal gas
(4)
University of Prince Edward Island Charlanetown, Prince Edward Island CIA 4P3. Canada
P V = RT
Equation (4) is shown to have validity by a number of unsatisfactory methods. I t has heen deduced by graphical arguments using algebra.' Often i t is justified2 by observing that for the special conditions it reduces to eqns. (1-3). A "prwf' using the calculus3erroneously employs the pressure variables a t constant temperature as equivalent to the total pressure without constraint. I t is worthwhile to present to students the derivation of the ideal gas law from a thermodynamic viewpoint such as that given below. Assume that P , V, and T a r e variables with the properties of thermodynamic functions. Then eqn. (5) may he written.
In a first-year chemistry rourse, we try to wach the students the basic principles of chemistry as well as the correctnrss of the subjert matter. Chemistry is ronstantlv rhmging and the textbooks can only report the present state of the art. Surelv. a great many improvementshave been mad? in firjt-ye& chemistry texts over the years. All we have tu do is to pick up a text written in the '50s and '60's to see the uwradine. The topic of the decomposition of acetaldehick CH,%HO, has found its way into many first-year chemistry texts (1-12). Unfortunately most authors cite the reaction, CH3CH0 CHa CO, as being second order and give the rate law as
-
+
Rate = k[CHsCH0]2 The order of the reaction is well known from experiments (13) and is equal to 312 or 1.5. Therefore, it is necessary to write the rate law as
d T = X d V + YdP
(6)
Applying the Euler criterion to eqn. (6) gives eqn. (7).
The simplest functions satisfying eqn. (7) are given in eqns. (8)and (9), where R is a constant per mole of gas.
Rate = k[CH3CH0]3" I d o hope that this misinformation will be corrected in the future; otherwise, we are doing a great disservice t o our students. I t is interesting to note that the elegant work of J. H. Sullivan (14) on the reaction of Hp 12 has been incorporated correctly into first-year chemistry texts.
+
Literature Cited (11 Ycder, C. H., Suydam,F.H., and Sssb,F.A.,"Chemkm,"kdd.,Harma Bra*,
Substitution from eqns. (8)and (9)into eqn. (6) gives eqns. (10) and (11). 1
dT = - (PdV + VdP
R
(10)
Jovanovieh, Ine.. New York, 1980. (21 Marterton, W.L.,andSlovinnki. E. J.,"ChemicalPrineiples."4th ed. W.B.Saunders Company. New York 1977. (31 Maatarton, W . L..Slowinski,E. J.,and Stanibki,C. L., "Chemical Principlps:6thd., Saunders College Publishing, New York, 1985. (41 Mantelton, W. L., Slowinski,E.J..and Sanit8ki.C.L., "Chemical Principles," Alternate Edition,Saunders CollegePublishing, NeuYork: Hdt,Rinehart and Winston, New
York. 1983.
(51 Chang, k.,"ChemistxyI). Isted., Random House Inc., NelvYork, 1981. (6) B o i k e s R. S., and Edelaon. E.. "Chemical Principles: 2nd ed.. Harper and Row Publishers, NewYork, 1981. (71 Brady, J.E., andHumIstot0, G.E.."Ge~e~alCh-Istry:3rd ed.,John WililyandSo~s, New V 19112~ -n r.k ~ (81 Brady, J. E.. and Ho1um.J. R,"Fundamcntdsaf Chemistri: John Wileyand Sons, ~
~
New York. 1981.
'
McCormick, W. W.. "Fundamemals of College Physics," Macmillan Co., New York, 1965, p. 227. See for example, Moore, W. S., "Physical Chemistry." 4th ed., Prentice-Hall, Englewood Cliffs, 1972, p. 16. Gucker, F. T., and R. L. Seifert. "Phvsical Chemishv." W. W. Nortorton, 1966, p. 202
Company, 1982. (141 Sullivan. J. H., J. Chem P h r s , 48,73 (1967).
Volume 62
.
Number 5
May 1985
399
