DERIVATION OF THE EQUATION P V = RT* LEON McCULLOCH

Westinghouse Research Laboratories, East Pittsburgh, Pennsylvania

"THE Equation of State of a Perfect Gas," by Rose- v = F(p)T man and Katzoff,' recalls a method of derivation of the P =f(v)T

equation PV = RT which came to the writer after in which the constants K and k have been replaced by reading the following question from Professor Ban- functions of p and v. Each equation expresses now a croft : relationship between p, o, and T, these relationships be-

"Why should not the student be shown how to corn- ing dependent upon the form chosen for F@) and f(v). bine 8 = KT and P = IT so as to get Pv = RT? The We must h d forms for these functions such that the most obvious way of combining them gives PV = RT2 two equations may become simultaneously true. which we know is not right."% We take T as a variable dependent for its value upon

w e may COmnence with the two statements from 9 and v, which we shall treat as independent variables. experiments with gases : We then consider the two equations as simultaneously

Y = KT (9 constant) true and combine them by eliminating T: p = kT (v constant)

V P

which are to be combined into one equation connecting % T = = - f (4 the three variables p, v, and T. vf(4 = PFW

We may write them thus: We now reason from this equation as follows: - * Scientific Paper NO. 763. The left-hand side of the equation contains only one 1 R. ROSEMAN AND S. KATZOPF, "The equation of state of a variable, v , and the right-hand side only the variable

perfect gas,'' J. CHEM. EDUC.. 11, 3504 (1934). W. ,,. B ~ ~ c n o a r , book review in J . phys. them., 33, 1118 quantity 9. These two variables are independent of

(1929). each other, consequently each side of the equation va-

ries independently, if at all. But the two sides of an Or, w = RT equation-cannot vary independently, therefore, there can be no variation; that is, they are constant. In a similar manner, we could have proceeded from

We write them equal to the conventional constant R: the two statements:

From these we find the required form of the two tions :

R F(P) = - P

Substituting, we obtain R

Y = F(P)T = - T P

8 func-

" = - X P

Y = K T

considering 9 and T as the independent variables, and eliminating v.

The method of derivation suggested here is purely algebraic, and is perhaps as nearly as possible self-con- tained. The reasoning may be difficult for some, since the conceptions of variables which are independent, of equations which are simultaneously true, of functions of a variable, and of functions which remain constant, are not easily and immediately formed.

Thanks are due Messrs. E. B. Ashcraft and R. C. Mason for helpful criticism and suggestions.

CORRESPONDENCE SOME STUDENT EXPERIMENTS IN THE

PRIMARY AMINES FOR USE HETEROCYCLIC SERIES-CORRECTION

IN ORGANIC LABORATORY COURSES To the Editor

N. BEVERLEY TUCKER

Virginia Military Institute, Lexington, Virginia

MANY elementary manuals of organic chemistry, in taking up the study of primary amines, use a dilute solution of methylamine prepared from acet- amide by Hoffman's hypohalite method. I t is sug- gested that the experiments usually performed with this solution might well be supplemented by some with a liquid amine which can be handled in concentrated solution.

For this purpose, ethylenediamine is suggested. I t can be purchased fairly reasonably in sixty per cent. aqueous solution. It shows quite satisfactorily the usual reactions of a prima~y amine, such as the formation of an odoriferous isocyanide in solution, precipitation and re-solution of silver and cupric hydroxides, precipi- tation of femc hydroxide, etc.' I t reacts violently with acid sodium nitrite. The hydrochloride and sulfate are easily prepared by simply adding the concentrated acid to the diamine solution diluted with alcohol.

The formation of a substituted amide by heating the ammonium salt may be illustrated by adding glacial acetic acid to the diamine solution and distilling to a temperature of about 175'C. The residue of diacetyl ethylenediamine2 is best purified by recrystallization from a mixture of ethyl acetate and alcohol. Many other simple experiments suggest themselves.

FISCRER am Kocn, "Reactions of diamines," Ann., 232,222 11 9%)

DEAR SIR: A letter from Drs. C. B. Pollard and L. G. Mac-

Dowel1 draws attention to an error in the paper, "Some Student Experiments in the Heterocyclic Series," [J. CHEM. EDUC., 13, 265-72 (1936)], by the under- signed. On page 271 the name "N-Pbenylpiperidine" appears instead of "N-Phenylpiperazine." The writers regret this slip and hasten to correct it.

The communication from Messrs. Pollard and MacDowell states further that a "practical" grade of diethanolamine, available at a moderate price, is. satisfactory for the preparation of N-phenylpiperaqine, and that the procedure outlined in their original note [J. Am. C h m . Soc., 56, 2199 (1934)], when amplified in certain details, has given good results in the hands. of their students.

A PLAN FOR THE OPEN HOUSE IN CHEMISTRY-CORRECTION

To the Editor DEAR SIR:

In the article "A Plan for the Open House in Chem- istry," [J. CHEM. EDUC., 13, 72-3 (1936)], the table showing the approximate composition of a one-hundred- pound girl should have included the item: slaked lime, 4.5 pounds.

The content of calcium fluoride should be changed to 25 g. ,--",.

a HOPPW, "Notiz iiber Anhydrobasen der aliphatischen Diarnhe," Ber.. 21, 2332 (1888).