I
RUDOLPH J. MARCUS Chemistry Department, Stanford Research Institute, Menlo Park, Calif
Graphical Estimation for Energies of Vaporization This rapid method gives a rough estimate from only
b
liquid density
T H E EI*'ERGY O F vaporization for a liquid can be calculated from its molar volume a n d boiling point only ( 7 , 2). However, the calculation inbolves a number of iterations of the equation AE, = R T l n ( 4 E , / V z P )
boiling point V,, cc/rnole
120 100 80
- _
0.012500 r
60
20
40
l l l t l ~ l ~ ;I t I l ,
I
......................
A€" 1.5
A parametric graph of Equation 1 is illustrated, from which it is possible to obtain the energy of vaporization directly. If the molecular weight is known, the only experimental d a t a needed are boiling point and density. T h e graph and the equation appear to be valid over a temperature range of 77' to 2500' K . ; the accuracy of the method has been shown earlier.
0.010000
1
-
loo
A€,= 2 0.007500
i
-
I
?Ib
A E v =3
Acknowledgment
1
I t is a pleasure to express appreciation to D a n McLachlan for valuable discussions, a n d to Eve Ellis for performing the calculations.
0.005000 -
]2OO
/AEv
4
I
AEv = 5 300
Literature Cited
0002500
(1) McLachlan, D., Marcus, R. J., J . Chern. Educ. 34, 460 (1957). (2) Marcus, R. J., J . Chem. Phys. 26, 1765 (1957). (3) van Zeggeren, F., Canadian Industries Ltd., McMasterville, Quebec, private communication. RECEIVED for review September 25, 1959 RESUBMITTED May 1, 1960 &CEPTED July 11, 1960 Work supported by the Physics Branch, Office of Naval Research, under contract Nonr-2629 (00).
Accuracy b Perfect liquids:
A
E
V
=
I
O
Energy o f vaporization (AEJ as a function of molar volume VI(V1 = M / d ) and boiling point (TB). The energy value can be obtained directly from the graph
liquids:
18%
b Fused salts (3):
for these
for these
Argon Krypton Xenon Radon Nitrogen Oxygen Carbon monoxide Methane
Silicon tetrabromide Stannic chloride Carbon tetrachloride Chloroform Methanol
Lithium chloride Lithium bromide Sodium chloride Sod ium bromide Sodium iodide Potassium chloride Potassi um bromide Potassi um iodide
For all liquids except the liquid metals, the calculated values for energies of vaporization are lower than the observed values
INDUSTRIAL AND ENGINEERING CHEMISTRY
400
log I/V,
for these
b
938
L
b Imperfect
5%
2
-
6%
