E. A. Guggenheim The University of Reading England
Molecules Versus Moles
It is almost universally known but almost universally overlooked that the gramme-molecule, tater renamed the mole, was introduced because the mass of molecules was then completely unknown. Now that the mass of molecules is known with an accuracy of one part in 105 there is nothing to be gained in continuing to use moles. The following table gives a comparison between parallel statements relating to molecules on the one hand and to n~oleson the other. From this table it will be seen that: the arithmetical factors relating to molecules are at least as convenient as those relating to moles; some of the statements, marked with an asterisk, relating to molecules are more easily visualised (anschaulich) than the corresponding statements relating to moles; some of the statements relating to molecules cannot be clearly expressed in terms of moles. This is because a molecule can collide with another molecule or with a photon but a mole cannot take part in such an event.
This table makes no mention of thermodynamic quantities. It is customary to give tables of standard entropies and analogous quantities in either cal '"I-' mole-' or J OK-' mole-'. Whenever such data are used for calculating equilibria one step is invariably t,o divide by the gas constant R. It would therefore be much more useful to have tables of SIR and related quantities. The quantity SIR is identical to the ratio of the molecular entropy to the Boltzmann constant. If the views expressed here are sound, the w e of the mole will gradually decrease, but its death will be a lingering one. There is, however, one step which can usefully be taken immediately. Whenever a comparison is made between a theoretical formula expressed in terms of molecules and experimental data expressed in moles it is to be recommended that the latter be converted into molecules, not the former into moles. This recommendation is especially relevant to reaction kinetics, to surface phenomena, and to the absorption of light.
Avogadro constant L
L
L-' = 1.660 X 10-24mole
=
6.022 X 10gamole-'
Perfeet Gas At ODCand 1 atm the volume per molecule is 3.72 X 10' A8 ' At 25'C and 1 tttm the volume per molecule is 4.05 X 10' 1 At 2 5 T the mean translational kinetic energy per molecule is
At OPCand 1 atm the volume per mole is 2.24 X 10' ema At 25°C and 1 atm the volume per mole is 2.44 X 10' ems At 25°C the mean translational kinetic energy per mole is
At 25'C the root mean square velocity of a N* molecule is 518 msec-'
Kinetic theory of gases The collision diameter of an Ar atom is D = 3.2 d The collision crosssection of an Ar atom is o = s 0 2 = 32 A2 At 25'C and 1 s t m the frequency of collision of a given Ar atom with other AT atoms is 4.4 X 100 sea-I At 25°C and 1 atm the molecular collision number of Ar gas is z -- 5.5 x 10' &a seo-' At 25°C themolecular second virial coefficientof NHI.is B/L . = -433 A*
* *
At 25'C and 1 atm the molar collision number of argon gas is LZ = 3.9 X 10' mole em-' see-' At 25'C the molar second virid coefficient of NH. is B = -261 cma mole-'
Cryslal
*
A t 25°C the volume per NaCl is 44.8 A"
L
Gas Kinetics
-
+
The molecular ~ t constant e at 698.6"K for the process HS 2HI is 57.5 A' seo-'
250
At 25'C the volume of crystalline NaCl is 27.0 cma mole-'
/
Journal of Chemical Educofion
b
-
The molar rate constant at 698.6% for the process H2 2HI is 34.7 mole-1 ema sec-'
+
Electrolytic c a d u c t w n i n inlinitely dilute aqueous solution
The Mgl+ ion has a charge ze = 2 X 1.60 X lo-" C I n a field of 1 V em-' the Mgn+ion has a speed u = 5.50 X lo-' cm specL The density of electric current, carried by Mglf, divided by the field and by the concentration of ions is 2 X 1.60 X X 5.50 X lo-+ C see-' V-I cmZ = 2 X 88.0 X R P em2
The charge associated with Mg2+is zLe = z 5 = 2 X 9.65 X 10' C mole-' The molar conductt~nceof Mgs+ is A(Mgz+) = 2 X 53.0 C s-I = 2 X 53.0 a-' emP mole-' or A('/2hlg'+) = 53.0 0-' em2 mole-1
V-1 ema mole-'
Optical Pmperties
Thecross-section (or target area) ofPe(CN)sS- absorption of 4360 A photons is cab = 1.23 X As The optical rotatory cross-secbion of a sucrose molecule is 3.98 X 10-8'
* *
is The molar absorption coefficient of Fe(cN)~a-a t 4360 L O S ~= 7.42 X 104 emPmole-' The optical rotatory power of sucrose is 2.40 X 106 cm2mole-'
Adsorptim
In a n aqueous solution containing 0.2 mole of phenol per k~ of water the moleculttr adsorption of ~ h e n oisl r / L = 2.7 X 10F A-? or ~ / =r 37 iP'
*
I n an aqueous solution containing 0.2 mole of phenol per kg of water the molar adsorption of phenol is I? = 4.5 X 10-lo mole or P-' = 2.2 X 109 cmZmole-'
Volume 43, Number 5, May 1966
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