What are Parachors?
The parachor [P] may be defined as the molar volume of a liquid at a temperatures so that its surface tension is unity.
From a study of a large number of liquids, Macleod (1923) showed that
where y is the surface tension, D its density and d the density of vapour at the same temperature, C is a constant. Sugden (1924) modified this equation by multiplying both sides by M, the molecular weight of the liquid,
My1/4 /D-d = MC = [P]
The quantity [P], which was constant for a liquid, was given the name Parachor. As d is negligible compared to D the equation (2) reduces to
M/D x y1/4 = [P]
V1/4 = [P]
V1/4 = [P]
where V is the molar volume of the liquid. If surface tension (y) is unity, from equation (3), we may write,
[P] = V
Thus, the parachor [P] may be defined as the molar volume of a liquid at a temperatures so that its surface tension is unity.
Use of Parachor in Elucidating Structure
Sugden examined the experimental parachor values of several organic compounds of known molecular structure. He showed that the parachor is both an additive and constitutive property. That is, the parachor of an individual compound can be expressed as a sum of:
(1) Atomic Parachors which are the contributions of each of the atoms present in the molecule.
(2) Structural Parachors which are the contributions of the various bonds and rings present in the molecule.
By correlating the experimental values of parachor with molecular structure, Sugden (1924) calculated the atomic and structural parachors listed in Table 13.1. These values were further revised by Vogel (1948) on the basis of more accurate measurements of surface tension.
Parachor Values
| Atom | Sugden | Vogel | Bond or Ring | Sugden | Vogel |
|---|---|---|---|---|---|
| C | 4.8 | 8.6 | Single bond | 0 | 0 |
| H | 17.1 | 15.7 | Double bond | 23.2 | 19.9 |
| O | 20.0 | 19.8 | Coordinate bond | -1.6 | 0 |
| N | 12.5 | - | 3-membered ring | 17.0 | 12.3 |
| Cl | 54.3 | 55.2 | 6-membered ring | 6.1 | 1.4 |
VISCOSITY AND CHEMICAL CONSTITUTION
Viscosity is largely due to the intermolecular attractions which resist the flow of a liquid.
Therefore, some sort of relationship between viscosity and molecular structure is to be expected.
Viscosity is also dependent on the shape, size and mass of the liquid molecules. The following general rules have been discovered.
1. Dunstan Rule
Dunstan (1909) showed that viscosity coefficient (n) and molecular volume (d/M) were related as
d/M x n x 106= 40 to 60
This expression holds only for normal (unassociated) liquids. For associated liquids this
number is much higher than 60. For example, the number for benzene (CH) is 73, while for ethanol (C₂H₂OH) it is 189. This shows that benzene is a normal liquid, while ethanol is an associated one. Thus Dunstan rule can be employed to know whether a given liquid is normal or associated.
2. Molar Viscosity
The molar surface of a liquid is (M/d) 2/3. The product of molar surface and viscosity is termed molar viscosity.
That is,
Molar Viscosity = Molar surface × Viscosity
=( M /d) 2/3 x η
Thorpe and Rodger (1894) found that molar viscosity is an additive property at the boiling point. They worked out the molar viscosity contributions of several atoms (C, H, O, S, etc) and groups. From these, they calculate the molar viscosity of a liquid from its proposed structure. By comparing this value with the experimental one, they were able to ascertain the structure.
3. Rheochor
Newton Friend (1943) showed that if molecular volume (M/d) be multiplied by the eighth root of the coefficient of viscosity, it gives a constant value [R]. The quantity [R] is termed Rheochor.
M/d × η¹/8 = [R]
The Rheochor may be defined as the molar volume of the liquid at the temperature at which its viscosity is unity.
Like parachor, rheochor is both additive and constitutive. However it has not proved of much use in solving structural problems.