CAPÍTULO V EVALUACIÓN AUDITORÍA DE CUMPLIMIENTO

11 ::::�:

v

e

where

6G•

is the energy of activation of the molecule to the mobile state.

Let A be the distance between equi librium positions in the direction of flow and A1 A2 A3 be distances bet�een neighbouring molecu les in the three

directions at right angles. Using the theory of absolut� reaction rates and postulating a symmetrical potential

energy barrier

Shearine-

( f

without shearing force

fore"'

with respect to another the applied force on & sing le

molecu le in direction of motion is f A2 A3 as A2 A3 is offective area per molecule.

He

nce the energy acquired by a molecu le at the

top of the barrier = fA2 A3 x

�

A

=

�f

A2 A3 A

29 t imes a mo le cule pas s e s o ver the barr ier per s econd is:-

F� and F are the partit i on f unctions for unit vo lume of mo lecu le in act i vated and in it ia l states .

Specific rate of flow in the forward direction i s

K.r F* =

liF

= xe

if A.2 A. 3)./kT

and in the backward d ir ec t i on

Hence the distance moved by a mo le cule per s e c ond is XfA. in one direction and xb). in the other .

• • Nett rate of f low in fo rward direction

by

l:lu =

r..(-q

- ')(b)

or Au = 2). x s i nh

f A.2 A. 2kT

( From above equat i on But we know by defin it ion that

Now

2kl' »

fA.1 Llu , = n = s inh

2). 3A

_/2kT) fA.2r..

3

A and on ex pand i n g

6 u is given

From above • • ,., A1 1Cr _3"i\."2 'K = kT F"' _eo/k'I' 'K ..

hF

e :: _{e o} e /k'I' Eyring here assumes that ·x

he obtains Nh F Tl= v F" e /kT e o 30 F

or replacing

plil

by ( _h

i

Vf� (which is equal to the 1 ratio of the partition functions).

N 1_ 1

fb

/k'l'

TT = V v f 3

(

2 II MkT

) �

e

The assumption that � = A1 =

�*��

appears to the author to be rather doubtful. This distance would be expected to lie somewhere between

�N�.;

and

�*j-!

- b

-3-

and. probably much closer to the latter.

• • •

Assuming that A =

�*�i -b�Nt�-!

T1

( b

�

1 depending on cell shape. The most likely value is b � 2) Nh _�

_E...

_Eb/kT

=

v-; F e ... Nh F

i*

Nh 2 1 V + b V3Vt3 F 1 F,.. vr� c0/kT e eo/k'l' e

31

N

= ₂

b f.;(

1. 1

t0/kT

2 II Mk'.l' )

�Vi� e

� or since K e0/kT e = t.

G

*/RI' e

Here, as in the equations of Bosworth, McLeod and others, the viscosity is inversely proportional to the

free

volume.

The replacement of

���i

by will increase the values of T') by a factor of approximately

1· 5

-

3.

This equation reduces to Eyring's for liquids

with small free volumes,

i. e.

vr;o f*l!, -

b

(

Y

�j

k =

(*li

and so we are left with

n = Nh

F

e

Co/kT

v :F*

Powel l, Roseveare and Eyring33 using their

equation T1 = e t.G..,. /RT found tha

t

6G* was a function of the energy of vaporisation of the liquid,

i ;tt ___

• e,

6 G

_{2 •45}

Since the energy of activation for viscous flow is related to the work required to form a hole in the liquid the

32

experimenta lly observed activation energy 6Evis may be

expected to be some fraction of 6Evap'

i.e. 6Evis =

n

Eyring finds the following values for n at n = 3 for CCl4, C6H6

n = 4 for CS2 1 CHCl3, Ether, Acetone n = 2�4 for water.

i.e. liquids with smaller free volumes ( o3Vf) have smaller

values of n.

The activation energy for viscosity 6Evia d iffers

•

from the free energy of activation 6Gvis on account of

the entropy change accompanying activation for viscous flow.

J:t,or gases (where V::f!:t,Vf) the author's equation for viscosity reduces to that obtained by Eyring2l,34·

e.g. T} =

1

( 2 IT

mkT)�

F

for the ratin p�.

From the above equation for viscosity it should be possible to calculate values of Vt when 11 and 6Evap are

known. This equation wi ll be referred to later in

connection with rates of s olution of gases where it is found to give much better agreement with experiment than

33

that of Eyr1ng et al. Prigogine4° found that values of �calculated from Eyring's equation were closer to the experimental values when values of Vf calculated from the

Lennard-Jones model were used. Summarising these

re lationshi ps between free volume and quantities capable of experimental measurement we have:- o3vf = Vf = ul. _lq Uliq

:::

:::

ET P e RT v 1

J(3":0cpp

((3cp

adiabatic compressi--· _

)

bilit:;

Nh

1 ₂ 41 e nR1; =

V

- 2b

V 3v

f � + b

V 3V

f

3

CORRELA'I'ION O:P GAS SOLUBILI'l'Y wiTH

PROPERr.riES OF 'l'HE SOLVENT

Many attempts have been made to discover

regularities in the solubility of gases.

G.

Just36

34

found that the solubility of one gas in a solvent may be found approximately by multiplying its solubility in another solvent by a factor which depends only on the solvents and not on the gases. He also observed a negative correlation between the refractive index and

the dissolving power of solvents. Skirrow37 and0hrdstoff8

found that surface tension and dissolving capacity are negatively correlated. This was also noted by Uhlig11 who found

ln y

where Y is the Ostwald coefficient.

i. e. a pJ.ot of ln y against a for one gas in a number of

solvents is linear.

Sisskind and Kassarnowsky7 examined the relation between electric polarisability, dipole moment, and solvent

power. An increase in either of these two appears to increase the solvent power but certain deviations are found. Hildebrand39 discussed the influence of cohesive forces on solubility and expressed these in terms of

35 more or less regularly as the function

(� )

a

�

increased .

He ascribed the discrepencies as d id �ammann41 to t he

d isconcertin g lack of agreement of the pub lished data . ihen it is remembered that the internal

�

o E )

press ure oV

)

appears in the equation for free volume

'.I.'

:::

[

_{( �E/�V) T} RT

-�3

_

it seems very likely tha t the solubility of any one gas in a number of solvent s should be pro�ortional to t he

free vo lumes of the solvents or to the product

�Vf ,

On plottin g values of YVl

[

i. e. solubili t y

conv

e

rted to 8 mole f ract ion basis

]

against o3Vf the author found that for a number of gases the points scattered about straight lines with remarkably small deviations when the accuracy of the data used was con­

sidered . ( Table II I . Graph I ) .

V c.-. lues of o3v f are only a va i lab le for a few solvent s so t hat from the remaining solubility figures

values of o3 for the solvent may be calculated and compared w i t h known o 3 va lues . Va lues ca lculated in this way are

compared in �nble IV with values from the work of Eyring

and Frank c::.nd Evans.

Frnnk and Evans calculate va lues of � from

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