CHAPTER
6
Rate of dissolution of salt
270
OBJECT OF THE STUDY
Huge quantity of common s a l t is used fo r the
manufacture of soda ash and ca u stic soda. Here s a l t is
dissolved in water to prepare sa tu ra te d .o r nearly satu ­
ra te d so lu tio n p rio r to i t s fu rth e r processing to obtain
the f in a l product. Mostly soda ash manufacturers in India
have th&ir own s a l t works, which supply th e ir s a lt demand
but cau stic soda manufacturers purchase s a l t from d iffe re n t
s a l t works. Sometimes soda ash manufacturers also purchase
s a l t from other sources.
For both these in d u stries good
q u a lity of s a l t is the f i r s t need, but when s a lts of
sim ilar q u a lity are av ailab le se le c tio n can be made on the
b asis of th e ir d isso lu tio n r a te s . The process of d isso lu tio n
consumes some amount of energy, so by selectin g a quick
dissolving s a lt,- good amount of energy is saved when
large q u an tity of s a l t consumed by these in d u stries is
taken in to account. Thus i t a ffe c ts the economics of the
process to some e x ten t.
-The object of the present work is to obtain
the comparative ra te s of d isso lu tio n of various eommon
s a l t samples and to c o rre la te them with th e ir physical
p ro p e rtie s . This r e s u lts may be u sefu l fo r the above men­
tioned in d u s trie s . Attempt is also made to c a lc u la te the
d iffu sio n c o e ffic ie n ts of some s a l t samples from the
equations given in the available lite r a tu r e .
RELEVANT LITERATURE ON RATE OF DISSOLUTION
Large number of publications have been devoted
to the applied and th e o re tic a l studies of ra te of d isso lu ­
tio n of s a l t . The r e s u lts of these in v estig atio n s are
271
q u ite u s e fu l p a r t i c u l a r l y in s a l t in d u s try and chem ical
f a c t o r i e s , Humber of w orkers have a ls o s u c c e s s fu lly
u t i l i s e d th e r e s u l t s of d is s o lu tio n r a t e s of s a l t as one
o f th e methods of physico-ch em ical a n a ly s is ,
F iek s71 was one of th e f i r s t w orkers who
ex p lain ed th e r a t e of s o lu tio n on t h e o r e t i c a l b a s is
as e a r ly as in 1855, and en unciated th e law which i s
w e ll known as F iek*s Law of d iffu sio n * One of th e ways
of s t a tin g th e law i s to say t h a t th e q u a n tity of s o lu te
d s , which d if f u s e s through an a re a fa i n tim e d t , when th e
c o n c e n tra tio n changes by an amount dc, through a d is ta n c e
dx a t r i g h t an g les to the p lan e of A, i s g iv en by th e
e x p re ssio n d s /d t a —DA.de/dx_,where D i s a c o n s ta n t.
Further,,W eber72 showed th a t d if f u s io n c o n s ta n t d ecreases
as th e c o n c e n tra tio n r i s e s . Noyes and Whitney73 proposed
th e fo llo w in g e q u a tio n t o e v a lu a te th e d if f u s io n c o n s ta n t,
-aS -
s K ( Cs —C)
where C = c o n c e n tra tio n of s o lid
in s o lu tio n in th e
beginning
Cs z c o n c e n tra tio n of s o lid
in s o lu tio n a t s a tu r a tio n
dc s c o n c e n tra tio n of s o lid a t
tim e £
K s d if f u s io n c o n sta n t
They used two s l i g h t l y so lu b le compounds- f o r t h e i r work
v i z . benzoic a c id and le a d c h lo r id e . These s a l t s were
c a s te d in to sm all c y l in d r i c a l s tic k s and d isso lv e d in w ater
i n a wide mouth b o ttl e k ep t w ith continuous r o ta tin g
movement in a th e rm o s ta t. The r e s u l t s o b ta in ed , supported
74 75 76 78
th e law d eriv ed by them . Number of o th e r in v e s tig a to r s * 9
272
have reported evidence in favour of Noyes and Whitney* s
•70
law in various kinds of reaction. Wood et al
carried
out the first practical study on the effect of agitation
on dissolution rates’. They measured the rate at which the
mixing of strong salt solution and a supernatant water
layer took place under different stirrer speeds. The
whole experiment was carried out in a wooden tank of
2700 litres capacity having a paddle agitator in centre.
The distribution of salt was determined by means of
electrical conductivity measurement at various
fixed
points.
Murphree80 studied the rate of dissolution of
soluble crystals and worked out the mathematical formula
based upon the change in the characteristic linear dimen­
sions of the average crystals, during the progress of
solution. His formula is based upon Noyes and Whitney*s
law, which he further elaborated by including the terms
signifying weight, dimension and concentration before and
after the experiment. He has dealt with four cases viz.
(1) the weight of crystals going in solution is not suffi
cient enough to saturate the solution,(2) the weight of
crystal is just sufficient to saturate the solution,
(3) the weight of the crystal is slightly more than suffi
ctnd.
cient to make the saturated solution^ (4) the weight of
crystals is very large compared to the amount required to
saturate the solution. Murphree supported his law by an
experimental evidence of rate of dissolution of potassium
dicfcpomate in laboratory scale experiment.
273
The quantitative approach to the study of agita­
tion in dissolution rate was advanced
by Hixon and Crowell81,
who used a diffusion rate constant as an index of agitation
in numerous experiments.
These authors integrated Noyes and
Whitney*s equation after expressing surface area of the
dissolving
solid in forms of weight* The resulting function
in which the cube root of the weight
of solid appears as a
term, was called "cube root law". This will be termed as
equation 1 for future reference. The equation Is as follows:
K ■ W q 1^
—
W V 3
where
K
m diffusion constant
W0
r
W
- weight of substance
remained at time %
after dissolution
initial weight of
the substance
Special cases were defined for initial weight
of solid equal to that necessary for saturation and for
systems with negligible change in concentration. Considerable
study of the effect on diffusion rate constant by agitation
variables, such as size of equipment, agitation speed, fluid
0 9
viscosity and such other was made by Hixon.and Wilkens
.
Wilhelm et al83 advanced the study further and
developed Noyes and Whitney's equation. This equation was
integrated by them taking into consideration the volume of
water used, amount of salt taken, size and shape of salt
particles, concentration of solution and increase in volume
of solution as dissolution of
solid salt proceeds. They
have assumed that salt particles
are freely auspended in
water or solution during dissolution process. The final form
of the derived equation is given below* This equation will be
274
term ed as e q u a tio n 2 f o r f u tu r e r e f e r e n c e .
2 /3
Z (P)
Vi
K *
1 /3
2 /3
9 a (n)
Ws
where
K s
d if f u s io n r a t e c o n s ta n t i . e . w eight of
s a l t d isso lv e d p er u n it tim e p er u n it
a re a
p
d e n s ity of s o lid , gms. p er c . c .
s
Vi s
i n i t i a l volume of w ater tak en f o r d is s o ­
lu ti o n i n ml.
q
s
tim e i n m inutes
a
s
shape f a c to r
n
*
number of p a r t i c l e s
Ws «
w eight of s a l t i n gms. re q u ire d t o s a tu r a te
th e volume of w ater ta k e n f o r th e experim ent
Z
v alu e g iv en in th e fa m ily curves in P ig .48
a t known v alu es of X and X.
x
X s weight of s a l t in gms. In s o lu tio n a t tim e Q
• ~ w eight of s a l t i n gms. re q u ire d t o s a tu r a te i t
„
1
*
w eight of s a l t i n gm s.taken f o r d is s o lu tio n
e x p e r i m e n t _______________________________
w eight of s a l t i n gms re q u ire d f o r s a t u r a t ­
in g th e s o lu tio n
E xperim ental evidence has been p rese n ted t o show
t h a t t h e i r d e r iv a tio n Is v a lid over e n t i r e c o n c e n tra tio n range
of sodium c h lo rid e s o lu tio n . They s tu d ie d th e r a t e of d is s o lu ­
t i o n of rock s a l t samples of v a rio u s p a r t i c l e s iz e ranges and
■r observed
y
th a t th e d if f u s io n r a t e c o n s ta n t d ecreases w ith th e
d ec re ase i n p a r t i c l e s i z e . T heir ex p erim en tal r e s u l t s are
summarised in Table 80.
£75
o
/ ■- ,osi;
ib : •
is
:' ? \ . ® '
Ficf’Q-8 Inieofi^al curves i*ela lin g tki^ee Variables
Ib^ljandZ C A fhr Wilhelm e l a l)
A'
%i s '
.V / ' U v
276
fa b le 80 : Experimental r e s u lts of ra te of d isso lu tio n
of rock sa lt;1of various' p a r tic le s iz e s
(a ft e r Wilhelm e t a l )
Experimental conditions
V essel used
-
Stoneware crock of 25 cms
diameter and 30 cms height
Volume of water
-
10 L itres
P ropellar rpm
-
1725
Temperature
-
15 - 16°C
gms*of
s a lt
• N o.of
, p a r tic le s
1
716
3060
5 .9
0 .2
0 ,6 1
2
1432
6100
5 .9
0 .4
, 0.60
3
2148
9190
5 .9
0 .6
0.58
4
2864
12230
5 .9
0 .8
0.59
5
3580
15300
5 .9
1.0
0.67
6
4296
18380
5.9
1.2
0 .5 6
7
1432
2820
7*7
0 .4
0.68
8
1432
14320
4 .4
0 .4
0.57
9
1432
35800
3 .3
0 ,4
0.52
L0
1432
ISO600
1,9
0 .4
0 .5 0
Exp.
Ho*
Average
diameter
in mm
J
K
FACTORS AFFECTIKG HATE OF DISSOLUTION
The factors affecting rate of dissolution can be
grouped as follows :
Factors concerning solid.
Factors concerning solvent.
Factors concerning both solute and solvent.
Other factors.
Factors concerning solid *
The rate at which a given mass
of solid dissolves in liquid depends upon following,other
variables being constant.
The rate of dissolution should be directly propor­
tional to the specific surface of solute which is the average
surface area per unit weight. The effective surface area in
turn depends upon the particle size, shape and physical
nature of the crystal. Thus, the uniform,spherical and compact
solids should give less rate of dissolution than irregularly
shaped, fractured and porous crystals. Different faces of
many crystals show anisotropy i.e, their physical properties
differ from
one face to another. This may have certain defi­
nite effect on the rate of dissolution.
All the solids or soluble substances have a definite
diffusion coefficient for a given solvent at particular
temperature. So, if other conditions are identical, the rate
of solution of two different solids should be proportional to
their diffusion coefficient.
Factors concerning solvent t
The movement of solvent in
contact with the surface of solid i.e. layers Immediately
adjacent to solid surface
is most Important In deciding the
278
rate of solution. The presence
of solute in solvent
affects the rate of solution and usually as the concen­
tration of solute in solvent increases, rate of solution
decreases. Similarly increase in temperature increases
the rate of dissolution of solute unless it has inverse
solubility. Temperature also affects the viscosity- and
therefore the movement of solvent and so.,with the increase
in temperature of solvent the rate of dissolution normally
increases.
Factors concerning both solute and solvent :
If the solvent
reacts chemically with solute, the products of reaction
formed, can decrease or increase the rate of dissolution.
Thus, when lime is added to sea water, magnesium hydroxide
deposits around the calcium oxide particles and forms a
protective layer which stops the further
solution of lime
in water. Similarly when zinc is dissolved in sulphuric acid,
hydrogen gas liberated?agitates the solution and rate
of
dissolution increases.
The relative density of solute, solvent and solution
have much to do on the rate of dissolution. The density
difference can set up
the currents and movement of solvent
which may increase the rate of dissolution.
The proportion of solute and solvent governs the
amount of total interfacial contact surface and therefore
other factors being similar, the rate varies according to
the contact, eurface between two phases.
Other factors s The average intensity of movement of the
solvent may be higher or lower compared to the solvent film
in immediate contact of the surface of solute. Fluctuation
279
in this causes variation in rate of dissolution. When
the particles of solute are stirred in a beaker like
cylindrical vessel, they get suspended at suitable
speed of stirrer.
Uniformity of agitation of solvent
distributes the solute uniformly throughout the mass
of solution but fluctuating stirring causes variation
and Influences the rate of dissolution.
DETERMINATION OF THE HATE OF DISSOLUTION OF VARIOUS SALT
SAMPLES UNDER SIMILAR EXPERIMENTAL CONDITIONS
The salt samples used in this study were those
used in washing experiments and their chemical composition
and physical characteristics have been described earlier
fen page 95. The salt samples were either dissolved as such
or fractionated to obtain required particle size range for
dissolution experiments. The method of dissolution was
batch as well as continuous.
Batch method
Beaker
** Stainless steel, capacity 4 litres
23 ems height and 15 ems diameter
with a baffle arrangement
Stirrer
-
Quantity
of water
-
Quantity of
salt
-
Electric motor driven, with three
propellars, covering area 7.5 ems
and speed 1000 rpm
3 litres
1.125 Kg.
The water was taken in the beaker and stirrer was
started. When the stirrer
rpm became steady, the salt was
added to the water in motion, quickly. The stopwatch was
started simultaneously with the addition of salt to the water.
280
A fte r t h i s , , to assess, th e r a t e o f d is s o lu tio n ,, samples, of s o lu r
t i o n were c o lle c te d w hile th e p ro cess of d is s o lu tio n was going on,
a t every one m inute in te r v a l from a fix e d d ep th by f i l t e r tip p e d
p i p e t t e . The amount of s o lu tio n sucked d id n o t exceed 10 - 12 ml,
from which 5 ml was d ilu te d to 50 ml and 10 ml of th e d ilu te d solu-r
t i o n was evaporated f i r s t on w ater b ath and th e n a t 110°C to d e te r ­
mine th e t o t a l d isso lv e d s o li d s . From th e se v a lu e s th e amount of
s a l t d isso lv e d a t d e f in it e tim e i n t e r v a l was c a l c u l a t e d . .
For th ese experim ents Kharaghoda, Bjhavnagar, Porbandar and
T u iic o rln s a l t samples were u sed . For each s a l t samples two e x p e ri­
ments were perform ed to o b ta in th e amount of s a l t d isso lv e d a t
v a rio u s f ix e d time in te r v a ls i n th e experim ents u p to 10 to 16 m inutes
and average am ounts.were c a lc u la te d from th e se r e s u l t s . These r e s u l t s
a re giv en in T able 81, These r e s u l t s a re a ls o p lo tte d as c o n c e n tra tio n
of s a l t i n s o lu tio n in grams p er l i t r e a g a in s t tim e in m inutes and
a re given in F ig .49 .
T able 81 * D is s o lu tio n of v a rio u s s a l t as such by b atch method
Kharaghoda
Bhavnagar Porbandar
T u tic o r in
Grams s a l t n er l i t r e o f s o lu tio n
i
i
r
r
i
V
i
i
i
f
i
i
i
i
i
i
i
i
i
i
199*6
235.9
256.0
273.2
278.0
283.6
287.0
291.8
292.6
296.1
<•
<
i
i
i
199.3
241.2
264.7
278.1
288.1
295.7
301.5
304.1
307.2
311.0
i
i
i
i
t
i
i
i
i
162.4
189.3
208.3
232.0
‘ 231.2
259.1
242.3 ; ■ , 284.5
252.1
288.2
257.6
■295.6
262.9
300.4
269.4
306.9
308.2
273,0
278.8
312.5
281.6
286.3
284.8
289,9
232.6
: 294.2
*•**M
» »
l
•i
5
6
7
8
9
10
11
12
13
14
15
16
——
iI
1
2
’3
i
i
T im e in te r v a l
i n m inutes
-
fig.43- R a te of d isso lu tio n o f s a lt sam ples
a s su ch by b a tc h m eth o d -
T I ME
IN MINUTES
17 r
GRAMS
S A L T /L IT R E OF
SOLUTION
281-
282
Continuous
method
Dissolution
of
of
salt
dissolution
rates
method,
is
5
shown
cms
by
D
a
diameter.
which
is
the
an
a
inside
only
B
tube
end
is
solution
of
for
separately
salt
5
required
was
of
noted
of
the
Tuticorin
and
1.0 K g
Orissa
other
When
glass
than
the
to
of K h a r a g h o d a ,
were
inlet
directions.
flow
rate
kept
definite
With
each
and
became
was
at
pra­
weighed
and
continuously
weight
salt
average
(3
or
5 Kg)
sample
time
for
calculated.
The
Bhavnagar,
determined
tube.
and
fed
bed
which
weighed
was
sample
the
filled
experiment,
salt
keep
was
was
salt
of
and
column
flowrate
out
E
the
the
carried
In
crystals.
reservoir
value,
the
out.
salt
the
C,
allowed
height
experiment
stopwatch.
were
the
valve
whose
which
experiment,
the
dissolve
with
dissolution
the
Then
comes
counter-current
desired
to
experiments
dissolution
rate
for
in
of
salt
at
the
through
experiment.
constant
upto
not
column
adjusted.
the
but
the
travel
i.e.
mesh
and
adjusted.
inserted
level
beginning
salt
it
be
which
length
control
can
constant
the
time
to
to
coarse
continuous
meter
solution
is
by
prepared
1
a
a
In
ctically
3
is
of
with
tube
the
comparison
was
flow
the
column
throughout
F
column
water
a
For
column
tube
small
the
salt
ready
of
to
and
extra
of
which
water
with
and
pass
water
was
inlet
rate
from
constant.
water
kept
an
glass
through
continuously
The
samples
to
fed
the
salt
with
fed
supplied
various
covered
salt
salt
was
t
is
D ?a n o t h e r
The
of
is
tube
such
dissolving
A
suitable
exit
exit
of
continuous
i n F i g . 50.
as
samples
six
Porbandar,
flow
rates
of
283
water by this method. These results are given in Table 82.
To compare
the rates of dissolution of these salt
samples in between them on the baSis of their physical
properties like bulk density, relative hardness and particle
size distribution, these properties were also determined.
Bulk density : Bulk density was determined by taking 1.0 Kg
of salt in 1.0 litre capacity measuring cylinder and tapping
it gently upon the hard surface (wooden table with a cloth
cushion). After 50 taps, the volume of salt in the measuring
cylinder was noted and from the weight and volume, the bulk
density was calculated. Average of 3 consistent readings was
taken.
Relative hardness ; Relative hardness was determined by ball
mill test. 500 gms of -f-5 B.S. mesh-salt was placed in ball
mill with definite number of
balls inside. The ball mill was
run for 1 hour and the salt was removed. The salt was again
sieved through 5 B.S. mesh and from the weight of salt passed
through the mesh, the per cent salt disintegrated was calcu­
lated. This was.taken as a measure of hardness of salt sample.
Here also average of 3 readings was taken into consideration.
Particle size distribution: Particle size distribution was
obtained from the sieve analysis of 1 Kg samples of various
salts. Bp to 5 mesh, British Standard sieves were used but
for coarser sizes, sieves with 6.45, 4.84, 3.23 and 1.61 sq.cms
holes were prepared locally and used. Average of 3 - 5 analyses
was taken for comparison.
Above mentioned properties are also given in Table 82
along with the dissolution rates.
-
fig -so . Sketch of c o n tin u o u s
dissolving column.
284-
4
3
1 .5 0
2.00
43
15
3
50
4
1 .2 5
3
6
1.00
38
4
7
8
0 .7 5
Min.
5
Sec.
8
40
14
39
59
56
Sec.
Bhavnagar
55
Min.
Kharaghoda
0 .5 0
L/mXn
Flow rate
2
3
4
5
Min.
10
30
43
32
4
36
Sec.
Porbandar
2
2
3
3
4
6
Min.
4
5
31
2
18
34
0
Sec.
Tutieorin
D issolution rates
Table 82 s Dissolution rates and physical properties of various s a lt samples
2
2
2
3
4
5
Min.
2
43
37
16
27
55
Sec,
Orissa
285
S f
m
3 .1
*
-4- 8 "
*10
*12
+14
- 5
- 6
- 8
-1 0
-1 2
"
"
"
< 1 .3
1 .3
1 .5
1 .9
5 .5 4
3 .7
5 .7
1 8 .4
11.8
1.0
2 .!
1.0
0 .3 2
4 .0 8
2 1 .7
1 9 .4
12.8
6 .9 3
9 .9
1 0 .9
21.6
8 .9
1 6 .9
0
1 4 .4
o
8.02
■p
c
7 .7
p
9 .1
h
0
p
"
u
C*
0
«
o
4 .6 0
o
a
•H
2 3 .7
p
€
o
5 3 .3
.26.0
0
2 .4
m
o
-P
•H
2 3 .7 0
0
H
P
■103
CO
-1 4
4 .8
- 1 / 4 " * 5 B .S .
3 4 .8 6
1 0 .5 0
0 .9 1
0 .4 4
1 6 .5
6 8 .2
9 .6
9 .3
1.0
2 0 .5
2 4 .8
1 0 .9
2 3 .9
- -
6 "
9 .5
1 5 .9
2 2 .2
1 /4 “
0
- 1 /2 " *
0
1/2"
0 0
p w rl
- 3 /4 " *
■Sit*
3/4"
0)
t, •
1" +
s
faos
-
0to
.
OQ
2 5 .4
oo
•
1"
H
to
to
+
03
4 6 .5
0*
•
CO 00
to
2 0 .8
•
D<0
P a r t i c l e s i z e d i s t r i b u t io n
03
IS
o
to
R e la tiv e hardness
P h y s ic a l p r o p e r tie s
10
B u lk d e n s ity l b s / c f t
T a b le 82 con tin u ed
286
0
287
D is s o lu tio n of f ix e d p a r t i c l e s iz e range of th e ' s a l t samples!
S im ila r experim ents as mentioned above were done w ith fix e d
p a r t i c l e s iz e range v iz . - 6 .4 + 3 * 3 mm ( —
+ 5 B .S . mesh)
of th e same s a l t samples a t two flow r a te s and d is s o lu tio n
r a t e s were compared w ith t h e i r bulk d e n s i t i e s , r e l a t i v e
hardness and approxim ate su rfa c e a r e a . These r e s u l t s a re
g iv en i n Table S3.
T able 83 * D is s o lu tio n ra te s of fix e d p a r t i c l e s iz e of
v a rio u s s a l t samples and t t i e i r p h y s ic a l
p r o p e r tie s
Name of
s a lt
Time re q u ire d f o r th e
Bulk
R elad is s o lu tio n of 1 K g .s a lt d e n s ity t i v e
Flow r a t e of w ater
~ l b s / c f t h ard .....r'1".......... .. '...11
ness
0 .5 I»/min.
1 .0 L/mln.
Min.
S ec. Min.
S ec."■
Approxi­
mate
s u rfa c e
a re a
sq.m ./Kg.
Kharaghoda 7
42
4
47
69.3
16.2
12.3
Bhavnagar
6
53
4
5
58.0
25.0
2 3 .4
Porbandar
6
44
.4 '
15
6 0 .4
29.0
2 4 .4
T u tic o rin
6
55
4
15
56.0
27.0
2 8 .7
O rissa
6
42
4
11 .
51.0
45.6
31.5
X X
*
The r e s u l t s of Tablesi 82 and 83 are p lo tte d g r a p h ic a lly andv are giv en in fig u re s
51 and 52.
'
8 -
9■
fO
If
12
PLOW
1o
IN
1 leg, o / s a l t s a m p le
1-25
— «—
S
^
Ift
_ i_
^
■saxnutw ni 3w ix
--- a-----•f
- * — ----- M---- -----M ----------
---- 9 -------- 1 ----— m— — p ---------
111........
H--------------- — i— -----4---------
--- a— -r*--■-— ■— -•--^ 1 .48
— i--- j
--- x— -*— -H--H— -X---
LITRES. PER m i n u t e
•So
TUtlCOklM
20
-4---------- 1POR&AHOAR
-¥ --------- ¥ BHAVNAGAR
- • ---------« KHARAGMOOA
i n c o n i i nMOUS dissolving
of
-M-
RATES
/ l o w r a te s
d is so lution
-
<SA-
colum n.
o/
d iffe re n t
sh o win g r a t e
a s suck, a t
Ckart
I)
\
•N
288 -
•«-
*-
<
at
O
5
in
---- ■------ ■------ ■------ a------«------ »-------
--^----
--- 1
------*---—*— —X—---K---—M——*4------
8
6
IA
-I____ L.
•sjxnmw
«J>
if)
i f
ni
su m .
Kl
«\|
FLOW
RATE
IN
coniin«ou5
LITRES.
co l umn
PER- MINUTE
dissolving
-«
-t
O R IS S A
TUTICOR1M
PO R b a n d a r
-K BHAVNAGAR
-* kharaghoda
Fig-51 Chart s h o w i n g y-ate of d i s s o l u t i o n o f l-k.g of fixed
p a r t i c l e si?e r a n g e of sa lt at d i f f e r e n t / low •rates
-
6
ID
289 -
i
i
290
Evaluation of results :
When the rates of dissolution of Kharaghoda,
Bhavnagar, Porbandar, Tuticorin and Orissa salt samples
as composite salt samples are
compared from the results
given in the tables 81 and 82, it
will be observed that
Kharaghoda salt dissolves at slowest rate in water in
batch as well as continuous method, than rest of the sea
salt samples. On the
otherhand, seasalt samples viz,
Bhavnagar, Porbandar, Tuticorin and Orissa show practically
similar rates of dissolution under identical experimental
conditions. The similarity of rates of dissolution of
sea salt samples can be explained on the basis of their
bulk densities and particle size distribution. The bulk
densities of composite salt samples of Bhavnagar, Porbandar,
Tuticorin and Orissa are 65.2, 68,7, 67,4 and 60.7 Ibs/cft.
respectively (Table 82), which can be considered similar .
that
except/of Orissa salt which is lower. Secondly if now
particle size distribution of these salt samples is compared
from.the same table, it will be observed that Porbandar,
Tuticorin and Orissa salt samples show broadly similar
salt
distribution of, various size crystals except Bhavnagar^/which
is some what coarser. Relative hardness of these salt samples
however shox/ed irregular trend and could not be correlated
with their dissolution rates. Similarly when bulk density,
particle size distribution and relative hardness of Kharaghoda
salt is compared with the rest of the samples one can easily
explain the slowest rate of dissolution of it,compared to
other salts, Cinder same conditions. Thus the reasonable
cause for the slow dissolution of Kharaghoda salt is its
291
maximum b u lk d e n s ity 77*8 l b s / c f t , p resen ce o f c o a rs e s t
s iz e c r y s t a l s and c r y s t a l ag g reg ates and maximum r e l a t i v e
hardness 3 .2 i n com parison t o a l l se a s a l t sam ples, . ,
These o b se rv a tio n s a re a ls o v a lid f o r the d is s o lu ­
tio n r a t e s of f ix e d p a r t i c l e s iz e range of th e se s a l t samples
(T able 8 3 ) . Here i t w i l l be seen t h a t , Bhavnagar, Porbandar
and f u t l e o r i n s a l t samples have s im ila r b u lk d e n s itie s which
a re 58, 60 and 56 l b s / c f t , s im ila r r e l a t i v e hardness 2 5 , 29
and 27 and s im ila r c a lc u la te d su rfa c e a re a s 2 3 , 24 and 29 sq.m*
p er Kg.and th e re fo r e have s im ila r r a t e s of d is s o lu tio n . On th e
o th er hand Kharaghoda s a l t has h ig h er b u lk d e n s ity 6 S .3 l b s / c f t ,
h ig h er r e l a t i v e hardness 16,2 and lower s u rfa c e a re a 12.3
sqm/Kg show co m p arativ ely slow er r a t e of d is s o lu tio n . O rissa
s a l t though showed s im ila r r a t e o f - d is s o lu tio n as form er
th r e e sam ples, i t s p h y s ic a l p r o p e r tie s could not be c o r r e la te d .
The r e s u l t s of r a t e o f d is s o lu tio n of v a rio u s s a l t samples
from T a b le 8 1 , 82 and 83 have been g r a p h ic a lly re p re s e n te d
i n f ig u re s 49, 51 and 52 f o r easy and re a d y com parison.
DETERMINATION OP DIFFUSION BATE CONSTANT OF SALT BY
EQUATION 1 AND 2
As mentioned e a r l i e r e q u a tio n 1 and 2 a re m o d ifi­
c a tio n s of Noyes and W hitney's law . The form er has been d eriv ed
by Hixon and Crow ell81 and l a t t e r by Wilhelm e t a l 83. They a re
as follow s*
K
K
E q u atio n 1
Z ( p )2/ 3
1 /3
9a (n ) '
*• **O
E q u atio n 2
292
The meaning of various terms in these equations
has been defined earlier. To calculate the diffusion rate
constant in equation 1, it is necessary to know the values
1/3
1/3
of W 0 *
and W ' . These values can be easily calculated
from the amouht of salt present in solution at
zero time
or beginning l.e. W Q and that present at time t i.e. Wt .
Now suppose that the amount of salt present in solution at
various time intervals are W0, Wt.-j_ , Wt2 , Wt3 and so on,
for finding out K value for first time interval, values
1/3
1/3
Wo
and
are calculated and from their difference
K is obtained. Similarly for finding out K for second time
1/3
1/3
interval values Wt^
and Wtg
are calculated and their
difference gives the required K value.
Thus for subsequent
time intervals K values can be calculated and average of
these is diffusion rate constant K.
Dissolution experiments with fixed particle size
range -6 *4*«8 B.S. mesh of Bhavnagar, Porbandar and Tuticorin
were carried out in duplicate by
batch method and K values
were calculated for various time intervals by equation 1, as
described above. These results are given in Table 84 along with
the common conditions of experiment*
0
For calculating K values by equation 2, it is
necessary to know all the values of the terms given on
right hand side
of it. This is slightly complicated and
is made clear by following sample calculation.
Samgle^calcuJLation s 3 litres of water was agitated by
power driven stirrer. To the water 1075 gms. of -6 +*8 B.S.
mesh size salt was added. After an interval of 1 minute,
the solution was analysed and found to contain 225.1 gms
of salt per litre of water. The solubility of salt was
o f w etter'
taken as 358 gms per litreAas that of pure sodium chloride
at room temperature (20 - 25°C). The number of particles
of salt in 1075 gms of salt were 70530 (calculated by
weighing five sets of 100 particles and finding average
value which was converted for total weight of salt ). The
density and shape factor of salt particles viere taken as
given by Wilhelm in his paper i.e. 2.16 gms/cc and 6.2
respectively. The value of Z wasc obtained from X and Y.
X » .
Y
z
Weight of dissolved salt in
initial volume of water at
.Q . --- -- ----------Weight of salt in gms
required to saturate the
initial volume of water
Initial weight of salt taken
f o r .the experiment__________
Weight of salt in gms required to saturate initial
volume of water
s
”
225.1^5, o
1074,---- '
1075
1074
,
Now from the family curves given in lower part
of Fig.48 at the above
X and
Y value, the value of Z is
1.75. Placing all these values in equation -2, it becomes
295
2/3
K
1.75 x (2.16)
x
1
17a
1 X 6.2 X (70530)
30Q0 2/3
. 0.33
=
x (1074)
Bhavnagar sea salt sample of different particle
size range was dissolved in water under identical experimental
conditions by batch method and samples of resulting solution
were drawn at every one minute intervals. From these samples,
the amount of salt dissolved
at definite time interval was
found out and corresponding K values were calculated as shown
above. Z values were taken from the graphs given in Fig.48.
The results of these experiments are given in Table 85 along
with the common conditions of experiment.
Table 85 : Rate of dissolution of various particle size
' £ a n g ! Q £ Bhavnagar salt ln terms of diffus ion
constant K
Experimental conditions
4 L capacity, with
baffle arrangement
3 L
Beaker
Volume of water
taken for dissolu­
tion
Time in
minutes
Wt.of salt taken
1.125 Kg
Stirrer r.p.m.
750 - 800
4-
s
1
2
. K
0.53
0.45
3
4
B . S . mesh
-
.
5 4 -6
-64-10
-104-ife
K
0.12
0.11
0.10
K '
0.39
0.34
K
0.33
0.28
0.41
0.30
0.26
K
0.17
0.13
0.13
0.34
• 5
0.37
0.39
0.23
0.22
0.13
0.12
0.10
0.10
6
7
8
9
10
0.38
0.34
0.33
0.30
0.28
0.22
0.22
0.20
0.18
0.17
0.11
0.11
0.11
0.11
0
0.099
0.098
0.099
0.099
0.099
0.37
0.32
0.27
0.24
0.21
0.20
296
Evaluation of results
Prom the
results given in Table 84 it will be
seen that the diffusion rate constant K calculated by Hlxon and
Growell's equation does not show consistency. In duplicate
experiments also fluctuations in K values when compared at
same time Intervals are
wide. In the individual experiments
also, it first increases, reaches to a maximum and again
decreases. In between 20 to 80 second time interval the
deviation from one another is less. Hixon and Growell have
carried out numerous dissolution experiments by subjecting
solid and liquid to various types of agitational movement
and claimed that the K values calculated by equation 1 in
each experiment showed only 3 to 5 per cent deviation from
an average value. However, the present experiments with sea
salt samples given in table 84 show that applicability of
the said equation is not good.
From the results given In Table 85 It Is seen
that diffusion rate constant, calculated by equation 2 shows
better consistency. It sho\i*s $ood consistency for finer
particle size ranges viz. -6 4-8, -8 -f*10 and -10 4*12 B.S.
mesh than coarser particle size ranges viz. 4-5 and -5 4-6
B.S. mesh. For finer sizes it is almost constant from 2
minutes onwards but for coarser sizes it decreases considerably
after 7 minutes. For all particle sizes, the 1 minute values
are higher than subsequent time interval values, which may
be due to some time gap in the adjustment of steady
state of
experiment. From 2 to 8 minutes time interval the deviation
297
in K values
is l e s s .
K
When mean
values
are c a l c u l a t e d b y
a v e r a g i n g 2 t o 8 minutefe v a l u e s f o r e a c h p a r t i c l e
following values were
obtained.
Particle size
B.S. mesh
M e a n K value
5
. 0.38
f s +• e
0.31
•8
4“ 8
0.23
► '8
4“
10
0.12
* 10-1- 12
0.10
The above K values
show decrease with the decrease
i n particle size and confirm the
reasons.
in
these experiments
W i l h e l m et
salt crystals w h i c h are
porous
to seme extent,
t h e r o c k sa l t )
Due
to this
get
salt
former
of
experiment
t a k e n for
whole
rock salt crystals
compact
Secondly,
is l a r g e r
but
out
to sea
f r a c t u r e d and
(obtained from crushing
and f r e e f r o m irregularities.
in the physical characteristics
in the c a s e
one cannot
fractionating the
of latter
it is
t h e e x p e r i m e n t a l s e t u p u s e d i n W i l h e l m ’s
t h a n i n present work.
d i s s o l u t i o n and speed
relative
some deviation was
the
the e q uation b y carrying
d e finite surface ar e a e v e n after
o n f l o w p a t t e r n l.e.
reasons
to be due to following
of h i g h l y i r r e g u l a r shapes,
are spheroidal,
difference
supposed
in*the coarser
in their experiments. C o m p a r e d
in narrow size range,
possible.
is
al have der i v e d
d i s s o l u t i o n of r o c k s a l t
,
o b s e r v a t i o n s m a d e b y W i l h e l m et al.
T h e p a r t i a l i n c o n s i s t e n c y of K v a l u e s
size ranges
size the
of
The
d i m e n s i o n of v e s s e l
stirring have
definite effect
solid liquid movement.
Due t o these
observed i n K v a l u e s h o w e v e r , o n the
a p p l i c a b i l i t y of W i l h e l m ' s
e q u a t i o n is g o o d .