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MEASUREMENT OF ULTRASONIC
VELOClTlES IN AQUEOUS SOLUTION-5
OF SEVERAL SALTS

Thesis {or the Degree 0! M. 3.
MICHIGAN STATE COLLEGE

Alton R. Kurtz
I942

 

 

 

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J LIBRARY
Michigan State
: ,University 7

 

 

 

 

PLACE IN RETURN BOXto remove this medcoutfromyourrecord.
TO AVOID FINE retum on or before date due.
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DATE DUE DATE DUE. DATE DUE

 

XEASURJESNT OF ULTRASOK C VLLOCITISS
IN AQUEOUS SOLUTIONS OF

SEVERAL SALTS

by
Alton R. Kurtz

A THESIS
Submitted to the Graduate School of Kicbigen
State College of Agriculture and Applied
Science in Partial Fulfilment of the
Requirements for the Degree of
MASTER OF SCIEN E
Department of Physics

1942

A CKI‘TO '. .1. 1:3 D (ELISE-IT

I wish to express my most sincere appreciation
to Dr. J.W.‘NcGrath who first aroused my interest
in ultrasonics and whose keen interest, constant
help, and many resourceful ideas have been of
great value to me. I am grateful to all the
members of the Department of Physics for their
encourarement and loan of apparatus. I am indebted
to Mr. Grant S. Bennett1 for part of the apparatus

used. It was constructed by him in 1940-1941.

TABLE OF CO}? LEXIS

Introduction

Purpose of This Research

Method and Apparatus

Specific Procedure

Equations Involved

Data and Results

Graphs

Analysis of Errors

Discussion of Results and Conclusions

Bibliography

Page

13
14
16, 17, 18

19

25

INTRODUCTION

 

Ultrasonic (or supersonic) waves are sound waves whose
frequency is above the audible range. The human ear can
hear sounds of frequencies up to about 20 kilocycles and
ultrasonic frequencies extend from.there upwards, 500,000
kilocycles being the highest frequency that it is now
possible to produce. rhe wave-length range of ultrasonic
sound waves in air is from 1.5 to 0.00006 cm. while the
wave-length of an audible sound whose frequency is, say,
256 vibrations per second (middle 0 on the musical scale)
is more than ‘00 cm. As sound velocity is usually obtain-
ed from wave-length measurements, this shortness of ultra-
sonic waves greatly simplifies measurement of sound
velocities.

fhere is a great concentration of energy in ultrasonic
waves as compared to audible waves, an intensity of 10
watts per cm? being not uncommon in ultrasonic waves as
contrasted with intensities in the order of 10"10 watts
per cm? in audible waves.

7 states that a dispersion of sound velocity with

Rae
frequency has been definitely established in gases but
that such a dispersion in liquids, if it exists, is only

1 or ameters per second and thus within the range of

eXperinental error. rhus, in general, ultrasonic velocit-

ies are the same as audible sound velocities.

Fortunately, the laws of sound which are valid for
the audible range also hold for the ultrasonic range,
although some phenomena appear in the latter which are
not observed in the former. Use of ultrasonics for
velocity measurements in liquids has three outstanding
advantages because of the shortness of the waves. These
are: (1) it is possible to make measurements in a small
space thus eliminating complicated and cumbersome equip-
ment otherwise necessary; (2) the influence of the walls
of the containing vessel, which is so difficult to correct
for with audible sound waves, is negligible with the short
waves; (3) it is possible to make velocity measurements
with small amounts of the medium. Because of these ad-
vantages it has been possible, for example, to make meas-

urements in liquid oxygen and heavy water.

h)
:3
In
C)
O.
I?)

OF THIS RESEARCH

 

Ultrasonic velocity measurements are chiefly important
in that they yield values for the adiabatic compressibil—
ity of the medium. Given this, and the isothermal com-
pressibility derived from static measurements, it is then
possible to calculate the ratio of the specific heats of
a liquid. There is also a good possibility that when
enough data has been accumulated it will be possible

to explain completely the changes of volume and compress-

ibility which occur when salts are dissolved in water.
Velocity measurements have been made in most of the
common organic liquids and the compressibilities computed
but very little work has been done with aqueous solutions
of salts. For this reason the author decided to work in
the latter field.

a series of velocity measurements in various concen-
trations of potassium and sodium halides have been made
by FreyerS. Only a few other investigators have made
measurements in electrolytic solutions and none of them
has dealt with a specific series of salts as did Freyer.
In choosing a series of salts for investigation it seemed
best to choose a series other than those studies by Freyer
in order that there might be a greater range of data from
which to make conclusions. A series of nitrates seemed
the best one to choose because they are easily obtained,
the nitrates of practically all metallic ions exist, and
especially because of their Very high solubility. The
three lowest mono-valent nitrates (potassium, sodium,
and lithium) and two di—valent nitrates of high solubil-
ity (magnesium and zinc) were the ones chosen for the
investigation. both mono—valent and di-valent nitrates
were chosen because the change of compressibility with

concentration was expected to differ in the two types.

METHOD AND AIPARATUS

 

Many different methods have been used for determining
the wave-length of ultrasonic waves in liquids and one of
the simplest and, strdhely enough, least used methods was
chosen. It is an optical method suggested by Bergmanng in
which light from a slit source is allowed to diverge
through the liquid containing stationary ultrasonic waves
and fall on a screen on the other side. The standing
acoustic waves also have associated with them, due to
standing density waves, standing waves in the Optical
index of refraction of the medium. This neans that there
is periodically set up in the medium a row of "lenses"
more or less of the cylindrical type. These "lenses" app-
ear and disappear with a frequency twice that of the ultra-
sonic wave and are spaced at intervals of one-half the
acoustic wave. There appears then on the screen a pattern
of parallel bright and dark lines of arproximately equal
width. If each dark line arises from a nodal point in the
liquid then the distance between the dark lines is one-
half of the wave-length of the sound wave. New 1% the
stationary wave pattern be moved parallel to the screen and
perpendicular to the light beam by moving the trough, the
lines on the screen will move along the screen. If a
point is chosen on the screen, at the center of the light
beam in order to eliminate all distortion, and the trough

moved until one dark line has passed this point, then the

distance through which the trough has moved must be one-
half of the wave-length of the ultrasonic waves in the
liquid. Because of the shortness of the ultrasonic waves
it is possible to cause a large number of lines to pass
the point on the screen by moving the trough a few centi-
meters and the wave-length may then be found by dividing
the distance moved by the trough by one-half the number of
dark lines passing the chosen point on the screen. if the
frequency is Known then the velocity is found by taking
the product of frequency and wave-length.

The Optical system is shown is figure I. The light
source was a 100 watt ribbon filament lamp which was
focused on the slit by a strong condensing lens. The
trough was mounted on a traveling micrOSCOpe base so that
it could be moved perpendicularly to the optical path.

The base Was firmly fastened to an Optical bench about

50 cm. from the slit. The position of he screen was

not critical as the lines could be seen at any distance
within several meters of the trough. However, it was not
desirable to have the screen older than 50 cm. because the
lines were too close together to be counted easily and,
since it was necessary to turn the microscope and count
the lines at the same time, the screen was usually placed
at about 80 cm. from the traugh.

It should be noted that no lenses were necessary between

the slit and the screen. a convergent lens may be placed

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A Bake/Me

5 Brass Leads

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between the slit and the trough to send parallel light
through the trough but the advantage of getting more
distinct lines is counterbalanced by the disadvantage of
bringing the lines closer together a) that the lens was
left out entirely.

The fiducial line on the screen was chosen exactly in
the center of the optical beam so that the light reaching
it would be passing perpendicularly through the trough
and liquid and the distortion would be at a minimum. It
should he noted here that the entire optical system was
fixed and that the standing ways pattern was moved per-
pendicularly to the light beam.

The sound trough was made of highh Optical quality
plate glass and the edges were sealed together with par-
affin. The desensions of the trough were 6 cm. x 7 cm.

x 20 cm., The glass was supported by a brass framework
wnich removed tension from the paraffin joints. Care was
taken to make the sides of the trough through which the
light passed exactly parallel to each other to prevent
distortion of the light beam. At first a trough with a
brass base was used but chemical action on the brass by
the electrolytes made it necessary to construct the trough
entirely of glass. The traveling microscope base had a
fine screw reading to 0.001 cm. It was possible to esti-

mate one more decimal place.

. “(a
In order to get stationary waves it ard' necessary to use

a plane reflector which can easily be adjusted to be
parallel to the crystal. The reflector was constructed
by fastening a flat piece of glass to a block of bake-
lite by means of paraffin. These materials were used
because no metal could be used inside the trough. The
reflector was moved in the plane of the crystal by rotat-
ing the whole block and perpendicular to the plane of the
crystal by means of a plastic screw in the back of the
bahelite block. This screw could be turned against the
bottom of the trough and thus tilt the reflector.

The best way to produce ultrasonic waves is by use of
quartz crystals. When a potential difference is applied
to the faCes of a slab of quartz, the quartz will either
expand or contract in a direction normal to the faces.
When the potential difference is reversed the effect is
opposite to the first. Thus, when an alternating poten-
tial is applied to the faces 0f the quartz, the crystal
will vibrate and produce s and waves. The change in thick-
ness of the crystal, and consequently the particle dis-
placement in the sound waves, is preportional to the po-
tential difference applied. A piece of quartz has a
natural frequency of vibration dependent on its dimensions.
when the impressed frequency is equal to the natural
frequency of the quartz the amplitude of vibration will be
a maximum. The crystal used was an X out crystal with

damensions 2.5 x 2.5 x .11 cm. and a rated frequency of

1802 kilocycles per second. A thin layer of gold was
evaporated on both sides of the crystal in order to make
a good electrical contact without adding appreciably to
the mass of the crystal.

When velocity measurements are made on organic liquids
the crystal may be in direct contact with the liquid, but
'this is not possible in the case of electrolytes for they
conducteiectricity and will not permit the crystal to
oscillate. Therefore it was necessary to isolate the
crystal from the solution. There is an additional ad-
vantage in the isolation if the crystal from the medium
for undesirable heating effects and disturbing striations
will be minimized. The methods tried for the solution of
this problem are worthy of note here.

Laximum s und transmission occurs from one medium to
a third medium when exactly an integral number of half-
wave—lengths of sound occur in the intermediate medium, for
certain specific acoustic resistivity relations. A piece
of aluminum was ground until it was exactly oneehalf-wave-
length thick and was then placed in the end of the trough
with the crystal pressing against it from the outside.
Satisfactory transmissions were not obtained in this way.
Then a very thin piece of copper foil was placed between
the crystal and the liquid across the end of the trough
with the idea that the foil would vibrate as a diaphragm.

But again transmission of the ultrasonic waves was unsat-

isfactory. Finally, a thin rubber diaphragm was placed
around the crystal and crystal holder (figure II) and
when this was filled with ethyl alcohol good sound
transmission was obtained.

The crystal holder is a slab of baKelite with two brass
leads to the crystal on one side and a clip to fasten it
to the end of the sound trough on the other. One lead
goes to a brass plate against whiCh the crystal rests and
the other goes to a phosphor bronze spring which presses
the crystal lightly against the plate as well as acting as
a lead. The crystal is thus held vertically in the trough
so that the wave fronts move horizontally across the light
beam.

It is essential that the front surface of the rubber
balloon be exactly parallel to the crystal face in order
that all portions of it will vibrate in phase. The bake-
lite element F (figure '11) was designed for this purpose
and also to Keep the ruober from touching the spring or
crystal face. The element 3 prevents the rubber fiom forc-
ing the spring too hard against the crystal face.

The space within the rubber enclosure must be filled
with a non-conducting liquid to give the best acoustic
transmission through the rubber. ethyl alcohol was found
to work well for this purpose. The level of the alcohol
inside the diaphragm was found to be quite critical for

if the pressure inside is even slightly different from

that outside at crystal level there will be a sligh
curvature of the diaphragm and it will be unable to vi-
brate as a unit. Thus the greater the density of the
liquid being measured, the greater must be the height of
the alcohol. The alcohol must be very pure in order to
work at all. If it becomes contaminated with a few drops
of water or a tiny drop of solution, the crystal ceases
to vibrate at once. The alcohol must be changed about
every half-hour for best results, either due to a reaction
between alcohol and rubber or due to absorption of water
from the air. This method of crystal isolation has these
advantages: the unit is simple in design, the location
and orientation of the crystal is Oily slightly limited,
mechanical binding is kept at a rinimum, and there is
very adequate ultrasonic intensity transmission into the
electrolyte.

There was a considerable heating effect near the cry-
stal due to some of the energy of the ultrasonic waves
being absorbed. Because of the fact that the velocity
changed with temperature in most liquids, there was
therefore a very slight shift of the standing wave pattern
while a reading was being taken. This was practically
eliminated, however, by carefully stiring the solution
before each naaiing was taken. If unstirred, the temp—
erature gradient directly in the path of the sound beam

may be as much as three degrees in two centimeters close

to the crystal, but due to the large volume, :hen the liq-
uid was carefully stirred the temperature rarely increased
more than 0.3 degree during one trial.

In adjusting the reflector it was possible to get a
good standing wave wnen the tOp was one or two wave-lengths
ahead or behind the base. When this condition existed there
was usually a discontinuity somewhere in the pattern which
could be seen to right itself when the reflector was tilted
slightly. in order to eliminate error due to the possible
lack of parallelism between the crystal and reflector it
was necessary to always very carefully set the relfector
where there was a pattern of maximum intensity.

The acoustic crystal was driven by a crystal-controlled
pentode oscillator. The control crystal was rated at
1806 I 0.03% kilocycles per second. The oscillator tube
was an RK-BOA and was Operated with a direct current po-
tential of 1000 volts on the plate, 300 volts on the
screen grid, and 40 volts on the suppressor grid, all of
these being positive. The power was supplied by a full
wave rectifier circuit with two 866 mercury vapor diodes..
Radio frequency power was transmitted from the oscillator
to the acoustic crystal circuit by means of a link coup-
ling. The coupled circuits were made as nearly alike
as possible so that their impedances would be e ual.l
The acoustic crystal circuit was composed of the cry-

stal in parallel with a coil and a tuning condenser and

in series with a thermo-amgeter which indicated a radio
frequency current of a out .15 amoeres when the crystal
was ocillating prOperly.

In the calculation of compressibility it is necessary
that the density be known. Rather than determining the
density experimentally, the density of the electrolytes
to be measured for several different concentrations were
taken from the International Critical Tables4. Those 70
concentrations were chosen such that the molar concentra-
tions would be about 0.1, 0.5, 1.0, 2.0, and 4.0. densi-
ties were taken for 25 degrees Centigrade. The product of
desired percent concentration and density gave the amount
of solvent neceSCary to make one ml. of solution of that
concentration, and the difference between the density and
weight of solvent was the amount of water necessary. These
were multiplied by 500 as half a liter of solution was
needed. iolar strengths were computed by dividing the
amount of solvent per Liter by the molecular weight of the
solvent. The salts were weighed on a fine cnenical balance
which could weigh to 0.0001 Cram. The water was weighed on
mechanical balances wnich weinhed to 0.01 grams.

‘The salts used were baker's C.P. The water was doubly
distilled and airfree, as any impurities were found to

change the velocity of ultrasonics in it.

H

SPECIFIC PROCEDU;

 

The trough w s filled with solution to a level slightly
above the top of the crystal. r;is took about 450 m1. of
solution. ethyl alcohol was pipetted inside the diaphragm
until it reached a level slightly higher than that of the
liquid outside. The cr~stal in the Control circuit was
made to oscillate by tuning the variable condenser until
the ammeter in the plate circuit showed a minimum va ue and
then the co denser in the acoustic circuit was carefully
tuned until the ammeter in series with the crystal showed
a deflectionl Both circuits were gery sensitive to a
small change in the condensers and had to be tuned very
carefully. With the light beam from the slit passing di-
rectly through the center of the trough and the acoustic
crystal oscillating, the reflector was carefully adjusted
until bright and dark line could be clearly seen over a
large portion of the screen. rhe liquid was carefully
stirred and the temperature taken with a dentigrade therm-
ometer reading to 0.05 degree. 3 dark line in the pattern
was then carefully set on the line on the screen at the
center of the light beam.and the scale reading at the base
of the trough recorded. The same line was then adjusted
to the fiducial line three more times and then the trough
moved until 119 lines had passed the Eiducial line. After

stirring and recording temperature, several readings were

taken on line number 120. About six readings were taken
for eacn solution. he mentioned previously, the fiducial
line should be at the center of the light beam. ihis line
was easily found by moving the screen and observing that
lines on both sides of the center hove toward the center
as the screen was moved towards the source.

To check he crystal frequency, a variable freq ency
oscillator was calibrated with a standard frequency os-
cillator. The standard was frequently checked with a rad-
io station of Known frequency. ihen, mixing the output of
the variable oscillator with the output of the acoustic
control oscillator by means of an electronic mixer, the var-
iable oscillator was adjusted to zero beat in the earphones
and the frequency read from the calibrated scale. It was
possible to read this scale to lO kilocycles per second and

to estimate to l rilocycl per second.

‘UATIONS INVOLVED

m
4‘)

. . -8
Sound waves whose wave-length is greater than 10 cm.

travel adiabatically and so the adiabatic compressibility

may be computed from the equation:7

I
sz. " yfltp
where v is the velocity of the sound waves and (9 is the

density of the medium. The following relationships also

exist: V : ’Z’i—F Z: YET—é"

_. 5" T
(3'25. 934. + '0? flO
where 6%5-is the isothermal compressibility, k is the ratio
between the specific heat at constant pressure and the spec—
ific heat at a constant volume,o@s.the coefficient of
thermal expansion, CD is the specific heat at constant
pressure and absolute temperature T, and J is the mechan-
ical equivalent of heat.
since the densities were obtainable in the International
Critical labies4 and the velocities were measured, all of
the adiabatic compres ibilities were computed.* Since
neither gaarmu'szere known in the second equation for
most of the solutions it was impossible to compute either.
The third equation is given mainly for interest as no
atte pt was made to calculate 9‘1. If on and dwere known
it would be possible to compute @“and fence R from equa-
tion 2. Approximate values for these can be found in the
International Critical Tables4 and Landolt-Bornstein Physik-

alisch-Chemische labellens.

* All compressibilities were computed except those for
zinc nitrate. These could not be accurately determined
because the d nsity was Known only at 180 C. and all the
data was taken at 250 C. The density for zinc nitrate

listed in table I is for l8° c.

TABLE I

AVQRAGE DATA AHD RESULTS

Salt % Cone. molar Density Temp. Wave Yel. Ad._§gmp.
by wt. Conc. g/cm (: length in m/ xlg
incm. sec. cm / dyne
KNO5 1.0 0.0992 1.00524 25.1 .08295 149719 44,425
" 6.0 0.513Jl 1.03479 24.9 308458 ‘ 1511.7 42.2;8
" 10.4 1.0980 1.06095 25.0 .08615 1557.7 40,387
" 18.0 1.987 1.11595 24.9 .08758 1556.1 37,007
" 24.0 2.755 1.15988 25.1 .08500 1581.9 52,452
Nano3 1.00 0.1181 1.0049 25.2 .08586 1499.2 44.274
’ v 4.0 0.4825 1.0254 25.0 .08508 1514.8 42.502
'" 8.0 0.9912 1.0632 25.3 .08764 1556.7 40.208
" 16.0 2.095 1.u18 24.9 .08911 1582.9 35,898
" 22.0 5.000 1.1589 25.2 .08991 1625.9 32,722
" >35.0 5.216 I 1.2668 24.8 .0949? 1715.4 26.827
L1N03 1.0 0.145 1.00287 25.0 ,oggg4 1499.9 44.550
" 4.0. 0.594 1.02054 25.2 .08410 1519.0 42,656
" 8.0 1.212 5.04477 25.2 .08525 1559.4 40,391
" 14.0 2.198 1.08276 25.2 .08754 1577.5 37,113
" 24.0 4.007 1.15125 25.5 .08120 1647.6 51.992
Mg(N03)2 2.0 0.156 1.0119 25.0 .08554 1505.5 43,618
" 8.0 ‘0.571 1.0584 25.5 .08540 1542.5 39,709
" 14.0 1.046 1.1079 24.9 .08746 1579.7 55,169
" 20.0 1.565 1.1607 25.1 .08985 1622.8 32,715
" 24.0 1.958 1.1977 25.5 .09174 1657.1 50,400
.n(503)2 2.0 0.11 1.0554 24.9 .08508 1500.7 -—_
" 10.0 0.57 1.0 59 24.9 .08449 1525.7 _--
" 16.0 0.97 1.1445 25.2 .08600 1555.4 ---
" 50.0 2.06 1.5029 25.2 .09009 1627.2 -_-

TABLE II

CO EXPRESS IB ILITY ANALYSI 8

Salt Slope-k* Log
KNO3 -.0419 .6518-11 44.85 x 1012
L1No3 -.05652 .6500-11 44.65 x 10 '12
NaNO5 -.0454 .6508-11 44.75 x 10-12
Mgm05);», ‘°0879 o6516-ll 44.85 x 10"12
(it for water - 44.79 x 10-12 average - 44.77 x 10"12

EMPIRICAL FORfiULAE
..k(:
.. _. .L
Q'ge V~\/oy_§_e’-KC
P
KNOS Q _ (4., 771/049.) ~.o7b-f¢ V“ .ovtac
__ . c: - "M""’f'—‘Z,§l’c

1 _. .os'nc.
NaN03 (3 ;(+¢.77X/a” J: 10*“: l/=-I‘f46'9y:i%j7'c

7" -. -— .7471 "WI-C
1.11103 (3 20,407“, )6 ”37¢ V-/+4e.9f_;:e

. “.AOABC ,9 .
I"«'i8(N03)2 (,7 :: (4+.77/r/04‘JC V 2: H 71...? [17.47/5 "WI-’-

* The logarithms are to the base 10 so that it is nec-
essary to multiply k by 2.303 in order to write it in the

exponential form.

-17...

TABLE III

VELOCITY FORIULA CHECK

Solution Molar Computed Measured Deviation

Conc. Velocity velocity

KNO3 .0992 ' 1499 1498 {l

.6151 1514 1512 {2

1.0980 1551 1528 f5

1.967 1557 1556 41

2.755 1584 1582 {2

NaNO3 .1181 1500 1499 f1

.4825 1515 1515 ' -2

.9912 1554 1557 -5

2.095 1581 1585 -2

5.000 1625 1624 fl

**5.216 1745 1715 f28

.145 1501 1500 fl

LiNO:5 .595 ‘ 1516 1519 -5

1.212 1558 1559 -1

2.194 1574 1577 -5

4.007 1648 1648 0

Mg(N03)2 .156 1507 1505 f2

.571 1540 1542 -2

1.046 1579 1580 —1

1.565 1626 1625 f3

1.958 1661 1657 f4

_"?

** This point for Nan05 does not appear on any of the

curves because it was not convenient to make the scale large

- 18 -

 

 

 

 

 

 

 

 

 

 

 

 

enough to include it. It was plotted on separate paper
land found to be considerably low so that the fact that it
is so far off here is not due to an error in the equation

but due to an experimental error.

‘1': ‘Vrt‘TI‘ (‘31? TP‘RD"D

I‘. u T 5‘
[114214.1 4.1.14) 4,- -1' .11.)
m — m

Errors occured in taxing the initial and final readings
of the position of the trough because of the difficulty in
setting a line from the projected stationary have pattern
exactly on the fiiducial line. The maximum value of this
error was judged to be 0.0020 cm. and, since the trough Was
moved between five and six centimeters, the maxi um per-
centage error in measuring the wave-length was 1 0.08%.
This is for one neasurerent. Since averages of several
measurements were obtained, the average wave-lengths have a
considerably smaller maximum error.

The salts were weiched on a fine chenical balance to
0.001 cm. and, as the minimum amount weished was 5 grams, the
maximum error here was I 0.02;. Water was weiehed accurately
to 0.1 am. and, the minimum weieht of water used in one
c ncentration being 500 grams, the maximum error here was
10.055. Hence the maximum error in concentration was at
the rest I 0.055. It is possible that there was an error
due to evaporation of water from the solutions while the
measurements were being tanen but such an ef ect must have

been very small and so it was judged to be a negligible source

of error.

_ lg _

The frequency of the control crystal was re ed at 1806

t 0.055 vibrations per second. The method used for check-
ing the frequency was estimated to be accurate within 2 kilo-
cycles per second. heasurenents gave 1506 10.11%. It seem-
ed 1ogica1 to assume that the rated control crystal frequency
was the actual acoustical frequency within the rated value.
The change of frequency when the circuit was being tuned was
new noticeable as a beat note in the earphones connected to
the electronic mixer but the variation was well below the
O . 05,14 .

In all but the first few neasurenents (on HR 3) the
liquid was carefully stirrrd before every reading. This elim-
inated practi‘aily all the possible error due to the existence
of a tenperature gradient in the stationary sound beam be-
tween the crystal and the reflector. It cannot be assumed
that he tenperature is everywhere exactly the same, but, when
the velocity change in pure water is only 2 meters per sec—
ond per degree (less for concentrated solutions), the error
due to temperature may be considered negligible.

The temperature always gradually increased while a
series of measurerents were being taken on a solution. The
temperature or the solutions was therefore taken initially as
240 C. and the readings were taken as the terperature in-
creased so that the averaje would be as nearly 250 C. as
possible. The average value of the tenpe ature in the sev—

eral trials is the value recorded in Table I.

The total maximum error in velocity was therefore es-
timated to be 10.113. This amounts to a velocity range

of 1 1.5 meters per second and a connressibility range of

-‘l O

A.

10.22% or 10.09 X 10 cm” per dyne (assuming the densi-
ties correct).

t 2350 c.

CD

For velocity of ultrasonic waves in water

Freyeré gives the value 1498.1 meters per sec

.4

nxLO E:e

0

states that his results are not accurate to less than one

Q
a (u . -
neter per second. herjrann g‘ves the veloc1ty as 1494 meters
yer sec nd at 240 C. From Freyer's data it can b shown

B

that the velocity of s und in water changes about a meters
per seCond per degree at 240 C. and this correction wvul
sake Bergzann's value 1496 meters rer second at 250 C. The
valueibr ultrasonic velocity in water was found in this

research to be 1496.8 t 1.6 haters per second at 250 0.

DISCUSSION ‘F RESVITS and COKCL7SIOUS

 

 

[‘7

Freyero is the only one who was found to have made a
complete series of measurements on electrolytic solutions
with the Specific purpose of investigating the relation-
ships existinq between concentration, velocity, comrressibil—
ity, and temperature. he measured ultrasonic velocities in
in the sodium and "otassium halides for several concentrations
and temperatures and cogyuted the adiabatic comoressibilities
and the ratio of the syecific heats. he rlotted corrressib-

ilities and velocity against per cent concentration but was

unable to find any empirical relationship between them.
The results of this research check rerfectly with all of his
conclusions and in addition two empirical relationships have
been deternined. So far as the author has been able :o find,
no one has ever previously determined these two empirical
formulas.

fihen the logarithm of the adiabatic compressibility was
plotted against molar conoentration the resulting curve was
a straisht line. role is the deternining factor for an

exponential relationship and it can be expressed as follows:

Q :2 (30 E-KC (1)

wherng is the adiabatic compressibility of the solution whos
nwlar concentration is C, (goitsthe compressibility at zero

0 ncentration or the comprgssibility of pure water at the

ease tenherature, and k is tte slope of the straight line
formed when the logarithm of compressibility is plotted again-
st the molar concentration. 3ee Table 11 for empirical

. l . . .
values. Since ,zry -—-— it follo s that the veloc1t

is related to molar concentration in the following way:

‘i’KC
V: V0 %’ ‘3 (7*)

where V is the velocity of the ultrasonic uaves in a solu-
tion of molar concentration 3 and densityf’, V0 is the
velocity of sound in pure water and (% its density at the

same temperature, (Dis the solution density, and k is the

same constant as that in the first equation. The relation
between logarithm of velocity and molar concentration was
found not linear. The cause is obviously the variable
dersity factor. Thus it is possible to evaluate K directly
only by use of the compressibility—concentration relation.
The values found for(g% from Graph # 3 were so nearly
equal for the different salts that the average value was
taken. rhis average value was 44.77 x 10’12 , While that
for pure water as calculated directly form the measured velo-
. . -12 ,
City and denszty was 44.79 x 10 . Tie value found from
the graph for k in equation 1 was substituted into equation
2 along with the already known factors and the computed
vdues found to check with the neasured ones with-in exoer-
imental error. (Table III). This is cansidered to be an
absolute check on the correctness of the two formulas.
Equation 1 shows that the compres:ibility decreases
exponentially with the molar concentration. This means that
for any Certain increrent, the addition of each increment
of salt to the solution causes the sare fractional decrease
in compressibility. This is not true for velocity because
the density is a function of the concentration. It is well

known that when a soluble salt is dissolved in water the

volume of the water decreases. Bergmannz

(quoting Debye)
suggests the following: when an ion, charged either posi-
tively or negatively, is placed in water the water molecules

are pulled toward the ion because of their high dipole

moment. The electrostatic pressure around the ions is of the
gder of 10,000 atm spheres and ceases the contraction of the
water. This electrostatic pressure causes a decrease in
compressibility in much the same may as does increasing the
external pressure. It seems logical that this effect should
decrease exponentia ly as the number of ions per unit volume
of solution increases.

Bergmann shows t?at the compressibility for the monovalent
salt so utions is greatest for sodium and potassium and sliaht-
ly less for lithium. It is much greater for haanesium. The
empirical results listed in Table II indicate that addition
of mono-valent positive ions to a solution lowers the compress-
ibility exponentially and trat the rower of e is practically
the same for all such ions. alt ough calculations have been
made on -nly one di-valent ion, from the results one may
guess that, in general, di-valent ions lower the compressibil-
ity exponentially also but here the exponent Of crcs, twice
as large. Thus it a“pears that the effect of increasing
concent*ati n on the compressibility depends mainly on the

ion charge and not on the mass or size of the ion.

I
{‘0
r¥>

1

(1)

(5)
(4)

(6)

(7)

BIBLIOGRAPHY

Bennett 0.3. The Production and Velocitv fleas-
, ’
urenents of ultrasonics in several Liouids,
(1941) Thesis, Kichigan state College.

Bergmann, Ludwig, Ultrasonics and Their Scientific
and Industrial nopligatigns, (1957), John
Wiley and eons, New York

Ereyer, E.B., Journal Am. Chem. Soc., 55: 1313 (1931)

International Critical Tables, Vol. g: 52, McGraw-
Hill Book Company, Raw York

Landolt-Eornstein, Physikalisch-Chemische Tabellen,
voi. g: 1261 (1925)

McGrath, J.W., and hurtz, A.R., Rev. Sci. Inst.,
lg: 128, (I942)

Rao, B.V.R. and Ramaida, D.3.S., Phys. Rev., go:
615 (1941)

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