Prakash, Satya

Srivastava, Satish Chandra

English

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VELOCITY OF ULTRASONIC W AVES IN SOLUTIONS OF ELECTRO LYTESSATYA PRAKASH anh SATISH OHAKTDEA SEJVASTAVA*(Dispartmknt of Chemistby, Aelauabad Univeuhity){Rtveived for <puhhcnHon August 21, 1!157)ABSTR ACT. An equation for the veloeily of ultmaonic' waves in solutions of electrolytes has been developed on tlio basis th a t  eloctrostatie forces between the  ions inorease the  ptessure w hereby the volum e elastic iiy  is inereased, incioasing the velocity.Mohanty and Deo (1955) published their results on ultrasonic volooities in teinc and magnesium sulphate solutions at different concentrations and over different ranges of temperatures. Similar experimental results published by Krishna* m urthi (lOfiO, 51) are available for solutions of eleetrolytes lilte potassium W ide, potassium bromide, potassium fluoride, sodium fluoride, sodium nitrate, potassium nitrate, strontium nitrate and barium nitrate, \Whereas it is easier to explain the variation of ultrasonic volocdties inHAse of solutions of non-electrolytes, the treatm ent becomes extremely difficult for solutions of electrolytes.Salts are ionised in solution and consequently the electrostatic forces exerted by the ions cause an extra loeal pressure and since the pressure of the liquid is increased, the liquid becomes harder to compress, i.e., the compressibility ^ ordvvdpdecreases. In other words, we may also say th at hack anci forth motionsof the particles or the ions are guided by two forces; firstly, the normal pressure P  experienced by the particles as if the salt was non-ionised and secondly, the pressure P* due to the electrostatic forces in case of electrolytes. Those two pressures comhined together, contribute towards the compressibility of, or the velocity in, the solutions of the electrolytes. From the equations.we may write,I  =: 27TvVdA^ -  (1)X =  27TV^ ... (2)K  ■ . .  CD_  p" 4)2id* P resent address— D epartm en t of Physical Oliemistry, I.A.C.S,, Calcutta-32.62Velocity of Ultrasonic Waves in Electrolytes 63where Jf ifl the intensity of ultrasonicj waves in ergs/sec/sq. cins. v is the frequency; y  is the velocity of the waves in the medium, d is the density of the solution; A IS the maximum particle displacement ; x is particle velocity; K  is the volume elasticity.As already stated this pressure p is the sum of the two pressures P  and P' and equation (4) may be written as,2/rf (5)Now P' may he calculated as given below The potential of an ion in solu­tion may he written from Debye-Huckel theory of electrolytes asVi ^  J) (6)where Z\ is the valency of an ion, t is electronic charge, D is dielectric constant of the medium and~  \ I (7)It(where k is Boltzmann constant given hy N  being the Avogadro number andR the gas constant, T  is temperature, is the number of ions per c.c. of i*'* kind.From the well known laws of electrostatics the force per unit area between two charged particles at a potential difference of ^  is given byforce per unit area ™ Sttwhere D is the dielectric constant of the medium. Hence foice per unit area, i.e, pressure is given by=F 2^ e'<“ ( - - S(8)Thus from equations (5) and (8)r z , w  yL ^  »itD J (9)2Id64 S .  P r a k a s h  a n d  S .  P ,  S r iv a s ta v aEquation (9) may be simplified with the help of the following equations,NC, _1000 ■S  C ,  Z f  =  2 / twhere is the number of gm. ions x)er litre ; is ionic strength. The final form of the equation may be written as,(11)(10)Fi : F\2Id)^(2/z)( 12)where B  =  -  -1 0 0 0 .2 ^ 2 RAssuming the pressure P  in equation (12) to be constant (this includes one constant term and the other term for osmotic i)ressure which can be oxilandcd for accuracy) to an extent (jf apjiroxiination, equation (12) represents a stitaiglit line. In  figure 1 we have plotted (F  . c?)i against (ionic strength) from thedata published by Mohanty and Deo (loc. cit), for zinc and magnesium sulphate. The graphs are straight lines. I t  is interesting to note, as is expected from ourVelocity of Ultrasonic Waves in Electrolytes 65equation, th a t the slopes of the straight lines for the  two electrolytes are almost the same.A C K N O W L E D G M E N T SW© owe our best thanks to Dr. Bal Krishna for his kind suggestions. R E F E R E N C E SKrishnatnurthi, 13h., 1960, J .  Sci .  Ind. Res., 9B, 251,„ „ 195] ibid., lOB, 149, 1951.Mohonty, B . S. and Deo, B. B ., Ind, J .  Phys., 1955, 29, 578.1. Gbaph  1. P lot of (F .d )i against /*,

Velocity of Ultrasonic Waves in Solutions of Electrolytes

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Velocity of Ultrasonic Waves in Solutions of Electrolytes

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