Septa,1902
EFFECT OB PRESSIJRE ON EQUTLIBRITX OF MA~-,YKSIUM SULFATE
1607
THE EFFECT OF PRESSURE ON TIIE E:QUILIBRITl&!t OF MAGNESIUM SULFATE1 University of C(ili,fornia, Sun Diego Marine Physical Laboratory of the Scripps Institution of Oceanography, Sun Diego 5W,
California
Receired Fehruary
16, 1902
Condurt,ivit,y at, 25" of aqueous solutiona of MgSOd has heen measured as a funrtion of pressure up to 2000 atm. for five concentrations from 0.0005 to 0.02 d l . The effect, of pressure on the dissociation constant, was calculated with the equation used by Davics, Ott,er, and Priic. l'hc difference of partial molal voliimes between prodiirts and reactant>s,AVO, was found to bo -7.3 k 0.4 cc./mole. Tha relat,ion of this work to result,s of sound absorption measurements in MgSO4 solut)ions is pointed out. Mcasurements of thc effect of pressura on conduct,ivity also were made for the following aqueous golut,ions: :KC1, Kz804,MgC12, and BaCl a t 25" over the sanie concentration range. Values of equivalent conductivity a t infinite dilution, h,O, were determined 8s a function of pressure for MgS04, BC1, K,S04, and MgCL Values of A J , h are given for MgSOa, KCl, K2901, and MgCl2 at each concentration. Since VzO = -6.4 cc./mole for MgSOI, thc partial molal volume of the state which dissociates into ions is +1 cc./mole. N
The unusually high sound absorption of sea water, about 30 times greater than that of fresh water, is due to a small concentration of magnesium siilfate, approximately 0.02 M.* Tamm and Kurtzea found that other 2-2 sulfates exhibit similar high absorption and Eigen4 has discussed their significance. Liebermann5 showed how a pressure dependent chemical reaction could produce this sound absorption and Bies,6 on the basis of pressure dependent dissociation, derived a theory by which he determined equilibrium constants of magnesium sulfate from sound absorption measurement's a t at,mospheric pressure in water and dioxane-water solvents. Verma' has made a recent summary of sound absorption in electrolytes which includes measurements as a function of concentration, temperature, dielectric constant, pressure, and the effect of heavy water as solvent. For any quantitative check of the t'heory of sound absorption based on pressure dependent dissociation reactions, it is vital t'o know the vo!ume change upon dissociation into ions, that is AVO which appears in eq. 1.*. It shsuld, in principle, be possible to use the same ( A P ) and degree
Since A v o has not been determined experimentally for any of the 2-2 sulfates from conductivity measurements as a fuiirtion of pressure, thc ob,,ect of this work is to do so a t 25' to facilitate comparison with valiies of AV determined by Bies.IL The molal dissoriation ronstant K i n was calculated from equation 2, in which it is as-
snmed that the activity coefficient of the associated salt is unity a t all pressures and concentrations. The degree of dissociation was determined a t 25' for magnesium sulfatc by dividing the measured equivalent conductivity by the theoretical value determined from the equation
used by Davies, Otter, and Prue.'Z The activity coefficient>s were calculated from the DebyeHuckel equation
(y)T,nl A PO
= - RT
(1)
of dissociation ( a ) to describe results of density and conductivity measurements; if sound absorption is due to dissociation icto ions, it should be possible, using the same (AVO) and a, to account for it also. This has been done for a weak electrolyte in the case of ammonium hydroxide in work reported by Hamann and Straussgand by Carnevale and Litovitx.lo (1) This work represents results of research under joint sponsorship of the Office of Naval Research, Contract Nonr 2216 ( 0 5 ) and the
Division of Physical Chemistry, Commonwealth Pcientific and Industrial Research Organization. Melbourne, Australia. Contribution frotn Scrippa Institu ion of Oceanography, New SPries. (2) R . W. Leonard, J. Acoust. Soc. Am., 20, 254 (1948). (3) K. Tamln a n d G. Kurtae. Acustica, 3, 33 (1953). 14) M. Eigen, Discussions Faraday Sor.. 24, 2 5 (19,57). ( 5 ) I,. N. Liebermann, Phvs. Rev.,76, 1520 (1949). ( 6 ) D . A . Iiies, J . Chem. Phys.. 23, 428 (1955). (7) G. S. Verma, Rev. M o d . Phys., 31, 1052 (1959). (8) 13. 13. Owen and S. R . I'winkley, Chem. Rev., 29, 461 (1941). (9) S. D. Haniann and W. Strauss, Trans. Faraday Soc., 51, 1684 (1955).
Tn both eq. 3 and 4 molar concentrations varying with pressure were used. In eq. 2 the rational activity coefficient is used for the molal activity coefficient. Tables I and I1 list constaiits for aqiieous solutions useful in evaluating eq. 3 and 4. The dielectric constant E was calculated using the Owen and Brinkley13equation ep = el/[1
(
23
- 0.4060 log 1 - -
(5)
where p is in atmospheres and the 25' value B = 2885 atm. from Gibsonl4 is used. The viscosity (IO) (a) M , Etgen, Z . Physak. Chem. (Frankfurt). 1, 176 (1951); (b) E. €1. Carnevale and T. A. Litovitz, J . Aroust. S o r . A m . , 30, 610 (1958). (11) Because of a n error in concentration (AT')% reported b y Rips was a factor of 108 low. T h e corrected value is ( A V ) * = 10 (cr./ mo1e)z. (12) W. G. Davies, R. J. Otter, and J. E. Prue. Dzscusszons Faraday Soc., 24, 103 (1957). (13) I3. B. Owen a n d S. R. Rrinkley, Phys. Rev.,64, 32 (1943). (14) R. E. Gibson, J. A m . Chem. Soc., 66, 4 (1934).
data were iiitcrpolated graphically from the measiir~rn~iits of J3ridgrnanI5 rind the rntio of densities or was oa1rul:itcd from I ) o r . ~ e y , ~The ~ valup o! = 14.28 a t atmospheric prassiirr iz that uscd by Robinson and Stokes1'; it drcroases as a f u i d n r i of pressure, vtli'ying iiivurscly a2c Ihc dielectric c.oristant.
TABLE I CoNwnN-ra ifon WATERA S
A FCNCTION OF
P. ntin.
1
e
CT
CY')^!^
~
~ E s ~ T - R ATE25'
(eT)''*
il
X 10'9
(poiso)
"*"l+. Pr
78.54 28,417
153.0 3.583 0.008937 1,0000 l55,2 3.739 ,009014 1.0220 82.88 24,712 157.2 3.885 .009132 1.0416 84.80 25,284 150.0 4.020 .00'3314 1.05'35 86,57 25,812 160,i' 4.148 ,009604 1.0758
500 80,81 24,094 1000 1500 2000
Materials and Method. Aqucous Bolutions of potassium chlorido, potassium sulfate, magnesium chloride, snd magncsiuin sulfate woro propared from analytiolil grade r e a p i t s . Cunductivitics of theso salts wwf! nieasured at three concentrytions a d Tor magric.siurn sulfate, For two additional r'onr,piit,rat,ions. Solveiit conductivity rorrectioris were made using erperimcnt,ally measured values. blcaaured r:quivdrnt, crmductivitsirs and calrulatcd values at, infinitc dilution a3 n, functicin of presnure were obtaincd ~ L Bfollows, 1. Water Conductivity Correction,- Subt,rec!t wittor conductnnac!maaauretl in Barno acll at wme pressure. -
-
H",o
-
H'slllL
€I*O
Specific Conductivit --Multiply water correckd conductance by pressure c&xmderii cell constant to get specilic conductivity as a function of pressure; cell constant was measured for each concent,ration. 2.
("salt
-
H1O)LD
=
xp
Pressurc dopendcnce of cell constant for the Teflon cell was dctcrmined by comparing 0.02 M KCl data in the Teflon TABLE I1 cell with 0.01 M XC1 data for the cell with a glass bar. CONDUCTIVITY AND ACTIVITYCOEFFICIWXT EQUATION CONIt is assumed that Ai,, Ai for KC1 is independent of concentraSTANTS AS A FUNCTION OF PRESSLRE FOR AQGEULJS SOLTJ- tioii,lB T I O N S AT 25' IN TIlB EQUATIONS TABLE I11 i)rp/.il ron AQCEOUSSOLUTIONS AT 25" C is atmospheric pressure conccntration in molcs/l.
MgSOi d __
p, atm.
R
E
B
A
MgSO,
1. 500 1000 1500 2000
0.9157 .8775 .8445 .8161 .7910
120.64 117.9 114.8 111.4 106.9
0.3286 .3239 ,3198 ,3162 ,3129
0.5092 ,4880 ,4696 .4538 ,4398
14.28 13.88 13.33 13.23 12.95
Experimental Apparatus.-The apparatus was essentially that described by Ellis.ls The conductivity cell consisted of a cylindrical Teflon tube closed at one end; a sliding Teflon plug inserted a t the other end of the cell supported the electrodes, transmitted the pressure, and isolated the conductivity cell from white p a r a f i oil used in the pressure vessel. Heavy platinum wire pins were mounted parallel to the axis of the cylindrical plug and went all the way through it to provide electrical contact with the electrodes. Corrections to the cell constant as a function of pressure due to compression of the Teflon were obtained by comparing potassium chloride conductivity results. These were obtained with a sliding plug in which one electrode was supported by heavy platinum wire as above; the other electrode was supported by a glass rod located at the edge of both electrodes and whose axis was perpendicular, to the plane of both elect,rodes and perpendicular to the axis of the cylindrical plug. A fine platinum wire provided electrical contact between the glass supported electrode and a shorter heavy platinum wire mounted in the sliding plug. Corrections for the solubility of the glass were made assuming the rate of solution or the change in conductivity A x proportional to pressure and time, A x = ZolPt, where 01 is assumed to be independent of pressure. A Wayne-Kerr universal bridge B221 was used for measuring conductance. The effects of series lead resistance and shunt resistance of the hydraulic oil as a function of pressure were measured; corrections for the 0.2 ohm series lead resistance were made where necessary. The temperature was 25 + 0.05". (15) P. W. Bridgman, "Physics of High Pressure," Bell and Sons, 1949. (16) E. N. Dorsey, "Properties of Ordinary Water Substance," Reinhold Publ. Co., New York, N. Y . , 1940. (17) R. A. Robinson and R. €1. Stokes, "Elrctrolyte Solutions," Hutterworths. London, 1955, p. 401. (18) 4. J. Ellis, .I. Chem. Soc., 3688 (1959).
c x 10' 5.000 10.01 20.00 100.1 200.0
c-------p, 600
*m t-, 1000
1500
2000
1.025 1.028 1.033 1.051 1.058
1.033 1.041 1.050 1.083 1.094
1.030 1.040 1.055 1.098 1.116
1.021 1.033 1.060 1.104 1.126
K2S0.4
5.000 20.00 220.6
1.015 1.016 1.021
1.016 1.017 1.029
1.007 1.011 1.026
0.995 0.998 1.018
MgC12
5.000 20.000 200. 7
1.019 1.021 1.023
1.023 1.024 1.029
1.015 1.019 1.025
0.999 1.005 1.014
KC1
5,000 20.00 99.99 200.0
1.015 1.015 1.016 1.016
1.018 1.016 1.018 1,018
1.010 1.008 1.010 1.012
0.996 ,994 ,996 ,998
3. Ratio of Equivalent Conductivities.-Divide (xP/m) by pr to get (&/Al) for each pressure a t each concentration. Plot (h,/hl) for each pressure us. the square root of the molality, extrapolate to find ( APO/AiO),and multiply by respective conductivities a t infinite dilution. For MgS04, calculate APo/Al0 according to the equation = (APpr/+)
[h,O]MgS04 = j'i,"]K,SO,
+ [IIpO]MgC12[Apo]KCI1
where
Results The values of Ap/Al for all the salts used are listed in Table 111. Equivalent conductance for MgSO4 is listed in Table IV and equivalent conductances at irifinite dilution are presented in Table T'. The dissociation constants, I
