Determination of the association constant of sulfuric acid
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0 < le < 1
The mean free activity coefficients of H2SO4 were calculated from the association constant of H2SO 4 and were found to decrease with an increase in the effective ionic strength.
I.
INTRODUCTION
IN order to understand
the reactions occurring in hydrometallurgy, it is necessary to know the thermodynamic and kinetic behavior of the solvent and solutes in aqueous solutions. To this end, the activities of water and solutes, [1'2'3] electrical conductivities, E4,5~ and diffusion coefficients of solutes [6,71 in the solution systems H2SO4Mx(SO4)y-n20 and HC1-MClx-H20 have been systematically studied in the authors' laboratory. These studies suggest that metal sulfates, such as CuSO4, in aqueous solution form ion pairs, such as CuSO4, to a great extent. In recent years, Johnson and Pytkowicz [s~ proposed a method to determine the stoichiometric association constants of some chlorides involving HC1, NaC1, and MgC12, using the data of electromotive force (emf) measurements. The method is based on the ionic strength principle, ~s~which treats the activity coefficients of the ionic species in aqueous solution as a function of only the effective ionic strength, le, under the condition of le < 1. The effective ionic strength is defined by Eq. [1] and is calculated from the concentrations of ionic species present in the solution. It is also expressed in a molar unit (mol dm -3) rather than a molal unit (tool kg-1), because the electrical interactions of the ions are a function of the distance between ions.
Ie----
I{Z
2
2
ZiJVli,y + Z Z~P, v
}
[1]
The first summation extends over the free concentration of the ions in solution and the second summation over the concentration of all ion pairs in the system. The terms zl and zp are the charge number on the ion and ion pair,
YASUHIRO AWAKURA, Associate Professor, KAZUYA KOYAMA, Graduate Student, and HIROSHI MAJIMA, Professor, are with the Department of Metallurgy, Kyoto University, Sakyo-ku, Kyoto 606, Japan. YOSHIYUKI TAKEGAWA, formerly Graduate Student, Department of Metallurgy, Kyoto University, is with Central Laboratory, Sharp Corporation, Tenri-City 632, Japan. Manuscript submitted May 10, 1989. METALLURGICALTRANSACTIONSB
respectively, and Mi, F and mp, F denote the molarities of these species. The stoichiometric association constant, K*, of, for example, NaC1 is related to the thermodynamic association constant, KNaO, by means of YNaYr KN*aCI= K N a C I YNaC!
[2]
where y denotes the activity coefficient of species in the solution. The thermodynamic association constant is invariant at a given temperature and pressure, and the stoichiometric association constant is a function only of the activity coefficients that depend upon the effective ionic strength. The calculation of equilibrium concentrations of species involved in the association reaction requires the data of the activity coefficients in addition to the K value. However, since the data of activity coefficients of ionic species are not available at present, this calculation often faces a big tr
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