MOLAR CONDUCTIVITY OF AQUEOUS HF, HCl, HBr, AND HI

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1 MOLAR CONDUCTIVITY OF AQUEOUS HF, HCl, HBr, AND HI The molar conductivity Λ of an electrolyte solution is defined as the conductivity divided by amount-of-substance concentration. The customary unit is S cm 2 mol 1 (i.e., Ω 1 cm 2 mol 1 ). The first part of this table gives the molar conductivity of the hydrohalogen acids at 25 C as a function of the concentration in mol/l. The second part gives the temperature dependence of Λ for HCl and HBr. More extensive tables and mathematical representations may be found in the reference. Reference Hamer, W. J., and DeWane, H. J., Electrolytic Conductance and the Conductances of the Hydrohalogen Acids in Water, Natl. Stand. Ref. Data Sys.- Natl. Bur. Standards (U.S.), No. 33, c/mol L 1 HF HCl HBr HI Inf. dil c/mol L 1 HF HCl HBr HI c/ mol L 1 20 C 10 C 0 C 10 C 20 C 30 C 40 C 50 C HCl c/ mol L 1 20 C 10 C 0 C 10 C 20 C 30 C 40 C 50 C HBr

2 STANDARD KCl SOLUTIONS FOR CALIBRATING CONDUCTIVITY CELLS This table presents recommended electrolytic conductivity (κ) values for aqueous potassium chloride solutions with molalities of 0.01 mol/kg, 0.1 mol/kg and 1.0 mol/kg at temperatures from 0 C to 50 C. The values, which are based on measurements at the National Institute of Standards and Technology, provide primary standards for the calibration of conductivity cells. The measurements at 0.01 and 0.1 molal are described in Reference 1, while those at 1.0 molal are in Reference 2. Temperatures are given on the ITS-90 scale. The uncertainty in the conductivity is about 0.03% for the 0.01 molal values and about 0.04% for the 0.1 and 1.0 molal values. The conductivity of water saturated with atmospheric CO 2 is given in the last column. These values were subtracted from the original measurements to give the values in the second, third, and fourth columns. All κ values are given in units of 10-4 S/m (numerically equal to µs/cm). The assistance of Kenneth W. Pratt is appreciated κ/s m 1 t/ C 0.01 m KCl 0.1 m KCl 1.0 m KCl H 2 O (CO 2 sat.) References 1. Wu, Y. C., Koch, W. F., and Pratt, K. W., J. Res. Natl. Inst. Stand. Technol. 96, 191, Wu, Y. C., Koch, W. F., Feng, D., Holland, L. A., Juhasz, E., Arvay, E., and Tomek, A., J. Res. Natl. Inst. Stand. Technol. 99, 241, Pratt, K. W., Koch, W. F., Wu, Y. C., and Berezansky, P. A., Pure Appl. Chem. 73, 1783,

3 EQUIVALENT CONDUCTIVITY OF ELECTROLYTES IN AQUEOUS SOLUTION This table gives the equivalent (molar) conductivity Λ at 25 C for some common electrolytes in aqueous solution at concentrations up to 0.1 mol/l. The units of Λ are 10 4 m 2 S mol 1. For very dilute solutions, the equivalent conductivity for any electrolyte of concentration c can be approximately calculated using the Debye-Hückel-Onsager equation, which can be written for a symmetrical (equal charge on cation and anion) electrolyte as Λ = Λ (A + BΛ )c 1/2 Petr Vanýsek For a solution at 25 C and both cation and anion with charge 1, the constants are A = and B = Λ can be found from the next table, Ionic Conductivity and Diffusion at Infinite Dilution. The equation is reliable for c < mol/l; with higher concentration the error increases. Concentration (mol/l) Compound Infinite dilution Λ Λ AgNO /2BaCl /2CaCl /2Ca(OH /2Cu HCl KBr KCl KClO /3K 3 Fe(CN) /4K 4 Fe(CN) KHCO KI KIO KNO KMnO KOH KReO /3LaCl LiCl LiClO /2MgCl NH 4 Cl NaCl NaClO NaI NaOOCCH NaOH Na picrate / /2SrCl /2Zn

4 IONIC CONDUCTIVITY AND DIFFUSION AT INFINITE DILUTION This table gives the molar (equivalent) conductivity λ for common ions at infinite dilution. All values refer to aqueous solutions at 25 C. It also lists the diffusion coefficient D of the ion in dilute aqueous solution, which is related to λ through the equation 2 D = ( RT / F )( λ/ z ) Petr Vanýsek Λ = Λ+ + Λ where Λ + and Λ are equivalent ionic conductivities of the cation and anion. The more general formula is Λ = v Λ + v Λ + + where R is the molar gas constant, T the temperature, F the Faraday constant, and z the charge on the ion. The variation with temperature is fairly sharp; for typical ions, λ and D increase by 2 to 3% per degree as the temperature increases from 25 C. The diffusion coefficient for a salt, D salt, may be calculated from the D + and D values of the constituent ions by the relation z z D D D = ( + ) salt z D + z D For solutions of simple, pure electrolytes (one positive and one negative ionic species), such as NaCl, equivalent ionic conductivity Λ, which is the molar conductivity per unit concentration of charge, is defined as where ν + and ν refer to the number of moles of cations and anions to which one mole of the electrolyte gives a rise in the solution. References 1. Gray, D. E., Ed., American Institute of Physics Handbook, McGraw- Hill, New York, 1972, Robinson, R. A., and Stokes, R. H., Electrolyte Solutions, Butterworths, London, Lobo, V. M. M., and Quaresma, J. L., Handbook of Electrolyte Solutions, Physical Science Data Series 41, Elsevier, Amsterdam, Conway, B. E., Electrochemical Data, Elsevier, Amsterdam, Milazzo, G., Electrochemistry: Theoretical Principles and Practical Applications, Elsevier, Amsterdam, Ion 10 4 m 2 S mol cm 2 s 1 Inorganic Cations Ag /3Al /2Ba /2Be /2Ca /2Cd /3Ce /2Co /3[Co(NH 3 ) 6 ] /3[Co(en) 3 ] /6[Co 2 (trien) 3 ] /3Cr Cs /2Cu D /3Dy /3Er /3Eu /2Fe /3Fe /3Gd H /2Hg /2Hg /3Ho K /3La Li /2Mg /2Mn NH N 2 H Λ ± D Ion 10 4 m 2 S mol cm 2 s 1 Na /3Nd /2Ni /4[Ni 2 (trien) 3 ] /2Pb /3Pr /2Ra Rb /3Sc /3Sm /2Sr Tl /3Tm /2UO /3Y /3Yb /2Zn Inorganic Anions Au(CN Au(CN) B(C 6 H 5 ) Br Br BrO CN CNO /2CO Cl ClO ClO ClO /3[Co(CN) 6 ] /2CrO Λ ± D 5-76

5 Ionic Conductivity and Diffusion at Infinite Dilution 5-77 Λ ± Ion 10 4 m 2 S mol cm 2 s 1 F /4[Fe(CN) 6 ] /3[Fe(CN) 6 ] H 2 AsO HCO HF /2HPO H 2 PO H 2 PO HS HSO H H 2 SbO I IO IO MnO /2MoO N(CN NO NO NH 2 SO N OCN OD OH PF /2PO 3 F /3PO /4P 2 O /3P 3 O /5P 3 O ReO SCN /2SO / /2S 2 O /2S 2 O /2S 2 O /2S 2 O Sb(OH) SeCN /2SeO /2WO Organic Cations Benzyltrimethylammonium Isobutylammonium Butyltrimethylammonium Decylpyridinium Decyltrimethylammonium Diethylammonium Dimethylammonium Dipropylammonium Dodecylammonium Dodecyltrimethylammonium Ethanolammonium Ethylammonium Ethyltrimethylammonium Hexadecyltrimethylammonium Hexyltrimethylammonium D Ion 10 4 m 2 S mol cm 2 s 1 Histidyl Hydroxyethyltrimethylarsonium Methylammonium Octadecylpyridinium Octadecyltributylammonium Octadecyltriethylammonium Octadecyltrimethylammonium Octadecyltripropylammonium Octyltrimethylammonium Pentylammonium Piperidinium Propylammonium Pyrilammonium Tetrabutylammonium Tetradecyltrimethylammonium Tetraethylammonium Tetramethylammonium Tetraisopentylammonium Tetrapentylammmonium Tetrapropylammonium Triethylammonium Triethylsulfonium Trimethylammonium Trimethylhexylammonium Trimethylsulfonium Tripropylammonium Organic Anions Acetate panisate /2Azelate Benzoate Bromoacetate Bromobenzoate Butyrate Chloroacetate mchlorobenzoate ochlorobenzoate /3Citrate Crotonate Cyanoacetate Cyclohexane carboxylate /2 1,1Cyclopropanedicarboxylate Decylsulfate Dichloroacetate /2Diethylbarbiturate Dihydrogencitrate /2Dimethylmalonate ,5Dinitrobenzoate Dodecylsulfate Ethylmalonate Ethylsulfate Fluoroacetate Fluorobenzoate Formate /2Fumarate /2Glutarate Hydrogenoxalate Isovalerate Iodoacetate Lactate Λ ± D

6 5-78 Ionic Conductivity and Diffusion at Infinite Dilution Λ ± Ion 10 4 m 2 S mol cm 2 s 1 1/2Malate /2Maleate /2Malonate Methylsulfate Naphthylacetate /2Oxalate Octylsulfate Phenylacetate /2oPhthalate /2mPhthalate D Ion 10 4 m 2 S mol cm 2 s 1 Picrate Pivalate Propionate Propylsulfate Salicylate /2Suberate /2Succinate psulfonate /2Tartarate Trichloroacetate Λ ± D

7 ACTIVITY COEFFICIENTS OF ACIDS, BASES, AND SALTS Petr Vanýsek This table gives mean activity coefficients at 25 C for molalities in the range 0.1 to 1.0. See the following table for definitions, references, and data over a wider concentration range AgNO AlCl Al 2 ( ) BaCl Be CaCl CdCl Cd(NO Cd CoCl CrCl Cr(NO 3 ) Cr 2 ( ) CsBr CsCl CsI CsNO CsOH CsOAc Cs CuCl Cu(NO Cu FeCl HBr HCl HClO HI HNO H KBr KCl KClO K 2 CrO KF K 3 Fe(CN) K 4 Fe(CN) KH 2 PO KI KNO KOAc KOH KSCN K LiBr LiCl LiClO LiI LiNO LiOH LiOAc Li MgCl Mg

8 5-80 Activity Coefficients of Acids, Bases, and Salts MnCl Mn NH 4 Cl NH 4 NO (NH NaBr NaCl NaClO NaClO CrO NaF NaH 2 PO NaI NaNO NaOAc NaOH NaSCN NiCl Ni Pb(NO RbBr RbCl RbI RbNO RbOAc Rb SrCl TlClO TlNO UO 2 Cl UO ZnCl Zn(NO Zn

9 MEAN ACTIVITY COEFFICIENTS OF ELECTROLYTES AS A FUNCTION OF CONCENTRATION The mean activity coefficient γ of an electrolyte X a Y b is defined as + γ = ( γ a + γ b ) l/( a b) where γ + and γ are activity coefficients of the individual ions (which cannot be directly measured). This table gives the mean activity coefficients of about 100 electrolytes in aqueous solution as a function of concentration, expressed in molality terms. All values refer to a temperature of 25 C. Substances are arranged in alphabetical order by formula. References 1. Hamer,W. J., and Wu, Y. C., J. Phys. Chem. Ref. Data, 1, 1047, Staples, B. R., J. Phys. Chem. Ref. Data, 6, 385, 1977; 10, 767, 1981; 10, 779, Goldberg, R. N. et al., J. Phys. Chem. Ref. Data, 7, 263, 1978; 8, 923, 1979; 8, 1005, 1979; 10, 1, 1981; 10, 671, Mean Activity Coefficient at 25 C m/mol kg 1 AgNO 3 BaBr 2 BaCl 2 BaI 2 CaBr 2 CaCl 2 CaI m/mol kg -1 Cd(NO 2 Cd(NO 3 CoBr 2 CoCl 2 CoI 2 Co(NO 3 CsBr m/mol kg -1 CsCl CsF CsI CsNO 3 CsOH Cs 2 CuBr

10 5-82 Mean Activity Coefficients of Electrolytes as a Function of Concentration m/mol kg 1 CuCl 2 Cu(ClO 4 Cu(NO 3 FeCl 2 HBr HCl HClO m/mol kg 1 HF HI HNO 3 H 2 KBr KCNS KCl m/mol kg 1 KClO 3 K 2 CrO 4 KF KH 2 PO 4 * K 2 HPO 4 ** KI KNO m/mol kg 1 KOH K 2 LiBr LiCl LiClO 4 LiI LiNO

11 Mean Activity Coefficients of Electrolytes as a Function of Concentration 5-83 m/mol kg 1 KOH K 2 LiBr LiCl LiClO 4 LiI LiNO m/mol kg 1 LiOH Li 2 MgBr 2 MgCl 2 MgI 2 MnBr 2 MnCl m/mol kg 1 Mn(ClO 4 NH 4 Cl NH 4 ClO 4 (NH 4 HPO 4 ** NH 4 NO 3 NaBr NaBrO m/mol kg 1 CO 3 NaCl NaClO 3 NaClO 4 CrO 4 NaF HPO 4 * m/mol kg 1 NaI NaNO 3 NaOH SO 3 WO 4 NiBr

12 5-84 Mean Activity Coefficients of Electrolytes as a Function of Concentration m/mol kg 1 NaI NaNO 3 NaOH SO 3 WO 4 NiBr m/mol kg 1 NiCl 2 Ni(ClO 4 Ni(NO 3 Pb(ClO 4 Pb(NO 3 RbBr RbCl m/mol kg 1 RbF RbI RbNO 3 Rb 2 SrBr 2 SrCl 2 SrI m/mol kg 1 UO 2 Cl 2 UO 2 (NO 3 ZnBr 2 ZnCl 2 ZnI * The anion is H 2 PO 4. 2 ** The anion is HPO 4.