§7.2 Conductivity and its application Chapter 7 Electrochemistry §7.2 Conductivity and its application 0.01 0.02 0.03 0.04 0.00 0.05 0.10 0.15 0.20 m / S·mol-1·m2 HCl H2SO4 KCl Na2SO4 HAc

Self reading: Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002. pp. 506-521 Section 16.5 electrical conductivity Section 16.6 electrical conductivity of electrolyte solutions

Main contents: 7.2.1 some concepts 7.2.2 measurement of electric conductance 7.2.3 factors on conductivity 7.2.4 molar conductivity: Kohlrausch empirical formula and law of independent migration 7.2.5 measurement of limiting molar conductivity of ions 7.2.6 factors on limiting molar conductivity of ions

7.2.1 Some concepts For metals: electric conductance (G) : Ohm’s Law For electrolyte solution: electric conductance (G) : Definition: G = 1/R Unit: -1, mho, Siemens, S Ohm’s Law R: resistance, Unit: Ohm,  Reciprocal of resistance conductivity () or specific conductance: Definition:  = 1/  Unit: S·m-1 resistivity/specific resistance Unit: Ohm·m, ·m

conductance cell conductance electrode with smooth or platinized platinum foil

High-frequency alternative current, ca. 1000 Hertz 7.2.2 Measurement of conductance: ~ G A C B D F R2 R1 R3 R4 I R2 Wheatstone Bridge Circuit High-frequency alternative current, ca. 1000 Hertz R3  R2 = R4  R1 Conductometer

Cell constant EXAMPLE The conductance of a solution is 0.689 -1. If the cell constant is 0.255 cm-1, calculate the specific conductance of the solution.

Relative standards are often used in scientific measurement. The conductance cell is usually calibrated using standard aqueous KCl (potassium chloride ) solution. 11.2 1.289 0.1411 0.0147 / S m-1 1.00 0.100 0.0100 0.001 c/ mol·dm-3 Relative standards are often used in scientific measurement.

EXAMPLE The conductance of a cell containing an aqueous 0.0560 mol·dm-3 KCl solution whose conductivity is 0.753 -1·m-1 is 0.0239 -1. When the same cell is filled with an aqueous 0.0836 mol·dm-3 NaCl solution, its conductance is 0.0285 -1. Calculate the conductivity of the NaCl solution.

7.2.3. Influential factors of conductivity 1) concentration – dependence of conductivity  /S·m-1 H2SO4 KOH LiCl MgSO4 HAc 5 10 15 c/mol·dm-3 20 30 40 50 60 70 80

2) Temperature-dependence of conductivity wt % H2SO4  / S m-1 50 oC 30 oC 10 oC -10 oC -30 oC Why do we usually used 38 % H2SO4 in acid-lead battery; Why do we usually conduct electrolysis and electroplating using warm electrolyte? ice

7.2.4 Molar conductivity Why do we introduce molar conductivity? 1) Definition degree of dilution The physical meaning of m:

2) Concentration-dependence of molar conductivity c / mol·dm-3 m / S·mol-1·m2 HCl KOH NaOH KCl NaCl HAc Why does m decrease with increasing concentration?

3) Kohlrausch’s empirical formula 0.01 0.02 0.03 0.04 0.00 0.05 0.10 0.15 0.20 m / S·mol-1·m2 HCl H2SO4 KCl Na2SO4 HAc Kohlrausch Why did Kohlrausch plot m against c1/2? Within what concentration range did the linear relation appear.

Kohlrausch empirical formula limiting molar conductivity Kohlrausch’s Square Root Law Within what concentration range is the Kohlrausch law valid?

0.01 0.02 0.03 0.04 0.00 0.05 0.10 0.15 0.20 m / S·mol-1·m2 Problem: Can we obtain the limiting molar conductivity of weak electrolytes just by extrapolating the m ~ c1/2 to infinite dilution?

Molar conductivity at infinite dilution for some electrolytes in water at 298 K. Salts /S mol-1 cm2 HCl 426.16 LiCl 115.03 NaCl 126.45 KCl 149.85 LiNO3 110.14 KNO3 144.96 NaNO3 121.56

4) Kohlrausch’s law of independent migration Salts KCl NaCl KNO3 NaNO3 /S mol-1 cm2 149.85 126.45 144.96 121.56 23.4 The difference in of the two electrolytes containing the same cation or anion is the same. The same differences in led Kohlrausch to postulate that molar conductivity at infinite dilution can be broken down into two contributions by the ions. ionic conductivities at infinite dilution

m at infinite dilution is made up of independent contributions from the cationic and anionic species. Explanation to the same difference

How can we determine the limiting molar conductivity of weak electrolyte Key: How to measure the ionic conductivity at infinite dilution?

7.2.5 measurement of limiting molar conductivity of ions 1) transference number and molar conductivity I+ = AU+Z+c+F I = AUZ c F I = I++ I = Ac+Z+F(U++ U)

For uni-univalent electrolyte: To measure m,+ or m,-, either t+ and t- or U+ and U- must be determined

7.2.6 Influential factors for 1) Nature of ions ions r / nm 102 H+  3.4982 OH¯ 1.98 Li+ 0.68 0.387 F¯ 1.23 0.554 Na+ 0.98 0.501 Cl¯ 1.81 0.763 K+ 1.37 0.735 Br¯ 1.96 0.784 Mg2+ 0.74 1.061 CO32 1.66 Ca2+ 1.04 1.190 C2O42 1.48 Sr2+ 1.189 Fe(CN)63 3.030 Al3+ 0.57 1.89 Fe(CN)64 4.420 Fe3+ 0.67 2.04 La3+ 2.09 Charge; Radius; charge character; transfer mechanism

Transport mechanism of hydrogen and hydroxyl ions Grotthus mechanism (1805) The ion can move along an extended hydrogen-bond network. Science, 2002, 297:587-590

2) Temperature Transference number of K+ in KCl solution at different concentration and temperature 0.000 0.005 0.01 0.02 15 0.4928 0.4926 0.4925 0.4924 25 0.4906 0.4903 0.4902 0.4901 35 0.4889 0.4887 0.4886 0.4885 c /mol·dm-3 T /℃

Table transference number on co-existing ions Electrolyte KCl KBr KI KNO3 t+ 0.4902 0.4833 0.4884 0.5084 LiCl NaCl HCl t– 0.6711 0.6080 0.5098 0.1749 Problem: Why does the transference number of certain ion differ a lot in different electrolytes?

Summary Macroscopic Microscopic G  Dynamic  U U t t

Exercise-1 The mobility of a chloride ion in water at 25 oC is 7.91  10-4 cm2·s-1·V-1. Calculate the molar conductivity of the ion at infinite dilution; How long will it take for the ion to travel between two electrodes separated by 4.0 cm if the electric field is 20 V·cm-1.