Chapter 7 Electrochemistry § 7.2 Conductivity and its application Main contents: some concepts measurement of electric conductance factors on conductivity molar conductivity: Kohlrausch empirical formula and law of independent migration measurement of limiting molar conductivity of ions factors on limiting molar conductivity of ions

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

conductance cell conductance electrode with smooth or platinized platinum foil ~ G A C B D R2R2 R1R1 R3R3 R4R4 I It is also a capacitor!

High-frequency alternative current, ca Hertz R 3  R 2 = R 4  R Measurement of conductance: ~ G A C B D F R2R2 R1R1 R3R3 R4R4 I R2R2 Wheatstone Bridge Circuit Conductometer

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

The conductance cell is usually calibrated using standard aqueous KCl (potassium chloride ) solution  / S m c/ mol·dm -3 Relative standards are often used in scientific measurement.

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

Influential factors of conductivity 1) concentration – dependence of conductivity H 2 SO 4 KOH LiCl MgSO 4 HAc c/mol·dm  /S ·m -1 What can we learn form this figure?

wt % H 2 SO 4  / S m o C 30 o C 10 o C -10 o C -30 o C 2) Temperature-dependence of conductivity 1.Why do we use 38 % H 2 SO 4 in acid-lead battery? 2.Why do we do electrolysis and electroplating using warm electrolyte? ice

7.2.4 Molar conductivity 1) Definition degree of dilution Why do we introduce molar conductivity? The physical meaning of  m : H 2 SO c/mol·dm Is there linear relationship between conductivity and concentration?

2) Concentration-dependence of molar conductivity Is molar conductivity  m independent of concentration? c / mol·dm -3  m / S · mol -1 · m 2 HCl KOH NaOH KCl NaCl HAc Why does molar conductivity decrease with increasing concentration? Does the curve shape inspire you?

Why did Kohlrausch plot  m against c 1/2 ? Within what concentration range does the linear relation appear. Kohlrausch 3) Kohlrausch’s empirical formula  m / S·mol -1 ·m 2 HCl H 2 SO 4 KCl Na 2 SO 4 HAc

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

Problem: Can we obtain the limiting molar conductivity of weak electrolytes just by extrapolating the  m ~ c 1/2 to infinite dilution?  m / S·mol -1 ·m 2

Salts /S mol -1 cm 2 HCl LiCl NaCl KCl LiNO KNO NaNO Molar conductivity at infinite dilution for some electrolytes in water at 298 K.

SaltsKClNaClKNO 3 NaNO 3 /S mol -1 cm ionic conductivities at infinite dilution 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. 4) Kohlrausch’s law of independent migration

 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? Key: How to measure the ionic conductivity at infinite dilution?

1) Ionic mobility Ionic mobility (U) : the ionic velocity per unit electric field, is a constant. Ionic velocity measurement of limiting molar conductivity of ions C －, Z －, U － ; C ＋, Z ＋, U ＋ ; For time t: Q + = A U + t C + Z + F Q  = A U  t C  Z  F BAC

I + = AU + Z + c + F I  = AU  Z  c  F I = I + + I  = Ac + Z + F(U + + U  ) For time t: Q + = A U + t C + Z + F Q  = A U  t C  Z  F

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

Transference number I = I ＋ + I － Q = Q ＋ + Q － The fraction of the current transported by an ion is its transference number or transport number t = t + + t - = 1 2) transference number How to measure ionic mobility and transference number?

3) Measure transference number (1) Hittorf method (1853) Example: Electrolysis of HCl solution When 4 Faraday pass through the electrolytic cell anodic region cathodic regionbulk solution    + = 1 F    4Cl - -4e -  2Cl 2  4H + +4e -  2H 2  3 mol H +  1 mol Cl -  3 mol H +  1 mol Cl - 

anodic region cathodic region bulk solution      For anodic region: The final result

EXAMPLE Pt electrode, FeCl 3 solution: In cathode compartment: Initial: FeCl mol·dm -3 Final: FeCl mol·dm -3 FeCl mol·dm -3 Calculate the transference number of Fe 3+ Hittorf’s transference cell Anode chamber Cathode chamber Cock stopper

(2) The moving-boundary method MA, MA’ have an ion in common. The boundary, rather different in color, refractivity, etc. is sharp. In the steady state, the two ions move with the same velocity. When Q coulomb passes, the boundary moves x, the cross-sectional area of the tube is A, then: xAcZ + F = t + Q Can you measure ionic mobility using this apparatus?

Example: Given A=1.05 × m 2, c(HCl)=10.0 mol·m -3, I = 0.01 A for 200 s, x was measured to be 0.17 m, calculate t (H + )

(1) Temperature and concentration Transference number of K + in KCl solution at different concentration and temperature T / ℃ c /mol·dm -3 4) Influential factors

(3) Co-existing ions ElectrolyteKClKBrKIKNO 3 t+ t ElectrolyteLiClNaClKClHCl t– t– Table transference number on co-existing ions Problem: Why does the transference number of certain ion differ a lot in different electrolytes?

ionsr / nm 10 2 ionsr / nm 10 2 H+H+  OH¯  1.98 Li F¯ Na Cl¯ K+K Br¯ Mg CO 3 2   1.66 Ca C2O42C2O42  1.48 Sr Fe(CN) 6 3   Al Fe(CN) 6 4   Fe La ) Nature of ions Charge; Radius; charge character; transfer mechanism Influential factors for

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

G   UUU ttt MacroscopicMicroscopic Dynamic Summary

Exercise-1 The mobility of a chloride ion in water at 25 o C is 7.91  cm 2 ·s -1 ·V -1. 1)Calculate the molar conductivity of the ion at infinite dilution; 2)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. Exercise-1 Yin, p. 227, exercise 8 exercise 12 exercise 15

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