/cce/news/artdown.php%3Ftype%3Dxxkejian%26id%3D Electrolytic+so lution+,coductivity+ppt&hl=en&gl=uk&pid=bl&srcid=ADGEEShp5BE7ta0cGFnesW N515HmVzSp9- rxCzk8phu5ieDG47OwD9ZaFIyMoxhV_kzvq9Mi6la9bYJISGtwXIqjdMAye- iSBC3SpcJ3ndh3i- M6AjQWBYSO1QlqsrJQ233scC5CWP5u&sig=AHIEtbTu6UaI4zEZGUdPk- K41SDmsGlnWg Conductivity of solution The work of an Asian professor was used after some modifications in addition to my work

Conducting mechanism of electrolytic solution

Motion of ions in the solution: Only the transfer can cause net electricity 1) Diffusion: due to difference in concentration 2) Convection: due to the difference in density or temperature 3) Transfer: due to electric field

Conductance and its measurement For metals: Ohm’s Law R: resistance,unit (Ohm,  ) resistivity, unit Ohm m,  m

For electrolytic solution: conductivity (  ) or spedific conductance: Definition:  = 1/  Dimension:  -1 m -1 OR S m -1 electric conductance (G) : G = 1/R G=  l Dimension:  -1, mho, Siemens, S

Type 206 conductance electrode conductivity cell

Wheatstone Bridge Circuit High-frequency alternative current, frequency = 1000 Hertz

R 1 / R 2 = R 3 / R 4 Cell constant of a conductivity cell

The conductance cell is usually calibrated with standard KCl (potassium chloride ) solution. C/ mol dm  / S m

Method of determining specific conductance : 1- Determine R1 from Wheatstone Bridge Circuit using KCl solution. 2- Determine Kcell for KCl from the equation, specific conductance is known from table. 3- Put the unknown solution in the conductivity cell & determine R 4- Apply the equation to calculate specific conductance of unknown solution:

Influential factors for conductivity 1)Concentration. 2)Type of electrolyte 3)Temperature

1.Acids and bases have higher conductance 2. C < 5 mol dm -3,  increases with C 3. For CH 3 COOH conductance does not depend on C

(2) Temperature- dependence of conductance

Molar conductivity 1) Definition V: degree of dilution The conductivity of a solution is approximately proportional to the concentration  m is the conductivity contributed by 1 mole of electrolyte between electrodes of 1 m apart

Dependence of molar conductivity on concentration  m decreases with concentration. Kohlrausch replotted  m against C 1/2 Due to the interaction between ions: interionic attraction

Linear relationship between  m and C 1/2 can be observed for 1:1 electrolytes: C < 0.002~ mol dm -3

Kohlrausch empirical formula To extrapolate the linear part of  m ~ C 1/2 at low concentration to C = 0,  m  can be obtained.  m  the limiting value of  m at infinite dilution: limiting molar conductivity. It is the conductivity of 1 mol of solution at infinite dilution.

Kohlrausch’s law of independent ionic mobilities At infinite dilution,  m  should be the sum of the separate contributions of the ions

limiting molar conductivity of weak electrolyte

Influential factors for m  1)Nature of ions (a) Charge (d) Mechanism of transfer (b) Radius

ionsr / nm m  /10 2 ionsr / nm m  /10 2 H+H OH – Li F–F– Na Cl – K+K Br – Mg CO 3 2 – Ca C 2 O Sr Fe(CN) 6 3 – Al Fe(CN) 6 4 – Fe La Limiting molar conductivity of ions

( c) Mechanism of hydrogen and hydroxyl ions transfer Grotthus mechanism (1805)

2) Viscosity of the solvents solvent acetoneMethyl alcohol Ethyl alcohol  / mPas m  /10 3 ( K +) m  /10 3 (Li + ) Table. Effect of Viscosity of solvent on limiting molar conductivity of ions

The Stokes’s law

Ionic mobility and transference number 1) Ionic mobility Under unit potential gradient: dV/dl = 1 V m -1 : v = u, ionic mobility

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

3) Relation between ionic mobility and transference number C -, Z -, u - ; C +, Z +, u + ; For time t: Q + = A Eu + t C + Z + F Q  = A Eu  t C  Z  F

Q = Q + + Q  = AtF E( u + C + Z + + u  C  Z  ) C + Z + = C  Z  Q = AtF C + Z + E( u + + u  )

Relation between transference number and molar conductivity I + = AEu + Z + C + F I  = AEu  Z  C  F I = I + + I  = AC + Z + F E(u + + u  )

For uni-univalent electrolyte:

To measure m+ or m-, either t + and t - or u + and u - must be determined

Measurement of transference numbers 1) Hittorf method (1853) Electrolysis of HCl solution Anodic regioncathodic regionBulk solution

4 Cl - -4e -  2 Cl 2  4 H + +4e -  2 H 2  When 4 Faraday pass through the electrolytic cell 3 mol H +  1 mol Cl - 

C residual = C initial – C react + C transfer For anodic region:

Hittorf’s transference cell

Example Pt electrode, FeCl 3 solution: In cathodic compartment: Initial: FeCl mol dm -3 Final: FeCl mol dm -3 FeCl mol dm -3 Calculate the transference number of Fe 3+

2) The moving-boundary method MA, MA’ have an ion in common. The boundary, rather difference 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: xACZ + F = t + Q

Factors affecting transference number a) temperature T / o C KCl( M) M0.01M0.02M Table : Transference number of K + in KCl solution at different concentration and temperature

b) Co-existed ions electrolyteKClKBrKIKNO 3 t electrolyteLiClNaClKClHCl t –

Sample: When 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 + ) Solution: t + = 0.17 m× 1.05 × m 2 × 10.0 mol m -3 ×1 × C mol -1 / 0.01 A × 200 S = 0.82

Problems 1. Make comparison between Hittorf’s method and moving boundary method. 2. Why the limiting molar conductivity of weak electrolyte can not be obtained by extrapolating of  m ~ C 1/2. 3. What experimental results back up the Kohlrausch’s Law of independent ionic mobilities 4. Summarize the effect of ionic nature on limiting molar conductivity of ions