Chapter 24b: Molecules in Motion Conductivity and Ion Mobility

1
Chapter 24b Molecules in Motion
Conductivity and Ion Mobility

• Homework
• Exercises (a only) 25, 26, 27, 28
• Problems8

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Conductance in Solution

• Conductance, G, is the inverse of electrical
  resistance
• G 1/R
• Units ohm-1, W-1, or mhos
• SI unit, S, siemens 1 S 1 W-11 1C/(Vs)
• Conductance decreases with length and increases
  with area
• G kA/l
• k is conductivity (S/m)
• l length (m)
• A area (m2 )
• Molar conductivity, Lm, where Lm k/c
• Variation of with concentration - function of the
  number of ions in solution and interaction
  between ions
• Strong electrolyte - weak dependence
• Weak electrolyte - strong dependence

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Variation of Molar Conductivity Strong
Electrolytes

• Strong Electrolytes
• Fully ionized in solution
• At low concentrations, L a vc
• L Lm - Kc (Kohlraushs Law)
• Lm - limiting molar conductivity
• L Lmas c 0
• Sum of contributions from individual ions
• Lm vl v-l- (Law of Independent Migration
  of Ions)
• l , l- molar conductivity of cations and anions
• v , v- of cations and anions per formula unit
• (MgCl2 v 1 v- 2)
• K depends on stoichiometry of electrolyte

4
Variation of Molar Conductivity Weak Electrolytes

• Not fully ionized in solution
• For weak Brønsted acids and bases (e.g., acetic
  acid, ammonia)
• HA(aq) H2O(l) ? A-(aq) H3O(aq)
• Conductivity depends on degree of ionization, a,
  (degree of deprotonation - weak acids)
• H3O a c A- a c HA (1-a)c
• Ignoring activity coefficients,
• Solving for a,
• The molar conductivity, Lm, becomes Lm a Lm

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Variation of Molar Conductivity Weak
Electrolytes - Ostwalds Dilution Law
Ostwalds Dilution Law

• If you plot 1/ Lm vs. Lmc, the intercept (c0) is
  1/Lm
• Youll do this in Lab 7!

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Mobilities of Ions

• Drift speed - terminal speed of an ion moving in
  an electric field
• Accelerating forces balanced by viscous drag
  forces
• Accelerating force
• Electric field, E Df/l
• l is separation between electodes and Df is
  potential difference
• Force, F, on an ion of charge ze is
• F zeE zeDf/l
• Cations go to negative electrode, anions to
  positive
• Drag force, Ffric, estimated from Stokes relation
• On sphere of radius a and speed, s, moving
  through a fluid
• of viscocity, h
• Ffric f s where f 6pah
• Net force is zero when F Ffric or
• s zeE/f
• Re-writing, define ionic mobility, u, such that s
  uE
• u ze/f ze/ 6pah

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Mobility, Ionic Size and Conductivity

• Drift speed governs rate of charge transport
• Solution viscosity important
• Effect of ionic size on drift speed
• Ionic radius -
• Bulky ions (RN) larger ionic radius lowers
  conductivity
• Other ions (e.g. alkali metals) hydrodynamic
  (Stokes)
• radius rather than ionic radius important
• Accounts for hydration sphere of ions which move
  with ions
• Small ions have higher charge density than large
  ions and larger hydration sphere
• Exception
• H - high conductivity and mobility
• May due to rapid reorientation of water
  molecules
• NH in liquid ammonia
• Mobility and Conductivity
• Molar conductivity (l) a mobility l zuF (F
  Faradays const.)
• For solutions in limit of infinite dilution L
  Lm
• Recall Lm vl v-l- so Lm (vz u v- z-
  u-)F
• If z z- z, Lm ( u u-)zF

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Transport Numbers

• Transport Number, t - fraction of total current
  carried by ions of a specified type
• Cations - t Anions t-
• If I is total current, then t I /I
• Since current carried by anions and cations in
  solution, t t- 1
• Limiting Transport Number, t - fraction of
  total current carried by ions of specified type
  in the limit of infinite dilution (c0)
• Current related to ionic mobility I
  (zuvcFA)(Df/l) 1
• Thus,
• 2

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Transport Numbers and Ionic Conductivity

• Because of this relationship ionic conductivities
  can be determined from limiting transport numbers
• Earlier we saw how to get Lm
• Plot of Lm vs cLm
• A variety of independent ways to get t
• Since l is related to mobility (l zuF), u can
  also be determined from transport numbers