Question

The limiting molar ionic conductivities for Mg2+ and Cl- are 0.0106 Ω-1 mol-1 m2 and 0.0076 Ω-1 mol-1 m2 respectively.

a) Calculate the limiting molar conductivity of an MgCl2 solution (2 marks).

b) Calculate the ionic mobility (2 marks), ionic conductivity (2 marks) and transport number (2 marks) for the magnesium and chloride ions in a 0.01 M MgCl2 solution.

c) What electric field strength would produce a current density of 1 mA cm-2 for this 0.01 M solution of MgCl2 (2 marks)?

d) Provide a graph of the molar conductivity vs. concentration that shows the trends for a strong, intermediate and weak electrolyte (3 marks). What is Khalraush’s law and which electrolyte would fit this law best (2 marks)?

Answer 1

a. using Khalraush's law

limiting molar conductivity of Mg Cl₂ is

0.0106 +2 0.0076

= 0.0258 ohm^-1 mol^-1 m²

b.

Transport no of Mg²⁺(t₊) = v⁺ .

where V⁺ = no of cation

or t₊ = 0.0106/0.0258 = 0.410

then, transport no of Cl^-is (t_-)  = 1-0.41 = 0.59

ionic mobility ()  =

where t_c = transport no , F = 95000 c

now , ionic mobility of Mg²⁺ (u) = 0.41*0.0258/96500 = 1.09 10^-7 m² volt -1 sec ^-1

ionic mobility of Cl- ( v) = 2.4*10^-7m² volt -1 sec ^-1

ionic conductivity (K) = Molality * ionic conductance  

ionic conductivity of Mg²⁺ = 0.01*0.0106 = 0.000106 Sm^-1

ionic conductivity of Cl^- = 2*0.01*0.0076 = 0.000152 Sm^-1

total conductvity = 0.00106+0.00152= 0.00258 Sm^-1

c.

Current density (J) = Conductivity (K) * E (electric field strength)

or , E = J/K = 1/0.00258 = 387.59 A/m²

d.

e. Kohlrausch's law states that the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations .

i,e .equivalent conductance ;

V⁺ = number of cation, V^-= number of anion

= conductance of cation

= conductance of anion

From the graph of molar conductivity Vs concentration the value of molar conductance at infinite dilution can be calculated by extrapolated for the solution of strong and intermediate electrolyte. But in case of weak electrolyte the line does not cut the Y axis ( i.e. Molar conductance ). Hence by extrapolated the curve the value of molar conductance can not be calculated . That is why  Kohlrausch's law is fitted best for weak electrolyte.