Question

Calculate the molar conductivity of water at infinite dilution (in S m2mol-1) (molar conductivity of hydrogen ions and the molar conductivity of hydroxide ions at infinite dilution are \[349.6 \times {10^{ - 4}}s{m^2}mo{l^{ - 1}}\]and \[198.3 \times {10^{ - 4}}s{m^2}mo{l^{ - 1}}\]
A.547.9
B.647.9
C.$647.9 x 10^-4$
D.$547.9 x 10^-4$

Answer 1

Hint:Molar conductivity is defined as the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution. It is denoted by (lambda). A correlation exists between the molar and the specific conductivity.

Complete step by step answer:
The other quantities such as specific and equivalent conductivities are also used frequently. The ability of the material to conduct electricity is known as specific conductivity. Molar conductivity and specific conductivity are interrelated as:
Specific conductance is given by K and molar conductance is given by λ(lambda)
The relation between the two terms is:
$Λ= K X 1000/M$
Also $Λ= {(1/R) X (l/a)} X 1000/M$
Where
Λ= Molar conductance
K = Specific conductance
R= Resistance
M= Molarity of the solution
l= length
a= area of cross section

The molar conductivity of the water can be calculated as:
\[
  {\lambda _{{H_2}O}}^0 = {\lambda ^0}_{{H^ + }} + {\lambda ^0}_{O{H^ - }} \\
   = 349.6 \times {10^{ - 4}}s{m^2}mo{l^{ - 1}} + 198.3 \times {10^{ - 4}}s{m^2}mo{l^{ - 1}} \\
   = 547.9 \times {10^{ - 4}}s{m^2}mo{l^{ - 1}} \\
\]
Thus it is evident from the above calculations that the molar conductivity of water at infinite dilution is equal to the molar conductivities of the H+ and OH- ions at the infinite dilution.
Metals are the good conductors of electricity while non –metals are poor conductors of electricity.
The conductivity of electrolytic solutions depends on:
1. The nature and the concentration of the electrolyte added
2. The size of the ions produced and their salvation.
3. Solvent nature and viscosity.
4. Temperature.
Thus option D. is the correct answer.

Note:
 Water in its pure form has less conductivity because of the inability to exist in the ionic form while when the water is distilled it does not conduct the electricity because no ions are present in the distil form.