Question

The specific conductance of a salt of 0.01 M concentration is $1.061\times {{10}^{-4}}$. Molar conductance of the same solution will be_________.
A.\[1.061\times {{10}^{-4}}\]
B.1.061
C.10.61
D.106.1

Answer 1

Hint: We know that specific conductance of an electrolyte solution is a measure of its ability to conduct electricity. And molar conductivity is the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution.

Step by step solution:
We know that, the molar conductance is denoted by lambda (${{\Lambda }_{m}}$) and its unit is $Sc{{m}^{2}}mo{{l}^{-1}}$. Specific conductance is represented by kappa ($\kappa $) and its unit is S/m. Here S is Siemens. And the formulas of molar conductance and specific conductance are:
Specific conductance ($\kappa $) = cell constant / resistance
Molar conductance (${{\Lambda }_{m}}$) = specific conductance x 1000 / C
                 = \[\dfrac{\kappa \times 1000}{C}\]
Where, C is the molarity
Given,
Molarity = 0.01 M,
Specific conductance = $1.061\times {{10}^{-4}}$
So, by putting all given data in the formula of molar conductance:
Molar conductance (${{\Lambda }_{m}}$) = $\dfrac{\kappa \times 1000}{C}$
                   = $\dfrac{1.061\times {{10}^{-4}}\times 1000}{0.01}$
                   = 10.61 $Sc{{m}^{2}}mo{{l}^{-1}}$

So, the correct answer is the option “C”.

Note: Here, Siemens(S) is the derived unit of electric conductance. So, here we should be careful about the given units, data and which formula we will use. Instead of giving direct specific conductance, cell constant and resistance can be given. If given then by applying the formula of specific conductance we can find its value.