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Question: The specific conductance (K) of an electrolyte of 0.1 N concentration is related to equivalent con...

The specific conductance (K) of an electrolyte of 0.1 N concentration is related to
equivalent conductance (Λe{{\Lambda }_{e}}) by the following formula.
(A) Λe{{\Lambda }_{e}}=K
(B) Λe{{\Lambda }_{e}}= 10K
(C) Λe{{\Lambda }_{e}}= 100K
(D) Λe{{\Lambda }_{e}}= 10000K

Explanation

Solution

Hint: Equivalent conductance is defined as the conductance of all the ions produced by one-gram equivalent of an electrolyte in a given solution. In case, if the concentration of the solution is c gram equivalent per litre, then the volume containing 1 g equivalent of the electrolyte will be 1000/e.
So, equivalent conductance, Λe=specific conductance(K)×1000N{{\Lambda }_{e}}=\dfrac{\text{specific}\,\text{conductance(K)}\times \text{1000}}{N}
Where, N = normality

Complete step by step solution:

  • Specific Conductance is the conductance of a given solution enclosed in a cell having two electrodes which are of unit area and are separated by 1cm.
    Equivalent Conductance is the conductance of all the ions produced by one-gram equivalent of an electrolyte in a given solution.
  • Specific Conductivity decreases with a decrease in concentration. As the number of ions per unit volume that carry current in a solution decreases on dilution. Thus, concentration and conductivity are directly proportional to each other.
  • Now, in the given question, the specific conductance is given as K,
    The concentration of the electrolyte = 0.1N

By applying the formula for equivalent conductance,

Λe=K×1000N{{\Lambda }_{e}}=\dfrac{K\times \text{1000}}{N}

Λe=K×10000.1{{\Lambda }_{e}}=\dfrac{K\times \text{1000}}{0.1}

Λe=10000K{{\Lambda }_{e}}=10000K

Therefore, the correct answer is (d).

Note: The formula for molar conductance is almost similar to that of equivalent conductance, but it is denoted by the symbol ‘μ’. The formula that can be used to calculate molar conductance is: μ = kV.
It is important to note that equivalent conductance can be calculated as:
equivalent conductance = molar conductancen\text{equivalent}\,\text{conductance = }\dfrac{\text{molar}\,\text{conductance}}{\text{n}}
where, n = molecular massequivalent mass\text{n = }\dfrac{\text{molecular}\,\text{mass}}{\text{equivalent}\,\text{mass}}