Question

The conductivity of \[0.1N\] \[NaOH\] solution is \[0.022s/cm\]. When equal volume of the \[0.1N\]\[HCl\] solution is added, the conductivity of the resultant solution decreases to \[0.0055s/cm\] . The equivalent conductivity in \[s - cm/equivalent\] of \[NaCl\] solution is:

Answer 1

Hint: The conductivity of a solution is its ability to conduct electricity. The unit of conductivity is expressed as Siemens per meter in SI units.

Complete step by step answer:
Equivalent conductivity of a solution is the conducting power of all the ions or the total conductance of every ion which are produced by dissolving one gram equivalent of an electrolyte into the solution. It is expressed as $\lambda $ and is related to specific conductance $\kappa $ .
The equivalent conductivity is calculated using the following formula:
$\lambda = \kappa \times V$ ; where $\kappa $ is the specific conductance and \[V\] is the volume in \[mL\] which contains one gram equivalent of the electrolyte.
The normality of a solution is the ratio of the number of gram equivalents of the solute and the volume of the solvent in litres. Thus normality is expressed as
$N = \dfrac{{{n_e}}}{{V(in{\text{ }}cc)}} \times 1000$. The number of equivalents for \[NaCl\] solution is \[1\] , so \[{n_e} = 1\] .
Thus, $V = \dfrac{{1000}}{N}$.
Substituting the value of \[V\] in the formula of equivalent conductivity,
$\lambda = \kappa \times \dfrac{{1000}}{N}$ .
The normality of the \[NaCl\] solution is $\dfrac{{0.1}}{2}N$ (due to presence of two ions coming from \[NaOH\] and \[HCl\] ). The specific conductance $\kappa $ is \[0.0055s/cm\]. Thus inserting the values in the equation gives,
\[\lambda = 0.0055 \times \dfrac{{1000}}{{\dfrac{{0.1}}{2}}}\]
$\lambda = 110$.
Thus, the equivalent conductivity in \[s - cm/equivalent\] of \[NaCl\] solution is \[110{\text{ }}s - cm/equivalent\].

Note: Another similar term is used to express the conductivity of a solution called molar conductance. It is defined as the total conductance of all the ions produced upon complete dissociation of one mole of an electrolyte undergoes into constituent ions. The formula for molar conductance is similar to equivalent conductance, and is denoted by the symbol ‘$\mu $’.