Question

Two solutions of X and Y electrolytes are taken in two beakers and diluted by adding $500\operatorname{ml}$ of water.${{\lambda }_{m}}$ of X increases by $1.5$ times while that of Y increases by $20$ times, what could be the electrolytes X and Y?
(A) $X\to \operatorname{NaCl},Y\to \operatorname{KCl}$
(B) $X\to \operatorname{NaCl},Y\to {{\operatorname{CH}}_{3}}COOH$
(C) $X\to KOH,Y\to NaOH$
(D) $X\to {{\operatorname{CH}}_{3}}COOH,Y\to \operatorname{NaCl}$

Answer 1

One electrolyte is a strong one and the other is a weak one. Use the concept of molar conductivity when a solution is diluted to solve this question.

Complete answer:
Let us take it slow and understand the concepts used in this question one by one. First we explain what is conductivity of an electrolyte.
Conductivity of an electrolyte can be defined as a physical quantity which is the conductance of a solution when the separation between the electrodes and their surface area are taken as unity. It is a constant which is the reciprocal of resistivity and is represented as “$\kappa$”. The equation to derive the above definition is as follows:

& G=\dfrac{\kappa A}{L} \\\ & \Rightarrow \kappa =\dfrac{GL}{A} \\\ \end{aligned}$$ Here, “G” is conductance of a solution; “A” is the surface area of the electrodes; “L” is the length of separation between two electrodes. If $A=L=1$, then $\kappa =G$ (as defined above). Conductivity is rather vague when we try to understand a solution consisting of many electrolytes. It is because the ability of these charge carrying species to conduct electricity depends on their individual shapes and sizes and also on their concentration. To tackle these cases, another term known as molar conductivity was introduced. It is represented as${{\lambda }_{m}}$and is defined as the conductivity of any electrolyte within a volume where its concentration is unity. It can be expressed as: $${{\lambda }_{m}}=\dfrac{\kappa }{c}$$ Where “$\kappa $” is conductivity and “c” is concentration of the electrolyte. It has been experimentally seen that conductivity of any electrolyte decreases and molar conductivity of that electrolyte increases on dilution. The increase in molar conductivity often compensates more than enough for the decrease in conductivity. And therefore, overall the conductance of the solution increases on dilution. Now let’s come to the type of electrolytes. They can be classified into two types: \- Strong electrolytes These are strong acids and bases which completely ionizes when dissolved in water or other polar solvents. \- Weak electrolytes These are organic acids and bases, which do not ionise completely. Their complete ionisation takes place only at infinite dilution which cannot be obtained physically. The molar conductivity of strong electrolytes increases in a very slow manner on dilution. This is because the ions have been completely dissociated and now only the volume carrying one mole of these electrolytes increases. On the other hand, as dilution increases the dissociation of weak electrolytes increases, which increases their molar conductivity many folds along with the increase in total volume. Keeping the above things in mind, we can conclude that “X” is a strong electrolyte and “Y” is a weak electrolyte. From the options given we can clearly see that, $X\to \operatorname{NaCl},Y\to {{\operatorname{CH}}_{3}}COOH$. **Hence the answer is option (B).** **Note:** According to Kohlrausch law, the dissociation of weak electrolytes at infinite dilution is hundred percent. Calculating the conductivity of weak electrolytes such as organic acids and bases at infinite dilution is not possible in our labs because infinity is not defined. Therefore, this statement is a theory based on the dilution we can achieve in our labs. If in the question two similar electrolytes would have been given, then we had to calculate the increase in molar conductivity.