In a conductance experiment, aqueous \( \text{AgNO}_3 \) solution is added to aqueous \( \text{KCl} \) solution gradually and simultaneously the molar conductivity (\( \lambda_m \)) is measured. The correct plot of \( \lambda_m \) versus volume of \( \text{AgNO}_3 \) solution is
Show Hint
In precipitation titrations where a highly mobile ion (like \( \text{Cl}^- \)) is replaced by another ion of similar mobility (like \( \text{NO}_3^- \)), the conductivity curve remains nearly horizontal up to the end point, followed by a sharp rise due to the excess added titrant.
Step 1: Understanding the Question:
The question asks for the correct conductometric titration curve representing how the molar conductivity (\( \lambda_m \)) of the solution changes as aqueous \( \text{AgNO}_3 \) is gradually added to a container containing aqueous \( \text{KCl} \). Step 2: Key Formula or Approach:
The conductivity of an electrolyte solution depends on the concentration and individual ionic mobilities (limiting molar conductivities, \( \lambda^\circ \)) of the ions present:
- Precipitation reaction:
\[ \text{KCl(aq)} + \text{AgNO}_3\text{(aq)} \rightarrow \text{AgCl(s)} \downarrow + \text{KNO}_3\text{(aq)} \]
- Keep in mind the limiting ionic conductivities of the participating ions:
\[ \lambda^\circ(\text{Cl}^-) = 76.3 \times 10^{-4}\text{ S m}^2\text{ mol}^{-1} \]
\[ \lambda^\circ(\text{NO}_3^-) = 71.4 \times 10^{-4}\text{ S m}^2\text{ mol}^{-1} \] Step 3: Detailed Explanation:
1. Before the Equivalence Point:
As \( \text{AgNO}_3 \) is added, highly mobile \( \text{Cl}^- \) ions precipitate out of the solution as insoluble \( \text{AgCl(s)} \). They are replaced in the solution by \( \text{NO}_3^- \) ions of nearly identical (but slightly lower) mobility. The concentration of \( \text{K}^+ \) remains constant. Consequently, the molar conductivity (\( \lambda_m \)) remains almost constant, exhibiting only a very slight decrease up to the equivalence point.
2. After the Equivalence Point:
Once all \( \text{Cl}^- \) ions are precipitated, any further addition of \( \text{AgNO}_3 \) introduces free, highly conducting \( \text{Ag}^+ \) and \( \text{NO}_3^- \) ions into the solution. This causes a rapid increase in the overall concentration of ions, leading to a steep, sharp increase in the molar conductivity (\( \lambda_m \)).
This behavior is correctly represented by the graph in option (D). Step 4: Final Answer:
The correct plot of molar conductivity is shown in option (D).
