`A_(AgCl)^(oo)` can be obtained:

Options

A. by extraplotation of the graph `Lambda` and `sqrtC` to zero concentration
B. by known values of `Lambda^oo` of `AgNO_3`, HCl and `HNO_3`
C. both (a) and (b)
D. None of these

Answer

To determine the ionic conductivity at infinite dilution for AgCl, we can analyze the options provided in the question step by step.

### Step 1: Understanding Ionic Conductivity
Ionic conductivity is a measure of a solution's ability to conduct electricity due to the movement of ions. At infinite dilution, the ionic conductivity reaches a limiting value because the ions are far apart and do not interact with each other.

### Step 2: Analyzing the Options
We have four options to consider:
1. Extrapolation of the graph between conductivity and the square root of concentration to zero concentration.
2. Using known values of the limiting ionic conductivities of AgNO3, HCl, and HNO3.
3. Both A and B.
4. None of these.

### Step 3: Option A - Extrapolation of the Graph
To find the limiting ionic conductivity of AgCl, we can plot a graph of molar conductivity (Λ) against the square root of concentration (√C). As the concentration approaches zero, we can extrapolate the graph to find the limiting molar conductivity (Λ°) at infinite dilution. This method is valid and commonly used in electrochemistry.

### Step 4: Option B - Known Values of Conductivities
The limiting ionic conductivity of AgCl can also be calculated using the known values of the limiting ionic conductivities of its constituent ions. The dissociation of AgCl can be represented as:
\[ \text{AgCl} \rightarrow \text{Ag}^+ + \text{Cl}^- \]
The limiting ionic conductivity of AgCl (Λ°) can be expressed as:
\[ \Lambda°_{\text{AgCl}} = \Lambda°_{\text{Ag}^+} + \Lambda°_{\text{Cl}^-} \]
Thus, if we know the limiting ionic conductivities of AgNO3, HCl, and HNO3, we can derive the limiting ionic conductivity for AgCl.

### Step 5: Conclusion
Both methods (A and B) are valid ways to determine the ionic conductivity at infinite dilution for AgCl. Therefore, the correct answer is option C: both A and B.

### Final Answer
The ionic conductivity at infinite dilution for AgCl can be obtained by both extrapolation of the graph and using known values of limiting ionic conductivities of AgNO3, HCl, and HNO3. Thus, the answer is **C: both A and B**.

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