Which of the following curve represents the variation of `lambda_(M)` with `sqrt(C)` for `AgNO_(3)`?

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of molar conductance (\( \lambda_M \)) with the square root of concentration (\( \sqrt{C} \)) for \( \text{AgNO}_3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between molar conductance (\( \lambda_M \)) and concentration (\( C \)) can be expressed as:
\[ \lambda_M = \lambda_0 + k \sqrt{C} \]
where \( \lambda_0 \) is the molar conductance at infinite dilution and \( k \) is a constant.

2. **Rearranging the Equation**:
We can rearrange the equation to fit the linear form \( y = mx + c \):
\[ \lambda_M = \lambda_0 + k \sqrt{C} \]
Here, \( y \) corresponds to \( \lambda_M \), \( x \) corresponds to \( \sqrt{C} \), \( m \) (the slope) is \( k \), and \( c \) (the y-intercept) is \( \lambda_0 \).

3. **Graph Characteristics**:
- The graph of \( \lambda_M \) versus \( \sqrt{C} \) will be a straight line.
- The slope \( k \) is positive, indicating that as \( \sqrt{C} \) increases, \( \lambda_M \) also increases.
- The y-intercept \( \lambda_0 \) is positive, representing the molar conductance at infinite dilution.

4. **Identifying the Correct Curve**:
Based on the above analysis, the graph will be a straight line that starts from a positive y-intercept and has a positive slope. Therefore, the correct option that represents this relationship is **Option A**.

### Final Answer:
The curve that represents the variation of \( \lambda_M \) with \( \sqrt{C} \) for \( \text{AgNO}_3 \) is **Option A**.