The equivalent conductance of NaCl at concentration C and at infinite dilution are `lambda_(C)` and `lambda_(oo)`, respectively. The correct relationship between `lambda_(C)` and `lambda_(oo)` is given as (where, the constant B is positive)

Options

A. `lambda_(C)=lambda_(oo)+(B)C`
B. `lambda_(C)=lambda_(oo)-(B)C`
C. `lambda_(C)=lambda_(oo)-(B)sqrt(C)`
D. `lambda_(C)=lambda_(oo)+(B)sqrt(C)`

Answer

To derive the relationship between the equivalent conductance of NaCl at concentration \( C \) (denoted as \( \lambda_C \)) and at infinite dilution (denoted as \( \lambda_{\infty} \)), we can use the following steps:

### Step 1: Understand the Concept of Equivalent Conductance
Equivalent conductance (\( \lambda \)) is defined as the conductance of an electrolyte solution divided by its concentration. It is a measure of how well ions can move through a solution.

### Step 2: Use the Formula for Equivalent Conductance
The relationship between the equivalent conductance at a concentration \( C \) and at infinite dilution can be expressed by the following equation:
\[ \lambda_C = \lambda_{\infty} - B \sqrt{C} \]
where:
- \( \lambda_C \) is the equivalent conductance at concentration \( C \),
- \( \lambda_{\infty} \) is the equivalent conductance at infinite dilution,
- \( B \) is a positive constant,
- \( C \) is the concentration of the solution.

### Step 3: Rearranging the Equation
From the equation above, we can see that as the concentration \( C \) increases, the term \( B \sqrt{C} \) will also increase, leading to a decrease in \( \lambda_C \) compared to \( \lambda_{\infty} \).

### Step 4: Analyzing the Relationship
This indicates that:
- At infinite dilution (\( C = 0 \)), \( \lambda_C \) approaches \( \lambda_{\infty} \).
- As \( C \) increases, \( \lambda_C \) decreases due to the negative term \( -B \sqrt{C} \).

### Step 5: Conclusion
Thus, the correct relationship between \( \lambda_C \) and \( \lambda_{\infty} \) is:
\[ \lambda_C = \lambda_{\infty} - B \sqrt{C} \]