Which one of the following is the correct plot of `^^_m("in s cm"^2mol^(-1)) and sqrtc("in" ((mol)/L)^(1/2))` for KCl solution ? `(y=^^_m,x=sqrtc)`

Options

A.
B.
C.
D.

Answer

To solve the question regarding the correct plot of molar conductance (λm) versus the square root of concentration (√C) for KCl solution, we will follow these steps:

### Step 1: Understand the relationship
The relationship between molar conductance (λm) and concentration (C) for strong electrolytes can be described by the Debye-Hückel-Onsager equation:
\[ \lambda_m = \lambda_m^0 - b \sqrt{C} \]
where:
- \( \lambda_m \) is the molar conductance at a given concentration,
- \( \lambda_m^0 \) is the molar conductance at infinite dilution,
- \( b \) is a constant (Debye constant),
- \( C \) is the concentration.

### Step 2: Rearranging the equation
From the equation, we can identify that:
- The y-axis will represent \( \lambda_m \),
- The x-axis will represent \( \sqrt{C} \).

This can be rewritten in the form of a linear equation:
\[ y = mx + c \]
where:
- \( y = \lambda_m \),
- \( m = -b \) (the slope, which is negative),
- \( x = \sqrt{C} \),
- \( c = \lambda_m^0 \) (the y-intercept).

### Step 3: Analyze the plot characteristics
Given that the slope (m) is negative, the plot will show a downward trend as we move along the x-axis (increasing \( \sqrt{C} \)). The y-intercept will be positive, indicating that at zero concentration, the molar conductance approaches \( \lambda_m^0 \).

### Step 4: Evaluate the options
Now, we need to evaluate the provided options based on the characteristics of the plot:
1. **Option 1**: Slope is not negative (incorrect).
2. **Option 2**: Slope is negative and there is a y-intercept (correct).
3. **Option 3**: Slope is not negative (incorrect).
4. **Option 4**: Slope is not negative (incorrect).

### Conclusion
The correct plot for the relationship between molar conductance and the square root of concentration for KCl solution is represented by **Option 2**, which shows a negative slope and a positive y-intercept.

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