Which one of the following is an incorrect form of Raoult's law?

Options

A. `(P_(s))/(P_(0)) = (N)/(n +N)`
B. `(P^(0))/(P^(0)-P_(s)) = 1+(N)/(n)`
C. `(P^(0) - P_(s))/(P_(s)) = (n)/(n+N)`
D. `(P_(s))/(P^(0) - P_(s)) = (N)/(n)`

Answer

To solve the question regarding which form of Raoult's law is incorrect, we need to analyze the given options based on the principles of Raoult's law and the relationships between vapor pressures and mole fractions.

### Step-by-Step Solution:

1. **Understand Raoult's Law**:
Raoult's law states that the vapor pressure of a solvent in a solution (P_s) is directly proportional to the mole fraction of the solvent (X_s) in the solution. The formula can be expressed as:
\[ P_s = X_s \cdot P_0 \]
where \( P_0 \) is the vapor pressure of the pure solvent.

2. **Relative Lowering of Vapor Pressure**:
The relative lowering of vapor pressure can be expressed as:
\[ \frac{P_0 - P_s}{P_0} = X_{solute} \]
This can also be rewritten in terms of moles of solute (n) and solvent (N):
\[ \frac{P_0 - P_s}{P_0} = \frac{n}{n + N} \]

3. **Evaluate Each Option**:
- **Option A**: \( \frac{P_s}{P_0} = \frac{N}{n + N} \)
- This is correct as it derives from the rearrangement of the original equation.

- **Option B**: \( \frac{P_0}{P_0 - P_s} = 1 + \frac{N}{n} \)
- This is also correct as it can be derived by taking the reciprocal of the relative lowering of vapor pressure.

- **Option C**: \( \frac{P_0 - P_s}{P_s} = \frac{n}{n + N} \)
- This is incorrect because it does not align with the established relationships. The correct form should be \( \frac{P_0 - P_s}{P_0} = \frac{n}{n + N} \).

- **Option D**: \( \frac{P_s}{P_0 - P_s} = \frac{N}{n} \)
- This is also correct as it can be derived from the original equation.

4. **Conclusion**:
The incorrect form of Raoult's law among the options provided is **Option C**.