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 determine which form of Raoult's law is incorrect, we will analyze the various forms presented in the options.

### Step-by-Step Solution:

1. **Understanding Raoult's Law**:
Raoult's law states that the relative lowering of vapor pressure of a solvent when a solute is added is equal to the mole fraction of the solute. Mathematically, it can be expressed as:
\[ \frac{P_0 - P_s}{P_0} = X_{solute} \]
where \( P_0 \) is the vapor pressure of the pure solvent, \( P_s \) is the vapor pressure of the solution, and \( X_{solute} \) is the mole fraction of the solute.

2. **Rearranging the General Form**:
From the general form, we can express it in various ways. For example:
\[ \frac{P_0}{P_0 - P_s} = 1 + \frac{N}{n} \]
where \( N \) is the number of moles of solvent and \( n \) is the number of moles of solute.

3. **Identifying the Forms**:
We will check each option provided in the question to see if they conform to the correct forms derived from Raoult's law.

4. **Evaluating Each Option**:
- **Option 1**: \( \frac{P_0 - P_s}{P_0} = \frac{n}{N + n} \)
- This is a correct form of Raoult's law.
- **Option 2**: \( \frac{P_0}{P_0 - P_s} = 1 + \frac{N}{n} \)
- This is also a correct form.
- **Option 3**: \( \frac{P_0 - P_s}{P_s} = \frac{N}{n} + 1 \)
- This form is incorrect. If we take the reciprocal of \( \frac{P_0 - P_s}{P_s} \), we should not get \( \frac{N}{n} + 1 \).
- **Option 4**: \( \frac{P_s}{P_0 - P_s} = \frac{N}{n} \)
- This is a correct form derived from rearranging the general equation.

5. **Conclusion**:
After evaluating all options, we find that **Option 3** is the incorrect form of Raoult's law.

### Final Answer:
The incorrect form of Raoult's law is **Option 3**.