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 given options one by one.

### Step 1: Understanding 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 in the solution. Mathematically, it can be expressed as:
\[ P_s = P_0 \cdot X_s \]
where:
- \( P_s \) = vapor pressure of the solvent in the solution
- \( P_0 \) = vapor pressure of the pure solvent
- \( X_s \) = mole fraction of the solvent in the solution

### Step 2: Analyze Each Option
We will analyze each option provided to see if it adheres to the principles of Raoult's law.

#### Option A:
\[ \frac{P_0 - P_s}{P_0} = \frac{n}{n + N} \]
This form is consistent with Raoult's law. It represents the relationship between the change in vapor pressure and the mole fraction of the solute.

#### Option B:
\[ \frac{P_0}{P_0 - P_s} = \frac{n + N}{n} \]
This equation can be manipulated and shown to be valid based on the principles of Raoult's law.

#### Option C:
\[ P_0 - P_s = P_0 \cdot \frac{n}{N} \]
This form is incorrect because it does not correctly represent the relationship dictated by Raoult's law. The correct relationship should involve the mole fractions rather than just the number of moles.

### Conclusion:
After analyzing all the options, we find that **Option C** is the incorrect form of Raoult's law.

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