Which of the following plots represents an ideal binary mixture?

Options

A. plot of `P_("total") v//s 1//X_(B)` is linear `(X_(B) =` mole fraction of 'B' in liquid phase)
B. plot of `P_("total")v//s Y_(A)` is linear `(Y_(B)=` mole fraction of 'A' in vapour phase)
C. plot of `(1)/(P_("total")) v//s Y_(A)` is linear
D. plot of `(1)/(P_("total"))v//s Y_(B)` is non linear

Explanation

To determine which plot represents an ideal binary mixture, we need to analyze the relationship between the total pressure and the mole fraction of one of the components in the mixture. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Ideal Binary Mixture
An ideal binary mixture is one where the components behave ideally, meaning that the interactions between different molecules are similar to those between like molecules. In such mixtures, the total vapor pressure can be predicted using Raoult's Law.

### Step 2: Apply Raoult's Law
According to Raoult's Law, the total vapor pressure (P_total) of an ideal binary mixture is given by:
\[ P_{total} = P_{A} + P_{B} \]
where \( P_{A} \) and \( P_{B} \) are the partial pressures of components A and B, respectively.

### Step 3: Relate Partial Pressures to Mole Fractions
The partial pressures can be expressed in terms of the mole fractions of the components:
\[ P_{A} = X_{A} \cdot P_{A}^{0} \]
\[ P_{B} = X_{B} \cdot P_{B}^{0} \]
where \( X_{A} \) and \( X_{B} \) are the mole fractions of A and B, and \( P_{A}^{0} \) and \( P_{B}^{0} \) are the vapor pressures of the pure components A and B.

### Step 4: Express Total Pressure in Terms of Mole Fractions
Substituting the expressions for \( P_{A} \) and \( P_{B} \) into the equation for \( P_{total} \):
\[ P_{total} = X_{A} \cdot P_{A}^{0} + X_{B} \cdot P_{B}^{0} \]
Since \( X_{B} = 1 - X_{A} \), we can rewrite this as:
\[ P_{total} = X_{A} \cdot P_{A}^{0} + (1 - X_{A}) \cdot P_{B}^{0} \]

### Step 5: Analyze the Plot
In the context of the question, we are interested in the relationship between \( 1/P_{total} \) and \( Y_{A} \) (the mole fraction of A in the vapor phase). The relationship can be derived from the above equations, leading to:
\[ \frac{1}{P_{total}} \propto Y_{A} \]
This indicates that if we plot \( 1/P_{total} \) against \( Y_{A} \), we will get a linear relationship.

### Step 6: Identify the Correct Plot
From the options provided, we need to identify which plot shows a linear relationship between \( 1/P_{total} \) and \( Y_{A} \). The correct option will show a straight line, confirming the ideal behavior of the binary mixture.

### Conclusion
The plot that represents an ideal binary mixture is the one that shows a linear relationship between \( 1/P_{total} \) and \( Y_{A} \).

---