For a binary ideal liquid solution, the variation total vapour pressure versus composition of solution is given by which of the curves?

Options

A.
B.
C.
D.

Explanation

To determine the variation of total vapor pressure versus composition of a binary ideal liquid solution, we can follow these steps:

### Step 1: Understand Raoult's Law
Raoult's Law states that the partial vapor pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution. Mathematically, it can be expressed as:
\[ P_1 = P_{1}^{0} \cdot X_1 \]
\[ P_2 = P_{2}^{0} \cdot X_2 \]
Where:
- \( P_1 \) and \( P_2 \) are the partial pressures of components 1 and 2.
- \( P_{1}^{0} \) and \( P_{2}^{0} \) are the vapor pressures of the pure components.
- \( X_1 \) and \( X_2 \) are the mole fractions of components 1 and 2 in the solution.

### Step 2: Calculate Total Vapor Pressure
The total vapor pressure \( P_{total} \) of the solution can be calculated by summing the partial pressures:
\[ P_{total} = P_1 + P_2 \]
Substituting the expressions from Raoult's Law:
\[ P_{total} = P_{1}^{0} \cdot X_1 + P_{2}^{0} \cdot X_2 \]

### Step 3: Express Mole Fractions
Since \( X_2 = 1 - X_1 \), we can rewrite the total vapor pressure as:
\[ P_{total} = P_{1}^{0} \cdot X_1 + P_{2}^{0} \cdot (1 - X_1) \]
This simplifies to:
\[ P_{total} = (P_{1}^{0} - P_{2}^{0}) \cdot X_1 + P_{2}^{0} \]

### Step 4: Analyze the Graph
The equation derived shows that \( P_{total} \) is a linear function of \( X_1 \) (the mole fraction of component 1). Therefore, the graph of total vapor pressure versus composition will be a straight line.

### Step 5: Identify the Correct Curve
In the options provided, we need to identify which curves represent linear relationships. From the analysis, we can conclude that the curves that depict linear relationships will be the correct answers.

### Conclusion
The correct options for the curves representing the variation of total vapor pressure versus composition of a binary ideal liquid solution are options A and D.

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