The key idea is Raoult's Law for ideal solutions and deviations from ideality.

For an ideal solution, the partial vapour pressure of each component is given by Raoult's Law, and the total pressure is the sum of these partial pressures.

To plot the ideal solution behavior, calculate $p_{acetone}$, $p_{chloroform}$, and $p_{total}$ for various $x_{acetone}$ values using the given pure vapour pressures ($p_{acetone}^\circ = 741.8$ mm Hg, $p_{chloroform}^\circ = 632.8$ mm Hg). Plot these calculated values against $x_{acetone}$ (from 0 to 1). On the same graph, plot the provided experimental $p_{acetone}$ and $p_{chloroform}$ values against their respective $x_{acetone}$. …

When two volatile liquids mix, the vapor pressure of the resulting solution depends on the mole fractions of the components and their pure vapor pressures. For an ideal solution, this relationship is described by Raoult's Law. Real solutions, however, often deviate from this ideal behavior due to differences in intermolecular forces.

Concept: Raoult's Law and Deviations

1. Raoult's Law for Ideal Solutions: For an ideal solution, the partial vapor pressure of each component ($p_A$) in the solution is directly proportional to its mole fraction ($x_A$) in the liquid phase and its vapor pressure in the pure state ($P^0_A$).

   $p_A = x_A P^0_A$

   $p_B = x_B P^0_B$

2. Dalton's Law of Partial Pressures: The total vapor pressure ($p_{total}$) of the solution is the sum of the partial vapor pressures of its components.

   $p_{total} = p_A + p_B = x_A P^0_A + x_B P^0_B$

   Since $x_A + x_B = 1$, we can also write $p_{total} = x_A P^0_A + (1 - x_A) P^0_B$. This shows that for an ideal solution, the total vapor pressure varies linearly with the mole fraction of one component.

3. Deviations from Ideal Behavior: Real solutions deviate from Raoult's Law when the intermolecular forces between unlike molecules (A-B) are different from those between like molecules (A-A and B-B).

   • Positive Deviation: Occurs when A-B interactions are weaker than A-A and B-B interactions. Molecules escape more easily into the vapor phase, leading to higher partial and total vapor pressures than predicted by Raoult's Law.
   • Negative Deviation: Occurs when A-B interactions are stronger than A-A and B-B interactions. Molecules are held more tightly in the liquid phase, making it harder for them to escape. This results in lower partial and total vapor pressures than predicted by Raoult's Law.

To determine the deviation, we first calculate the ideal vapor pressures using Raoult's Law for various compositions and then compare these theoretical values with the experimentally observed values.

Step-by-Step Solution

1. Identify Given Data

We are given the pure vapor pressures at 328 K:

• Vapor pressure of pure acetone ($P^0_{acetone}$) = 741.8 mm Hg
• Vapor pressure of pure chloroform ($P^0_{chloroform}$) = 632.8 mm Hg

We are also provided with experimental data for different compositions:

2. Calculate Ideal Partial and Total Vapor Pressures

Using Raoult's Law, we calculate the ideal partial pressures for acetone and chloroform, and then the ideal total pressure for each given composition. We also calculate the experimental total pressure by summing the experimental partial pressures.

• Ideal $p_{acetone} = x_{acetone} \times P^0_{acetone}$
• Ideal $p_{chloroform} = x_{chloroform} \times P^0_{chloroform}$ (where $x_{chloroform} = 1 - x_{acetone}$)
• Ideal $p_{total} = \text{Ideal } p_{acetone} + \text{Ideal } p_{chloroform}$
• Experimental $p_{total} = \text{Experimental } p_{acetone} + \text{Experimental } p_{chloroform}$

Here is a table summarizing the calculated ideal values alongside the experimental data:

3. Plot the Data …

Method: Raoult’s Law Plotting & Deviation Analysis

Concept First

For an ideal solution, each component obeys Raoult’s Law:

• $p_A = x_A \cdot p_A^*$
• $p_B = x_B \cdot p_B^*$
• $p_{total} = p_A + p_B$

Where $p_A^*$ and $p_B^*$ are vapour pressures of pure components.

Steps

Step 1: Calculate ideal values using Raoult’s Law

Given at 328 K:

• $p_{acetone}^* = 741.8$ mm Hg
• $p_{chloroform}^* = 632.8$ mm Hg

For any $x_{acetone}$:

• $p_{acetone}^{ideal} = x_{acetone} \times 741.8$
• $p_{chloroform}^{ideal} = (1 - x_{acetone}) \times 632.8$
• $p_{total}^{ideal} = p_{acetone}^{ideal} + p_{chloroform}^{ideal}$

Step 2: Plot the ideal lines

On a graph with $x_{acetone}$ on x-axis (0 to 1) and pressure (mm Hg) on y-axis:

• Plot $p_{acetone}^{ideal}$ as a straight line from (0,0) to (1, 741.8)
• Plot $p_{chloroform}^{ideal}$ as a straight line from (0, 632.8) to (1, 0)
• Plot $p_{total}^{ideal}$ as a straight line from (0, 632.8) to (1, 741.8)

Step 3: Plot the experimental data

Using the given table:

• Convert $100 \times x_{acetone}$ to $x_{acetone}$ (divide by 100)
• Plot experimental $p_{acetone}$, $p_{chloroform}$, and $p_{total}$ as points

Step 4: Compare and identify deviation …

✗ Mistake 1: Confusing mole fraction with molality

Why it happens:

Both start with “mole” and use $x$ as a symbol. Students sometimes try to convert given $x_{acetone}$ values into molality or mass percent.

How to avoid:

• Mole fraction ($x$) is dimensionless — it’s moles of one component divided by total moles.
• Molality (m) has units mol/kg.
• In this problem, $x_{acetone}$ is already given — no conversion needed.
• Key check: If the problem says “$100 \times x_{acetone}$”, it’s just mole fraction in percentage form.

✗ Mistake 2: Plotting $p_{total}$ incorrectly for the ideal case

Why it happens:

Students often plot only the given experimental data and forget to compute and plot the ideal $p_{total}$ line.

How to avoid:

• For an ideal solution, Raoult’s Law says:

• Given: $p_{acetone}^0 = 741.8$ mm Hg, $p_{chloroform}^0 = 632.8$ mm Hg
• Compute $p_{total}$ for at least 3–4 values of $x_{acetone}$ (e.g., 0, 0.25, 0.5, 0.75, 1) and plot as a straight line (since ideal).

✗ Mistake 3: Misidentifying deviation direction

Why it happens:

Students look only at one component’s data and guess.

How to avoid:

• Positive deviation: Experimental $p_{total}$ > Ideal $p_{total}$ (weaker intermolecular forces in mixture).
• Negative deviation: Experimental $p_{total}$ < Ideal $p_{total}$ (stronger forces in mixture).
• Check both components:
  • For acetone: ideal $p_{acetone} = x_{acetone} \times 741.8$
  • Compare with experimental $p_{acetone}$ — if experimental is higher, that’s positive deviation.
  • For chloroform: ideal $p_{chloroform} = (1 - x_{acetone}) \times 632.8$
  • Compare similarly.

Quick check with data:

At $x_{acetone} = 0.5$ (approx):

• Ideal $p_{acetone} = 0.5 \times 741.8 = 370.9$ mm Hg
• Experimental $p_{acetone} = 322.7$ mm Hg → lower
• Ideal $p_{chloroform} = 0.5 \times 632.8 = 316.4$ mm Hg …