At `35^@C` , the vapour pressure of `CS_2` is 512 mm Hg and that of acetone is 344 mm Hg . A solution of `CS_2` in acetone has a total vopour pressure of 600 mm Hg. The false statement amongst the following is

Options

A. A mixture of 100 mL `CS_2` and 100 mL acetone has a volume `lt200 mL`
B. Roult's law is not obeyed by this system
C. Heat must be adsorbed in order to produce the solution at `35^@C`
D. `CS_2` and acetone are less attracted to each other than to themselves

Answer

To solve the problem, we need to analyze the given data and apply Raoult's Law to determine which statement is false.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Vapor pressure of pure carbon disulfide (CS₂) at 35°C = 512 mm Hg
- Vapor pressure of pure acetone at 35°C = 344 mm Hg
- Total vapor pressure of the solution (CS₂ in acetone) = 600 mm Hg

2. **Apply Raoult's Law:**
- Raoult's Law states that the total vapor pressure (P_total) of a solution is the sum of the partial vapor pressures of each component:
\[ P_{\text{total}} = P^0_A \cdot X_A + P^0_B \cdot X_B \]
- Where \(P^0_A\) and \(P^0_B\) are the vapor pressures of the pure components, and \(X_A\) and \(X_B\) are their mole fractions in the solution.

3. **Determine the Maximum Possible Total Vapor Pressure:**
- The maximum total vapor pressure occurs when the mole fraction of one component is 1 (i.e., pure component). In this case, the maximum vapor pressure is equal to the vapor pressure of the more volatile component, which is CS₂ (512 mm Hg).
- Since the total vapor pressure of the solution (600 mm Hg) is greater than 512 mm Hg, this indicates a positive deviation from Raoult's Law.

4. **Interpret the Positive Deviation:**
- A positive deviation means that the interactions between the molecules of different components (CS₂ and acetone) are weaker than the interactions between the molecules of the same component. Therefore, the solution has a higher vapor pressure than predicted by Raoult's Law.

5. **Evaluate the Statements:**
- **Statement A:** A mixture of 100 ml carbon disulfide and 100 ml acetone has a volume less than 200 ml. (This is likely false because volumes of miscible liquids typically add up.)
- **Statement B:** Raoult's law is not obeyed by this solution. (This is true as we observed a positive deviation.)
- **Statement C:** Heat must be absorbed in order to produce the solution at 35°C. (This is true as the solution formation is endothermic due to weaker interactions.)
- **Statement D:** CS₂ and acetone are less attracted to each other than to themselves. (This is true as it explains the positive deviation.)

6. **Identify the False Statement:**
- The false statement is **Statement A**: A mixture of 100 ml carbon disulfide and 100 ml acetone has a volume less than 200 ml.

### Final Answer:
The false statement is **Statement A**.