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 information regarding the vapor pressures of CS2 and acetone, and determine which statement is false based on Raoult's law and the concept of positive deviation.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Vapor pressure of CS2 (P_CS2) = 512 mm Hg
- Vapor pressure of acetone (P_acetone) = 344 mm Hg
- Total vapor pressure of the solution (P_total) = 600 mm Hg

2. **Understanding Raoult's Law:**
- According to Raoult's law, the total vapor pressure (P_total) of a solution is given by:
\[ P_{total} = P_{CS2} \cdot X_{CS2} + P_{acetone} \cdot X_{acetone} \]
where \(X_{CS2}\) and \(X_{acetone}\) are the mole fractions of CS2 and acetone, respectively.

3. **Determine Maximum Total Vapor Pressure:**
- The maximum total vapor pressure occurs when one component is present in pure form. If CS2 is pure, \(X_{CS2} = 1\) and \(X_{acetone} = 0\):
\[ P_{total (max)} = P_{CS2} = 512 \text{ mm Hg} \]
- If acetone is pure, \(X_{acetone} = 1\) and \(X_{CS2} = 0\):
\[ P_{total (max)} = P_{acetone} = 344 \text{ mm Hg} \]
- Therefore, the maximum total vapor pressure of the solution can only be 512 mm Hg or 344 mm Hg, which is less than the observed 600 mm Hg.

4. **Identify Positive Deviation from Raoult's Law:**
- Since the observed total vapor pressure (600 mm Hg) is greater than the maximum calculated vapor pressure (512 mm Hg), this indicates a positive deviation from Raoult's law.
- In a positive deviation, the interactions between the components (CS2 and acetone) are weaker than the interactions within each pure component.

5. **Analyze the Statements:**
- We need to determine which statement is false based on our analysis:
1. A mixture of 100 ml CS2 and 100 ml acetone has a volume less than 200 ml. (This is false; the volume will be greater than 200 ml due to positive deviation.)
2. Raoult's law is not obeyed in this system. (This is true.)
3. Heat must be absorbed in order to produce the solution at 35 degrees Celsius. (This is true; positive deviation generally indicates endothermic mixing.)
4. CS2 and acetone are less attracted to each other than to themselves. (This is true; it explains the positive deviation.)

6. **Conclusion:**
- The false statement is the first one: "A mixture of 100 ml CS2 and 100 ml acetone has a volume less than 200 ml."