Which one of the following is correctly matched :-
`{:((i)z=1,,,,(A)-"ve deviation"),((ii)zlt1,,,,(B) +"ve deviation"),((iii)zgt1,,,,( C)"Ideal behaviour"),((iv)z_(c)=3//8,,,,(D) "At crtical conditions"):}`

Options

A. (i)-A (ii)-B (iii)-C,(iv)-D
B. (i)-B (ii)-A (iii)-D,(iv)-C
C. (i)-C (ii)-A (iii)-B,(iv)-D
D. (i)-D (ii)-B (iii)-A,(iv)-C

Answer

To solve the question of matching the compressibility factor (Z) with its corresponding behavior, we will analyze each option step by step.

### Step 1: Understanding the Compressibility Factor (Z)
The compressibility factor (Z) is defined as:
\[ Z = \frac{PV}{nRT} \]
Where:
- P = Pressure
- V = Volume
- n = Number of moles
- R = Universal gas constant
- T = Temperature

### Step 2: Analyzing the Values of Z
1. **Z = 1**: This indicates ideal gas behavior. Therefore, it should be matched with "Ideal behavior".
2. **Z < 1**: This indicates a negative deviation from ideal behavior. Hence, it should be matched with "Negative deviation".
3. **Z > 1**: This indicates a positive deviation from ideal behavior. Therefore, it should be matched with "Positive deviation".
4. **Zc = 3/8**: This value corresponds to critical conditions for real gases.

### Step 3: Matching Each Option
Now, we will match each given option with the correct description:

- **(i) Z = 1**: This should be matched with (C) "Ideal behavior".
- **(ii) Z < 1**: This should be matched with (A) "Negative deviation".
- **(iii) Z > 1**: This should be matched with (B) "Positive deviation".
- **(iv) Zc = 3/8**: This should be matched with (D) "At critical conditions".

### Step 4: Conclusion
Now we can summarize the correct matches:
- (i) Z = 1 → (C) "Ideal behavior"
- (ii) Z < 1 → (A) "Negative deviation"
- (iii) Z > 1 → (B) "Positive deviation"
- (iv) Zc = 3/8 → (D) "At critical conditions"

### Final Answer
The correctly matched option is:
- (i) Z = 1 → (C) "Ideal behavior"