Assertion : Compressibility factor (Z) is the ratio of actual molar volume of a gas to the molar volume of it , if it were an ideal gas at that temperature and pressure .
Reason : At high pressure all the gases have Z lt 1 and can be easily compressed .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion .
B. If both assertion and reason are true but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false .
D. If both assertion and reason are false .

Explanation

To solve the assertion and reason question regarding the compressibility factor (Z), we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that the compressibility factor (Z) is the ratio of the actual molar volume of a gas to the molar volume of it if it were an ideal gas at that temperature and pressure.

- **Definition of Compressibility Factor (Z)**:
\[ Z = \frac{V_m \text{ (real gas)}}{V_m \text{ (ideal gas)}} \]
where \( V_m \) is the molar volume.

### Step 2: Understanding the Ideal Gas Behavior
For an ideal gas, the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) is given by the ideal gas equation:
\[ PV = nRT \]
For one mole of an ideal gas, we can rearrange this to find the molar volume:
\[ V_m = \frac{RT}{P} \]

### Step 3: Relating Z to Real Gas Behavior
Now, substituting the ideal gas molar volume into the equation for Z:
\[ Z = \frac{V_m \text{ (real gas)}}{\frac{RT}{P}} \]
This shows that Z indicates how much a real gas deviates from ideal behavior.

### Step 4: Evaluating the Reason
The reason states that at high pressure, all gases have \( Z < 1 \) and can be easily compressed.

- **Evaluating the Statement**:
- At high pressures, real gases tend to deviate from ideal behavior. Typically, \( Z > 1 \) at high pressures, indicating that real gases are less compressible than ideal gases.
- Therefore, the statement that "all gases have \( Z < 1 \) at high pressure" is incorrect.

### Step 5: Conclusion
- **Assertion**: True (Z is indeed the ratio of the actual molar volume of a gas to that of an ideal gas).
- **Reason**: False (At high pressures, \( Z \) is generally greater than 1, indicating that gases are not easily compressed).

### Final Answer
The correct conclusion is that the assertion is true, but the reason is false.