Determine which of the following statements are true at very high pressure for a real gas:
(a) Compressibility factor is greater than 1.
(b) Compressibility factor varies linearly with pressure.
(c) Molar volume occupied by gas is more as compared to ideal gas at similar pressure and temperature.
(d) Gas is less compressible as compare to ideal gas.
(e) Compressibility factor is given by
`Z=1+(Pb)/(RT)`.

Answer

To determine which statements are true for a real gas at very high pressure, we will analyze each statement one by one based on the properties of real gases and the compressibility factor (Z).

### Step-by-Step Solution:

1. **Understanding the Compressibility Factor (Z)**:
- The compressibility factor (Z) is defined as \( Z = \frac{PV}{nRT} \).
- For ideal gases, \( Z = 1 \). For real gases, especially at high pressures, \( Z \) can be greater than 1.

2. **Analyzing Statement (a)**: "Compressibility factor is greater than 1."
- At very high pressures, real gases tend to have a compressibility factor \( Z > 1 \).
- **Conclusion**: This statement is **True**.

3. **Analyzing Statement (b)**: "Compressibility factor varies linearly with pressure."
- The behavior of \( Z \) with pressure is not linear for real gases. It can decrease initially with increasing pressure and then increase after reaching a certain point.
- **Conclusion**: This statement is **False**.

4. **Analyzing Statement (c)**: "Molar volume occupied by gas is more as compared to ideal gas at similar pressure and temperature."
- The compressibility factor can also be expressed as \( Z = \frac{V_{real}}{V_{ideal}} \). At high pressures, \( Z > 1 \) implies \( V_{real} > V_{ideal} \).
- **Conclusion**: This statement is **True**.

5. **Analyzing Statement (d)**: "Gas is less compressible as compared to ideal gas."
- At high pressures, real gases behave more like ideal gases, which means they are less compressible than ideal gases.
- **Conclusion**: This statement is **True**.

6. **Analyzing Statement (e)**: "Compressibility factor is given by \( Z = 1 + \frac{Pb}{RT} \)."
- The derivation shows that at very high pressure, the compressibility factor can be approximated as \( Z = 1 + \frac{Pb}{RT} \).
- **Conclusion**: This statement is **True**.

### Final Summary of Statements:
- (a) True
- (b) False
- (c) True
- (d) True
- (e) True

### True Statements:
The true statements at very high pressure for a real gas are (a), (c), (d), and (e).