Compressibility factor for H2 behaving as real gas is

Options

A. 1
B. `(1-a/(RTV))`
C. `(1+(Pb)/(RT))`
D. `(RTV)/(1-a)`

Answer

To find the compressibility factor (Z) for hydrogen (H2) behaving as a real gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Compressibility Factor (Z)**:
The compressibility factor (Z) is defined as:
\[ Z = \frac{PV}{RT} \]
where P is the pressure, V is the volume, R is the universal gas constant, and T is the temperature.

2. **Use the Van der Waals Equation**:
The Van der Waals equation for real gases is given by:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT \]
where \(a\) and \(b\) are constants that account for intermolecular forces and molecular volume, respectively.

3. **Consider Hydrogen Gas (H2)**:
For hydrogen gas, the intermolecular forces are negligible. Therefore, the term involving \(a\) becomes very small, and we can approximate:
\[ \frac{a}{V^2} \approx 0 \]

4. **Simplify the Van der Waals Equation**:
With the negligible intermolecular forces, the Van der Waals equation simplifies to:
\[ P(V - nb) = nRT \]

5. **Rearranging the Equation**:
Dividing both sides by \(RT\) gives:
\[ \frac{PV}{RT} - \frac{Pnb}{RT} = 1 \]
Rearranging this leads to:
\[ \frac{PV}{RT} = 1 + \frac{Pnb}{RT} \]

6. **Expressing the Compressibility Factor (Z)**:
From the definition of Z, we can see that:
\[ Z = \frac{PV}{RT} \]
Thus, substituting our previous result:
\[ Z = 1 + \frac{Pnb}{RT} \]

7. **Conclusion**:
Since \(b\) is a constant for hydrogen, we can conclude that the compressibility factor \(Z\) for hydrogen gas behaving as a real gas is approximately equal to 1, plus a small correction term due to the volume excluded by the gas molecules.

### Final Answer:
The compressibility factor (Z) for H2 behaving as a real gas is approximately:
\[ Z \approx 1 \]