The compressibility factor for `H_2` and He is usually

Options

A. gt1
B. `=1`
C. lt1
D. Either of these

Answer

To determine the compressibility factor for hydrogen (H₂) and helium (He), we need to understand the concept of the compressibility factor (Z) and how it relates to the behavior of gases.

### Step-by-Step Solution:

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

2. **Ideal Gas Behavior**:
For an ideal gas, the compressibility factor \(Z\) is equal to 1. This means that the gas behaves according to the ideal gas law without any deviations.

3. **Deviations from Ideal Behavior**:
Real gases do not always behave ideally, especially under high pressure or low temperature. The compressibility factor can indicate whether a gas behaves more like an ideal gas or deviates from this behavior:
- If \(Z < 1\), attractive forces dominate (the gas is more compressible).
- If \(Z > 1\), repulsive forces dominate (the gas is less compressible).

4. **Behavior of Hydrogen (H₂) and Helium (He)**:
Both hydrogen and helium are light gases with weak intermolecular forces. However, at certain conditions, particularly at higher pressures, the repulsive forces between gas molecules become significant.

5. **Conclusion on Compressibility Factor for H₂ and He**:
For both hydrogen and helium, the repulsive forces dominate under typical conditions. Therefore, the compressibility factor \(Z\) for these gases is usually greater than 1:
\[ Z > 1 \quad \text{for H₂ and He} \]

### Summary:
The compressibility factor for hydrogen (H₂) and helium (He) is usually greater than 1, indicating that repulsive forces dominate in these gases.