To solve the question regarding the dominance of strong repulsive forces among the molecules of a gas and its relationship with the compressibility factor (Z), we can follow these steps:
### Step-by-Step Solution:
1. **Understanding 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 ideal gas constant, and T is the temperature. It provides insight into how a real gas deviates from ideal gas behavior.
2. **Identifying the Role of Repulsive Forces**:
- In the context of gases, strong repulsive forces dominate when the molecules are close together. This typically occurs at high pressures or low volumes, where the volume occupied by the gas molecules becomes significant compared to the volume of the container.
3. **Using the Van der Waals Equation**:
- The Van der Waals equation for real gases is given by:
\[
\left(P + \frac{a}{V^2}\right)(V - b) = RT
\]
- Here, \( a \) accounts for attractive forces between molecules, and \( b \) accounts for the volume occupied by the gas molecules themselves. When strong repulsive forces dominate, we can consider \( a \) to be negligible (i.e., \( a = 0 \)).
4. **Simplifying the Equation**:
- For a gas where repulsive forces are dominant, the equation simplifies to:
\[
P(V - b) = RT
\]
- Rearranging this gives:
\[
PV = P b + RT
\]
5. **Relating to the Compressibility Factor**:
- Dividing through by \( RT \):
\[
\frac{PV}{RT} = \frac{Pb}{RT} + 1
\]
- Thus, we can express Z as:
\[
Z = 1 + \frac{Pb}{RT}
\]
6. **Analyzing the Result**:
- Since \( P \), \( b \), and \( R \) are all positive values, it follows that \( \frac{Pb}{RT} \) is also positive. Therefore, we conclude:
\[
Z > 1
\]
- This indicates that when strong repulsive forces dominate among gas molecules, the compressibility factor Z is greater than 1.
7. **Conclusion**:
- Based on the analysis, the dominance of strong repulsive forces among the molecules of a gas indicates that \( Z > 1 \). Therefore, the correct answer to the question is option B: "depends on Z and indicates that Z is greater than 1."
