Question

Compressibility factor at very high pressures (1) becomes negative (2) decreases with increasing pressure (3) increases with increasing pressure (4) becomes zero

Short answer

3. Increases with increasing pressure

Step-by-step solution

- Understand the Compressibility Factor

The compressibility factor, usually denoted as Z, is a measure of how much the behavior of a real gas deviates from an ideal gas. For an ideal gas, Z = 1.

- Analyze Behavior at High Pressures

At very high pressures, gases deviate significantly from ideal behavior. Real gas interactions become more apparent and must be taken into account.

- Predict the Trend

As pressure increases, the volume of the gas decreases. The particles get closer and the repulsive forces dominate once the gas is compressed significantly.

- Conclusion from Choices

Given that at high pressures repulsive forces dominate, the distance between particles causes the compressibility factor Z to increase. Thus, the correct conclusion is that Z increases with increasing pressure.

Key concepts

Real Gas Behavior

Real gases differ significantly from ideal gases, especially under certain conditions such as high pressure and low temperature. Ideal gases are theoretical gases composed of random non-interacting particles that obey the Ideal Gas Law perfectly. However, real gases have interactions between molecules, like attractive and repulsive forces. These interactions affect their behavior and cause deviations from the Ideal Gas Law. For instance, at high pressures, the molecules are closer together, increasing intermolecular forces. This makes the gas non-ideal, and requires additional corrections when predicting the gas's behavior using thermodynamic equations.
The most common model to describe real gas behavior is the Van der Waals equation, which corrects for both the finite size of molecules and the intermolecular forces.

Ideal Gas Law

The Ideal Gas Law is an equation of state for a hypothetical ideal gas. It is denoted as:
\[ PV = nRT \]
where:

• P is the pressure of the gas
• V is the volume of the gas
• n is the amount of substance (in moles)
• R is the universal gas constant
• T is the temperature of the gas in Kelvin

This Law is derived from the kinetic theory of gases, which assumes particles move randomly and only interact through elastic collisions. But, it does not consider intermolecular forces or the volume occupied by gas molecules themselves. Hence, under extreme conditions, such as high pressures or low temperatures, real gases show significant deviations from this behavior. Corrective models like the Van der Waals equation or the compressibility factor (Z) become essential in these scenarios.

High Pressure Effects

At high pressures, the properties of gases alter considerably due to molecular interactions which become more pronounced. High pressure forces gas molecules closer together. This proximity amplifies both repulsive and attractive forces between them.
As the gas is compressed beyond a certain limit, the repulsive forces tend to dominate because molecules cannot be compressed beyond a certain point due to their finite size. This dominance increases the compressibility factor (Z), indicating that the gas becomes less compressible. As a result, Z tends to be greater than one under these conditions.
Real gases at high pressures do not follow the Ideal Gas Law. Instead, their behavior can be better predicted using models like the Van der Waals equation, which consider volume occupied by gas molecules and the intermolecular forces. Understanding these high-pressure effects is crucial for applications in industrial processes and understanding natural phenomena.