Question

Compressibility factor of a gas is given by the equation \(Z=\frac{P V}{n R T} .\) On this basis, mark the correct statement. (a) When \(Z>1\), real gases get compressed easily. (b) When \(Z=1\) real gases get compressed easily. (c) When \(Z>1\), real gases are difficult to compress. (d) When \(Z=1\), real gases are difficult to compress

Short answer

When Z > 1, real gases are difficult to compress (c).

Step-by-step solution

Understanding Compressibility Factor

The compressibility factor (Z) is a measure of how much the real gas deviates from ideal gas behavior. It is defined by the equation: \(Z = \frac{PV}{nRT}\). For ideal gases, the compressibility factor is equal to 1, which means the gas behaves exactly as predicted by the ideal gas law. When Z differs from 1, it indicates either easier or more difficult compression compared to an ideal gas.

Analyzing When Z > 1

If the compressibility factor (Z) is greater than 1, it signifies that the gas occupies more volume than predicted by the ideal gas law at the same temperature and pressure. This larger volume suggests that the molecules are repelling each other or are further apart, making them harder to compress.

Analyzing When Z = 1

When Z equals 1, the gas behaves as an ideal gas. This implies that the gas follows the ideal gas law, and its compression is neither easier nor more difficult than that predicated by the law.

Key concepts

Real Gases vs Ideal Gases

When studying gases, we come across two prominent models: ideal gases and real gases. Ideal gases are hypothetical gases that perfectly follow the ideal gas law, represented mathematically by the equation \(PV=nRT\), where P is pressure, V is volume, n is the mole count, R is the gas constant, and T is temperature. In this model, gas particles are assumed to have no volume and do not interact with each other beyond elastic collisions.

In contrast, real gases consist of particles with finite volume and forces of attraction or repulsion between them. These interactions cause real gases to deviate from the ideal gas behavior, especially under conditions of high pressure and low temperature where particles are closer together. The degree to which a real gas deviates from an ideal gas is measured by the compressibility factor (Z). A Z value of 1 suggests ideal gas behavior, while values greater than or less than 1 indicate real gas behavior with more complex particle interactions.

Deviations from Ideal Gas Law

Real gases deviate from the ideal gas law, primarily due to the factors ignored in the ideal gas approximation. These deviations are important to understand because they affect how gases behave under different conditions. One primary reason for the deviation is the volume occupied by gas molecules; in the ideal gas law, particles are assumed to be point-like with no volume, but real gas particles do have volume.

Another reason is the interactions between gas molecules, such as Van der Waals forces, which include attractions and repulsions not accounted for in the ideal model. High pressures increase these interactions as particles are forced closer together. At low temperatures, the kinetic energy of the gas particles decreases, making attractive forces more significant. This complex behavior of real gases versus ideal gases can be understood through the compressibility factor—a useful tool to measure these deviations.

PV=nRT

The equation \(PV=nRT\) represents the Ideal Gas Law, which is a cornerstone in understanding gas behavior in chemistry and physics. It describes the relationship between pressure (P), volume (V), amount of gas in moles (n), temperature (T), and the ideal gas constant (R). This simple but profound relationship assumes that the gas molecules themselves take up no space and there are no interactions between the molecules other than perfect elastic collisions.

However, in real-world scenarios, gases do not always behave ideally, which makes the Ideal Gas Law less accurate under certain conditions. The Ideal Gas Law is most accurate at high temperatures and low pressures, where gas molecules are far apart and interact less with one another. Understanding the limits of this law is essential for studying gas behavior in more realistic situations.

Gas Compression

Gas compression refers to the process of reducing the volume of a gas, which in turn increases its pressure—as described by Boyle's Law, a component of the ideal gas law relations. In an ideal gas scenario, gas compression is predictable and follows the simple inverse relation between pressure and volume. However, for real gases, compressibility can be more complex due to factors like intermolecular forces and the physical space occupied by molecules, reflected in Z, the compressibility factor.

When \(Z>1\), real gases are more difficult to compress than predicted by the Ideal Gas Law due to increased repulsion or decreased attraction between molecules. This means the gas will occupy a larger volume than an ideal gas would under the same conditions. Conversely, when \(Z<1\), gases can be compressed more easily due to stronger attractive forces between molecules, resulting in a smaller volume than that predicted for an ideal gas. The correct interpretation of compressibility is crucial for various applications, including industrial gas storage and the study of atmospheric physics.