At \(200 \mathrm{~K}\), the compression factor of oxygen varies with pressure as shown below. Evaluate the fugacity of oxygen at this temperature and 100 atm. $$ \begin{array}{llllllll} \text { p/atm } & 1.0000 & 4.00000 & 7.00000 & 10.0000 & 40.00 & 70.00 & 100.0 \\\ Z & 0.9971 & 0.98796 & 0.97880 & 0.96956 & 0.8734 & 0.7764 & 0.6871 \end{array} $$

In the world of physical chemistry, the compression factor, also known as the Z-factor, is a crucial property when studying the behavior of gases under varying pressures. It compares the behavior of a real gas with that of an ideal gas under the same conditions. For an ideal gas, which is a hypothetical gas that perfectly follows the gas laws, the compression factor is always 1. However, real gases deviate from this ideal behavior due to molecular interactions and the finite volume of gas molecules.

When the pressure on a gas increases, the particles get closer together, and the intermolecular forces become significant. This deviation from ideality is quantified by the compression factor. Mathematically, the compression factor is defined as the ratio of the actual molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure. It's an essential factor for refining the precision of gas-related calculations in thermodynamics.

Thermodynamics is a branch of physical science that deals with the relations between heat and other forms of energy, such as work. It describes how thermal energy is converted to other forms of energy and how it affects matter. The study of thermodynamics involves several key laws which underpin the physical behavior of systems in thermal equilibrium. These laws can be applied to a wide range of topics, from designing engines and refrigerators to predicting the behavior of weather systems and stars.

Within thermodynamics, the concept of fugacity represents an advanced way of understanding a gas's pressure, accounting for non-ideality. The four fundamental laws of thermodynamics—zeroth, first, second, and third—outline the principles of energy conservation, the direction of energy transfer, and the conditions for thermal equilibrium. Utilizing these principles, scientists and engineers can predict how a gas, such as oxygen, behaves under various temperature and pressure conditions.

Physical chemistry is the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. It is the discipline where physics and chemistry intersect and is essential for understanding the physical properties of molecules and the forces that act upon them. In physical chemistry, the behavior of gases plays a significant role, and it involves concepts such as fugacity and the compression factor.

Subjects like kinetics, quantum mechanics, and thermodynamics fall under this area of chemistry. The study of how real gases deviate from ideal gas behavior through the use of concepts such as the compression factor (Z) is a practical application of physical chemistry. Understanding these concepts helps scientists and engineers to manipulate the physical world in useful ways, from creating new materials to understanding biological systems and the environment.

Gas laws are fundamental principles that predict the behavior of gases under various conditions of pressure, volume, and temperature. These laws include Boyle's law, Charles's law, Avogadro's law, and the ideal gas law. While these laws describe the relationship between these variables for ideal gases, real gases often display behaviors that diverge from these ideal predictions due to their intermolecular interactions.

The ideal gas law, which is the unification of Boyle's, Charles's, and Avogadro's laws, can be stated as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. However, to account for non-ideal behavior, the concept of the compression factor (Z) is introduced, modifying the ideal gas equation to PV = nZRT. This improvement allows the estimation of real gas behavior under conditions where they do not act as ideal gases.