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The ideal gas law is an equation demonstrating the relationship between temperature, pressure, and volume for gases (see Graph. The Ideal Gas Law). These specific relationships stem from Charles's, Boyle's, and Gay-Lussac's laws. Charles's law identifies the direct proportionality between volume and temperature at constant pressure. Boyle's law identifies the inverse proportionality of pressure and volume at a constant temperature, and Gay-Lussac's law identifies the direct proportionality of pressure and temperature at a constant volume. Collectively, these laws form the ideal gas law equation: PV=nRT where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the absolute temperature. The modified version, the Van Der Waals equation, includes a for intermolecular forces and b to represent the volume of 1 mole of molecules. As such, this version better quantifies the behavior of real gases. The universal gas constant R is a number that satisfies the proportionalities of the pressure-volume-temperature relationship. R has different values and units that depend on the pressure, volume, moles, and temperature specifications. Various values are accepted for R through online databases, or dimensional analysis converts the observed units of pressure, volume, moles, and temperature to match a known R-value. As long as the units for pressure, volume, moles, and temperature are consistent, either approach is acceptable. The temperature value in the ideal gas law must be in absolute units, either Rankine (°R) or Kelvin (K), to prevent the right-hand side of the equation from being zero, which violates the pressure-volume-temperature relationship. The conversion from Fahrenheit (F) or Celsius (C) to absolute temperature units is a simple addition of a fixed value to the Fahrenheit (F) or the Celsius (C) temperature—°R=F+459.67 and K=C+273.15. Assumptions of an Ideal Gas For a gas to be ideal, 4 governing assumptions must be true: The gas particles have negligible volume compared to the total volume of a gas. The gas particles are equally sized and do not have intermolecular forces, such as attraction or repulsion, with other gas particles. The gas particles move randomly in agreement with Newton's laws of motion that describe kinetic energy. The gas particles have perfect elastic collisions with no energy loss or gain.

The gas particles have negligible volume compared to the total volume of a gas. The gas particles are equally sized and do not have intermolecular forces, such as attraction or repulsion, with other gas particles. The gas particles move randomly in agreement with Newton's laws of motion that describe kinetic energy. The gas particles have perfect elastic collisions with no energy loss or gain. The Behavior of Real Gases In reality, ideal gases do not exist. Any gas particle possesses a volume within the system (a minute amount, but present nonetheless), violating the first assumption. In addition, gas particles are of different sizes; for example, hydrogen gas is significantly smaller compared to xenon gas. Gas particles in a system exhibit intermolecular forces with adjacent gas particles, especially at low temperatures when the particles do not move quickly and interact with each other. Although gas particles move randomly, they do not have perfect elastic collisions due to the conservation of energy and momentum within the system.[1][2] Although ideal gases are theoretical constructs, real gases can behave ideally under certain conditions. Real gases behave ideally when subjected to either very low pressures or high temperatures. The low pressure of a system allows the gas particles to experience less intermolecular forces with other gas particles. Similarly, high-temperature systems allow gas particles to move quickly within the system and exhibit less intermolecular forces. Therefore, real gases can be considered ideal for calculation purposes in either low-pressure or high-temperature systems. Some liquids also exhibit the properties of ideal gases.[3][4] Ideal Gas Mixture The ideal gas law also holds for a system containing multiple ideal gases, known as an ideal gas mixture. With multiple ideal gases in a system, these particles are still assumed not to have any intermolecular interactions with one another and to meet all criteria of an ideal gas law independently. An ideal gas mixture partitions the system's total pressure into the partial pressure contributions of each gas particle. Consequently, the previous ideal gas equation can be rewritten as: PiV=niRT

The ideal gas law also holds for a system containing multiple ideal gases, known as an ideal gas mixture. With multiple ideal gases in a system, these particles are still assumed not to have any intermolecular interactions with one another and to meet all criteria of an ideal gas law independently. An ideal gas mixture partitions the system's total pressure into the partial pressure contributions of each gas particle. Consequently, the previous ideal gas equation can be rewritten as: PiV=niRT where Pi is the partial pressure of species i and ni are the moles of species i. Gas mixtures are ideal for easy calculation at low-pressure or high-temperature conditions. When systems are not at low pressures or high temperatures, the gas particles interact, inhibiting the ideal gas law accuracy. However, other models, such as the Van der Waals equation of state, account for the volume of the gas particles and the intermolecular interactions. A recent take on the Boltzmann model proposes separate equations for mass and momentum and for total energy to account for the volume of gas particles. These simulations compare ideal gas mixtures to real gas mixtures. Consequently, electrolyte mixtures have been developed in biotechnology and clinical medicine.[5][6]

Understanding ideal gas behavior is crucial for healthcare professionals in various contexts. A thorough understanding of ideal gas behavior empowers healthcare providers to navigate intricate scenarios and make informed decisions regarding patient care. Healthcare professionals with a nuanced understanding of ideal gas behavior can effectively evaluate realistic representations and discern which variables are fixed and which can be manipulated for experimentation. Although current research is grounded in theories dating back hundreds of years, clinicians should remain familiar with the thermodynamic understanding of pressure, volume, and temperature, especially when delivering medical care in areas such as ventilation, acid-base status, pain management, or sedation. Familiarity with the ideal gas formula can prevent medical errors and optimize patient care. Furthermore, several opportunities exist to explore the precise delivery of oxygen and carbon dioxide under changing environmental conditions. These areas are most pertinent to clinicians in anesthesiology and critical care, where meticulous attention to gas dynamics can significantly impact patient outcomes and overall quality of care.