Ideal Gas Behavior

Function

Despite the existence of more rigorous models for gases, the ideal gas law remains versatile in representing other phases and mixtures. Christensen et al performed a study to create calibration mixtures of oxygen, isoflurane, enflurane, and halothane. These gases are commonly used in anesthetics, which require accurate measurements to ensure patient safety. In this study, Christensen et al compared the ideal gas assumption to more rigorous models to identify the partial pressures of each gas. The ideal gas assumptions had a 0.03% error for the calibration experiment. This study concluded that the error from the ideal gas assumption could be used to tune the calibration of the anesthetics, but the deviation was not appreciable to prevent use on patients.[7][8][9]

Furthermore, the ideal gas law can be used to model the behavior of certain plasmas and gaseous mixtures. In a study by Oxtoby et al, they found that ideal gas could model dusty plasma particles. The study suggests that the similarity between dusty plasma and ideal gas behavior is due to the low compression ratios of dusty plasma. Although more complex models are required, the ideal gas law accurately represents the plasma phase models. Ideal gases have also contributed to the study of surface tension in water. Sega et al proved that the ideal gas contribution to surface tension in water was not trivial but rather finite. Sega et al created a new expression that better represented the ideal gas contribution to surface tension. As a result, the relationship of ideal gases to surface tension better represents gas-liquid interfaces. The ideal gas law also applies to obtain dimensional limitations about a thermodynamic system in the gas-to-liquid transition.[10][11]

Issues of Concern

The main concern with the ideal gas law is that no true ideal gases exist; therefore, the application is theoretical. This limitation is demonstrated by the approach of considering the thermodynamics of an empty box. If all the constraints are set to ideal, then the expected behavior of ideal gases is exhibited. When each parameter of a box is changed, the behavior of real gases is studied.[12] The ideal gas law does not account for chemical reactions in the gaseous phase, which could change the system's pressure, volume, or temperature. This omission is a significant concern, particularly because the pressure can rapidly increase in gaseous reactions and quickly become a safety hazard in real systems. 

In reality, gases exist in dynamic systems, and some constraints are variable. When considering the circuitry of the cardiovascular system, parallel and perpendicular resistors consisting of capillaries, veins, and arteries complicate the movement of gas and liquid, leading to complex and occasionally sudden changes in pressure or volume. Alternatively, when considering hemodialysis circuitry, the renal system variables must be translated to facilitate continued electrolyte balances within the body. These are 2 areas where pressure, volume, and temperature are extensively compared in real and ideal conditions. Consequently, the Van der Waals equation of state that considers intermolecular forces and volume is more accurate when modeling real gas systems.

The impact of the size of the system is also under debate, with smaller systems exhibiting more excellent ideal gas behavior due to a finite degree of freedom compared to large systems.[13] To test the size constraint, 2 small systems were studied separately and in proximity to assess deviations from ideal gas assumptions with inconclusive results.[14] Simulations incorporating size show deviations from classical thermodynamics, as demonstrated by the variables of the ideal gas law.[15]

Clinical Significance

Respiratory Physiology

As studied by Christensen et al, the ideal gas law can be used to calibrate anesthetic mixtures with a nominal error. In high-altitude environments, the ideal gas law may be more accurate for monitoring gas flow pressure into patients compared to sea-level conditions. If significant temperature fluctuations occur, the pressure required to deliver oxygen to a patient could be adjusted. These considerations address the inconsistencies between ideal gas behavior and application to a real system. The variables of the ideal gas law make assumptions concerning the exchange of oxygen and carbon dioxide at the alveolar membrane, especially given the proportion of ventilation (V) to perfusion (Q) at different parts of the lungs, from apices to bases. As such, applying classic thermodynamics requires adjustments, accounting for factors such as alveolar dead space, pathological barriers to ideal gas behavior, and the unpredictability of carbon dioxide and oxygen, given fluctuations in volume or temperature. Assuming maximum exchange is possible at all parts of the lungs could limit the ability to oxygenate a patient. A recent study described this variability as V/Q scatter; the impact of V/Q scatter is observed when considering the solubility of anesthetic agents in blood and the distribution difference in different parts of the lungs. In this context, ideal gas behavior is the ideal V/Q ratio based on fixed blood solubility.[16][17] 

Applications in Clinical Practice

Many anesthesiology, emergency medicine, critical care, and primary care clinicians utilize gas mixtures for analgesia and sedation. Opioids are a source of substance abuse, and alternatives are being explored. In particular, a fixed nitrous oxide/oxygen mixture has been studied in self-administered delivery, although not yet applicable worldwide.[7] Mixtures of several anesthetics are utilized pre- and postoperatively.[11] The context of gas exchange is also pertinent when considering types of postoperative care in managing and returning patients to baseline levels of function. Relating gas behavior to weight and clinical context is important in mechanical ventilation.[8] In terms of ideal gas behavior, the gas particles interact with real systems, which are dynamic due to the changing parameters of the human body.[9] This dynamic interaction explains why treating clinicians must consider factors such as tidal volume, respiratory rate, and fraction of oxygen to determine how much gas exchange should occur concerning a patient's clinical status.[10][18] Alveolar-arterial oxygen difference is typically calculated using an ideal oxygen partial pressure. However, newer methods consider the alveolar steady state or the end-tidal partial pressure, bridging ideal gas behavior to application.[19]

Enhancing Healthcare Team Outcomes

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.