Tenny Kevin M., Cooper Jeffrey S.
The Massachusetts Institute of Technology
University of Nebraska Medical Center
The ideal gas law is an equation demonstrating the relationship between temperature, pressure, and volume for gases (see 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: = where is the pressure, is the volume, is the number of moles of gas, is the universal gas constant, and is the absolute temperature. The modified version, the Van Der Waals equation, includes for intermolecular forces and to represent the volume of 1 mole of molecules. As such, this version better quantifies the behavior of real gases. The universal gas constant is a number that satisfies the proportionalities of the pressure-volume-temperature relationship. has different values and units that depend on the pressure, volume, moles, and temperature specifications. Various values are accepted for 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. 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. 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. 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. 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: = where is the partial pressure of species i and 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.
理想气体定律是一个展示气体温度、压力和体积之间关系的方程（见“理想气体定律”）。这些特定关系源于查理定律、波义耳定律和盖 - 吕萨克定律。查理定律指出在恒定压力下体积与温度成正比。波义耳定律指出在恒定温度下压力与体积成反比，盖 - 吕萨克定律指出在恒定体积下压力与温度成正比。这些定律共同构成了理想气体定律方程：(PV = nRT)，其中(P)是压力，(V)是体积，(n)是气体的摩尔数，(R)是通用气体常数，(T)是绝对温度。修改后的范德华方程，包含了(a)用于表示分子间作用力，以及(b)来代表(1)摩尔分子的体积。因此，这个版本能更好地量化实际气体的行为。通用气体常数(R)是一个满足压力 - 体积 - 温度关系比例性的数值。(R)有不同的值和单位，这取决于压力、体积、摩尔数和温度的具体规定。通过在线数据库可以接受各种(R)值，或者通过量纲分析将观察到的压力、体积、摩尔数和温度单位转换为与已知(R)值相匹配的单位。只要压力、体积、摩尔数和温度的单位一致，任何一种方法都是可以接受的。理想气体定律中的温度值必须采用绝对单位，即兰金温标（°R）或开尔文温标（K），以防止方程右边为零，因为这会违反压力 - 体积 - 温度关系。从华氏温标（F）或摄氏温标（C）转换为绝对温度单位，只需在华氏温度（F）或摄氏温度（C）上加上一个固定值——°R = F + 459.67，K = C + 273.15。对于一种气体要成为理想气体，必须满足4个主导假设：与气体的总体积相比，气体粒子的体积可忽略不计。气体粒子大小相同，并且与其他气体粒子之间不存在分子间作用力，如吸引力或排斥力。气体粒子按照描述动能的牛顿运动定律随机运动。气体粒子进行完全弹性碰撞，没有能量损失或增加。实际上，理想气体并不存在。任何气体粒子在系统中都占有一定体积（尽管数量极少，但仍然存在），这违反了第一个假设。此外，气体粒子大小不同；例如，氢气与氙气相比要小得多。系统中的气体粒子与相邻气体粒子之间存在分子间作用力，特别是在低温时，粒子运动不快且相互作用。尽管气体粒子随机运动，但由于系统内能量和动量守恒，它们并非进行完全弹性碰撞。尽管理想气体是理论概念，但实际气体在某些条件下可以表现得像理想气体。当处于极低压力或高温时，实际气体表现得像理想气体。系统的低压使得气体粒子与其他气体粒子之间的分子间作用力减小。同样，高温系统使气体粒子在系统内快速运动，分子间作用力减小。因此，在低压或高温系统中，为了计算目的，可以将实际气体视为理想气体。一些液体也表现出理想气体的性质。理想气体定律也适用于包含多种理想气体的系统，即理想气体混合物。在一个系统中有多种理想气体时，这些粒子仍然被假定彼此之间不存在任何分子间相互作用，并且各自独立满足理想气体定律的所有标准。理想气体混合物将系统的总压力分配到每个气体粒子的分压力贡献上。因此，之前的理想气体方程可以改写为：(P_{total}V = \sum_{i}n_{i}RT)，其中(P_{i})是第(i)种物质的分压力，(n_{i})是第(i)种物质的摩尔数。气体混合物在低压或高温条件下便于计算。当系统不是处于低压或高温时，气体粒子相互作用，这会影响理想气体定律的准确性。然而，其他模型，如范德华状态方程，考虑了气体粒子的体积和分子间相互作用。最近对玻尔兹曼模型的一种改进提出了分别针对质量和动量以及总能量的方程，以考虑气体粒子的体积。这些模拟将理想气体混合物与实际气体混合物进行比较。因此，在生物技术和临床医学中已经开发出了电解质混合物。
