The Applicability Of The Ideal Gas Law To Helium

The ideal gas law, PV = NkBT, is an equation of state that relates the quantities of pressure, volume, and temperature. While no real gas behaves exactly as an ideal gas, helium is often described as the most ideal of real gases. This is because helium has a low atomic weight, is extremely non-polarizable, and has very low inter-atomic forces. This results in a very low boiling point, allowing helium to demonstrate ideal gas law behaviour at temperatures much closer to its boiling point and at higher pressures when compared to other gases.

The ideal gas law

While no real gas behaves exactly as an ideal gas, helium is often described as the most ideal of real gases. This is because helium is a very small, non-polarizable noble gas with extremely low interatomic forces. As a result, helium has a very low boiling point of about 4 Kelvins, and it demonstrates ideal gas law behaviour at temperatures much closer to its boiling point and at higher pressures when compared to other gases like nitrogen.

However, helium does not behave as an ideal gas at high pressures and low temperatures. This is because helium, despite being highly inert, still has Van der Waals' interactions and non-zero volume. As pressure increases, the space available for the atoms to occupy decreases, and the volume of the helium particles becomes significant, increasing the pressure further. Similarly, as temperature decreases, the attractive forces between helium atoms become more prominent, deviating further from ideal gas behaviour.

Therefore, helium behaves like an ideal gas under specific conditions of low pressure and high temperature.

Compressibility factor

The compressibility factor, also known as the compression factor or the gas deviation factor, is a dimensionless correction factor that accounts for the deviation of a real gas from ideal gas behaviour. It is defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure.

The compressibility factor is given by the equation:

Z = (PV)/(nRT)

Where:

• P is the pressure
• V is the unit volume
• N is the number of moles of gas
• R is the gas constant
• T is the absolute temperature

For an ideal gas, the compressibility factor is always 1. However, for real gases, the compressibility factor may deviate significantly from 1. This deviation becomes more significant as the gas approaches a phase change, or when the temperature decreases or pressure increases.

The compressibility factor is linked to the fugacity by the relation:

F = Pexp[(Z-1)/P]

The compressibility factor is an important concept in thermodynamics and engineering, and it is used to modify the ideal gas law to account for real gas behaviour. It is also used to evaluate the suitability of the ideal gas equation of state for a given gas at a specific range of pressures and temperatures.

For helium, the most ideal of real gases, the compressibility factor is close to 1 at standard temperature and pressure (STP). However, as pressure and temperature deviate from STP, the compressibility factor of helium may change, indicating that it behaves less like an ideal gas under those conditions.

Intermolecular forces

The ideal gas law assumes that the individual particles of the gas do not interact and do not collide. In reality, no gas behaves exactly as an ideal gas. However, helium comes very close to behaving as an ideal gas at standard temperature and pressure (STP). This is because helium atoms are very small, extremely non-polarizable, and have very low inter-atomic forces.

The intermolecular forces in liquid helium are solely attributed to London dispersion forces, also known as Van der Waals forces or induced dipole-induced dipole interactions. These forces are the weakest type of intermolecular force and arise due to the temporary dipoles caused by the motion of electrons in atoms or molecules.

Since helium is a noble gas, its atoms do not possess a permanent dipole moment or any ionic or hydrogen bonding characteristics. Therefore, other types of intermolecular forces such as dipole-dipole interactions, hydrogen bonding, or ion-dipole interactions are not present in helium.

London dispersion forces are present in all molecules, but they are the only force in nonpolar molecules like helium. In contrast, dipole-dipole interactions occur between molecules with permanent dipoles, and hydrogen bonding is a special type of dipole-dipole interaction that occurs when hydrogen is bonded to fluorine, oxygen, or nitrogen.

Gas behaviour at different temperatures

Gases behave differently at different temperatures, and this behaviour can be predicted and explained by the Ideal Gas Law. The Ideal Gas Law is an equation that demonstrates the relationship between temperature, pressure, and volume for gases. It combines Charles's, Boyle's, and Gay-Lussac's laws, which describe the direct proportionality between volume and temperature at constant pressure, the inverse proportionality of pressure and volume at a constant temperature, and the direct proportionality of pressure and temperature at a constant volume, respectively.

The Ideal Gas Law equation is PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is absolute temperature. The universal gas constant, R, is a number that satisfies the proportionalities of the pressure-volume-temperature relationship.

The behaviour of a gas changes at different temperatures. Any gas will deviate from the ideal gas law if the pressure is increased or the temperature is lowered. At low temperatures, gas particles do not move as quickly and interact more with each other. However, at high temperatures, gas particles move more quickly and exhibit fewer intermolecular forces. Therefore, real gases can behave ideally at high temperatures.

Additionally, the Ideal Gas Law holds for a system containing multiple ideal gases, known as an ideal gas mixture. In such a mixture, the total pressure of the system is partitioned into the partial pressure contributions of each gas particle. The 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.

In summary, the behaviour of gases at different temperatures is a complex topic that can be modelled using the Ideal Gas Law. While no real physical gas behaves exactly as an ideal gas, understanding the behaviour of gases at varying temperatures is crucial for various applications, including in clinical practice and healthcare.

Ideal vs real gases

The ideal gas law is often one of the first concepts taught in high school chemistry. It was developed in the 1830s when scientists were running experiments on different gases and recording the relationship between pressure, volume, temperature, and the number of moles. They noticed that, at standard pressure and temperature, the direct relationships they observed between these variables held regardless of the type of gas.

An ideal gas is one that follows the gas laws at all conditions of temperature and pressure. However, for a gas to do so, it needs to completely abide by the kinetic-molecular theory. This means that the gas particles need to occupy zero volume and exhibit no attractive forces toward each other. Since neither of these conditions can be true, there is no such thing as an ideal gas. A real gas is simply a gas that does not behave according to the assumptions of the kinetic-molecular theory.

At low pressures and high temperatures, real gases behave like ideal gases. This is because, at low pressures or large volumes, the volume of the real gas particles is negligible in comparison to the volume of the container. This means that we can assume the particles of the real gas to be volumeless, which makes them like an ideal gas. Secondly, as the temperature of a gas is increased, the average speed of the particles increases. This means that when the particles pass each other, they have very little time to interact, which, again, helps them mimic the behaviour of an ideal gas.

Helium is often described as an ideal gas. This is because helium is a very small particle (a noble gas, with atoms, not molecules) that is extremely non-polarizable and has very low inter-atomic forces. This results in a very low boiling point, about 4 Kelvins. Thus, helium will demonstrate ideal gas law behaviour at temperatures much closer to its boiling point and at much higher pressures when compared to other gases.

However, there is no sharp transition between ideal and non-ideal gas behaviour. The change is gradual and dependent on pressure and temperature. At high pressure, real gas particles are forced closer together as the empty space between them is diminished. A decrease in the empty space means that the assumption that the volume of the particles themselves is negligible is less valid. When a gas is cooled, the decrease in kinetic energy causes the particles to slow down. If the particles are moving at slower speeds, the attractive forces between them are more prominent.

Frequently asked questions