3.2 – Modelling a Gas

Jyväskylän Lyseon lukio International Baccalaureate

December 11, 2019

The amount of substance is one of the seven fundamental units in the SI system. The amount of substance is measured in moles (1 mol). Deﬁnition of Mole One mole of substance contains as many particles as there are atoms in 12 g of carbon-12.

Avogadro Constant The number of particles in a mole of substance is known as the Avogadro Constant

23 −1 NA = 6.022 × 10 mol .

The particles may be atoms or molecules. For example, a silicon atom S, helium atom He, hydrogen molecule H2, and carbon dioxide molecule CO2. © Kari Eloranta 2019 Amount of Substance 2 / 7 Amount of Substance n

Amount of Substance n If a sample of substance contains N particles, has mass m and molar mass M, the amount of substance in the sample is N m n = = (1) NA M

23 −1 where NA = 6.022 × 10 mol is the Avogadro constant.

In chemistry, the mass is usually measured in grams, and the molar mass in gmol−1 (grams per mole). [m] ¡g The SI unit of amount of substance is [n] = = − = mol. [M] gmol¡ 1

Most real gases exhibit similar physical behaviour when the pressure of a gas is low, and temperature of the gas well above the liquidation point. In these conditions, the behaviour of real gases can be understood in terms of the ideal gas model. If an ideal gas is at thermal equilibrium with its surroundings at temperature T , pressure P, and volume V , it follows the equation of state of ideal gas. Equation of State of Ideal Gas The equation of state of an ideal gas is

PV = nRT (2)

where P is the pressure, V volume, n amount of substance, and T − − temperature (in kelvins) of the gas. R = 8.31JK 1 mol 1 is the universal gas constant.

Equation of state of ideal gas deﬁnes the universal gas constant R. Universal Gas Constant R Solving for the universal gas constant R in the equation of state of an ideal gas gives PV R = (3) nT where P is the pressure, V volume, n amount of substance, and T temperature (in kelvins) of the gas.

If we assume that a real gas follows ideal gas behaviour, we can determine the value of universal gas constant by measuring the pressure, volume, temperature and amount of substance of the gas. The value of the universal gas constant is − − R = 8.31JK 1 mol 1. © Kari Eloranta 2019 Behaviour of Gases 5 / 7 Assumptions of the Ideal Gas Model

The ideal gas model is based on the following assumptions:

1 A gas consists of a large amount of point-like particles. Because the gas particles are point-like, the total volume of the molecules is negligible compared to the volume occupied by the gas. 2 The gas particles are in random motion with varying speeds. 3 There are no forces between the particles besides the forces caused by inter-particle collisions. 4 When the particles collide with each other, and with the walls of a container, the collisions are elastic. The duration of a collision is negligible compared to the time between the collisions.

When the pressure and temperature of a real gas are far enough from the liquidation point, the intermolecular forces in the gas are negligible. Because there are no intermolecular forces, an ideal gas does not have internal potential energy, and molecules interact in elastic collisions only. As a result, ideal gases cannot be liqueﬁed. Real gases follow ideal gas behaviour in any state far enough from their liquidation point. When the density of a real gas increases, the intermolecular forces increase as well, and the average separation of the particles decreases. As a result, the assumptions of the ideal gas model do not hold any more, and the deviations from the ideal gas law become greater.