An ideal gas is a fundamental theoretical model in chemistry and physics that simplifies the behavior of real gases. This hypothetical gas assumes molecules have negligible volume and experience no intermolecular forces, perfectly following kinetic theory principles. While no real gas is truly ideal, this model provides essential insights into pressure, volume, and temperature relationships for gases like hydrogen or nitrogen under standard conditions, serving as a cornerstone for understanding gas behavior.

The Ideal Gas Law

Boyle’s, Charles’s, and Gay-Lussac’s laws refer to an ideal situation where no intermolecular interactions exist, and collisions are perfectly elastic (thus no energy is exchanged upon collision). Ideality allows for these assumptions to derive the gas laws. Boyle’s law specifically relates the volume and pressure of a given mass of gas at constant temperature,

$$ P∝\frac{1}{V} $$

or

$$ PV=k $$

The law of Gay-Lussac and Charles states that the volume and absolute temperature of a given mass of gas at constant pressure are directly proportional,

$$ V∝T $$

$$ V=kT $$

These equations can be combined to obtain the familiar relationship,

$$ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} $$

In this equation, P₁, V₁, and T₁ are the values under one set of conditions and P₂, V₂, and T₂ the values under another set.

The Ideal Gas Constant

From the last equation it is seen thatPV/T under one set of conditions is equal to PV/T under another set, and so on. Thus, one reasons that although P, V, and T change, the ratio PV/T is constant and can be expressed mathematically as

$$ \frac{PV}{T}=R $$

or

$$ PV=RT $$

in which R is the constant value for the PV/T ratio of an ideal gas.This equation iscorrect only for 1 mole (i.e., 1g molecular weight) of gas; for n moles it becomes

$$ PV=nRT $$

This equation is known as the general ideal gas law, and because it relates the specific conditions or state, that is, the pressure, volume, and temperature of agiven mass of gas, it is called the equation of state of an ideal gas. Real gases do not interact without energy exchange, and therefore do not follow the laws of Boyle and of Gay-Lussac and Charles as ideal gases are assumed to do.

The molar gas constant R is highly important in physical chemical science. To obtain a numerical value for R, let us proceed as follows. If 1 mole of an ideal gas is chosen, its volume under standard conditions of temperature and pressure (i.e., at 0◦C and 760 mm Hg) has been found by experiment to be 22.414 liters. Substituting this value in the ideal gas equation, we obtain
$$ R=\frac{1atm×22.414liters}{1mole×273.16K} $$

$$ R=0.08205\frac{liter.atm}{mole.K} $$

The molar gas constant can also be given in energy units by expressing the pressure in dynes/cm² (1 atm = 1.0133× 10⁶ dynes/cm²) and the volume in the corresponding units of cm³ (22.414 liters = 22,414 cm³). Then

$$ R=\frac{(1.0133×10^6)×22.414}{273.16} $$

$$ R=8.314×10^7\frac{erg}{mole.K} $$

or, because 1 joule=10⁷ ergs,

$$ R=8.314\frac{joules}{mole.K} $$

One must be particularly careful to use the value of R commensurate with the appropriate units under consideration in each problem.

Reference:

• Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.