The Ideal Gas Law

Core Concepts

In this tutorial, you will learn the gas laws, how the ideal gas law equation was derived and how to use it. You will also learn what defines an ideal gas, what the ideal gas constant is, ideal gas law units, and what assumptions we make to call a gas ideal – the ideal gas properties.

Topics Covered in Other Articles

What are the Gas Laws?

The gas laws are a set of laws that describe the behavior of gases under different conditions of temperature, pressure, and volume. These laws were developed by scientists such as Robert Boyle, Charles’s Law, and Gay-Lussac’s Law, and they are based on the idea that the particles in a gas are in constant motion and interact with each other only through collisions. The gas laws describe how the pressure, volume, and temperature of a gas relate to one another, and chemists use them to predict the behavior of gases under different conditions.

What is the Ideal Gas Law?

For example, the ideal gas law states that the pressure, volume, and temperature of a gas are directly proportional to each other, as long as the number of particles and the mass of the gas remain constant. This law can be used to calculate the properties of a gas, such as its density or molar mass, given certain information about its pressure, volume, and temperature. The gas laws are an important concept in chemistry, and chemists use them to explain many of the properties and behavior of gases.

The ideal gas law is an equation of state that describes ideal gases. This equation of state relates a gas’s pressure, volume, temperature, and mass, and is very useful for describing how gases will behave in ideal conditions. This is the most common equation of state for gases.

A few notable other gas laws are the Van der Waal’s and the Virial equation of state, which both describe the state of gases in non-ideal states. See our article on Van der Waal’s Equation to learn more about this.

The ideal gas equation was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. Clapeyton was a French engineer, and one of the founders of thermodynamics.

What are the Ideal Gas Properties?

Gases consist of a large number of particles constantly colliding with each other randomly. In order to model and predict the behavior of gases, the concept of an ideal gas was thus created. If a gas is ideal, then a few assumptions need to be made. These can also be viewed as the ideal gas properties.

Firstly , we assume that the volume of the gas particles is negligible. This means that the volume of the container is much larger than the volume of the gas particles.
Secondly, we assume that the gas particles have equal size, and do not have intermolecular forces with other gas particles.
Thirdly, we assume that the gas particles move randomly according to Newton’s Laws of Motion.
Lastly, we assume that all collisions are perfectly elastic and have no energy loss. This means that the collisions between gas particles and the walls don’t lose energy, and exert constant pressure.

Although no gas is perfectly ideal most gases are close enough at room temperature and are nearly ideal.

Combining the Gas Laws into the Ideal Gas Law Equation

the basic gas laws that combine into the ideal gas law — Graph representations of the three basic gas laws.

If we consider the three basic gas laws, Charles’ Law, Avogadro’s Law, and Boyle’s Law, we can make relations between a gas’s pressure, volume, temperature, and quantity of moles. By taking each equation and combining them, we can derive the ideal gas law equation.

$\begin{align*} P&\propto\frac{1}{V}\\ V&\propto T\\ n&\propto V\\ \implies PV&\propto nT\\ \implies \frac{PV}{nT}&=c \end{align*}$

Because this proportionality takes into account all changes of state of gases, it will be constant for an ideal gas. This constant is known as the Ideal Gas Constant, or Universal Gas Constant, and has a value of $0.0082057\frac{\text{atm L}}{\text{mol K}}$ . We can plug this constant, labeled $R$ , into the equation to derive the ideal gas law, $\boxed{PV=nRT}$ .

Ideal Gas Law Units

The following units are used in the ideal gas law equation, when SI units (international system of units) are used.

P equals pressure measured in Pascals, Pa.
V equals the volume measured in cubic meters, m³
n equals the number of moles.
R = 8.3145 represents the universal gas constant measured in J/(K · mol), or alternatively m³·Pa / (K · mol)
T equals the temperature measured in Kelvin.

If you are using liters and atmospheres of pressure, instead of Pascals and cubic meters, then you have the following:

P equals pressure measured in atmospheres
V equals the volume measured in liters
n equals the number of moles.
R = 0.08206 represents the universal gas constant measured in L·atm /(K · mol)
T equals the temperature measured in Kelvin.

Ideal Gas Law Practice Problems

Problem 1

Ethanol and methanol combust according to the following chemical equations:

$\begin{align*} {\text{Ethanol:}& \hspace{1in} CH_{3}CH_{2}OH +3O_{2} \rightarrow 3H_{2}O + 2CO_{2}} \\ {\text{Methanol:}& \hspace{1in} CH_{3}OH +1.5O_{2} \rightarrow 2H_{2}O + CO_{2}} \end{align*}$

A mixture of ethanol and methanol combusts in oxygen to produce 35 cm³ of CO₂ and 55 cm³ of H₂O. Complete combustion occurs and the volumes of both products are measured at 101 kPa and 120 degrees centigrade. What is the molar ratio, ethanol to methanol, in the mixture?

$\text{a)}\hspace{0.1in}1:3\hspace{0.2in}\text{b)}\hspace{0.1in}2:3\hspace{0.2in}\text{c)}\hspace{0.1in}3:2\hspace{0.2in}\text{d)}\hspace{0.1in}3:1\hspace{0.2in}$

Problem 2

In a 1.00L vessel at 273K, a sample of gas has 112atm of pressure. You know that 355g of gas are present in the vessel. What is the identity of the gas? (Hint: you have to find the molar mass of the gas)

$\text{a)}\hspace{0.1in}H_{2}\hspace{0.2in}\text{b)}\hspace{0.1in}CH_{4}\hspace{0.2in}\text{c)}\hspace{0.1in}Cl_{2}\hspace{0.2in}\text{d)}\hspace{0.1in}C_{6}H_{6}\hspace{0.2in}$

Ideal Gas Law Practice Problem Solutions

$\text{(d)}$
$\text{(c)}$