The Behavior of Ideal Gases and the Factors Affecting Them

Ideal gases are the gases which have elastic collisions between their molecules and there are no intermolecular attractive forces. In reality, there is no such thing as ideal gases. The gases just show ideal behaviour under certain conditions of temperature and pressure.

When we talk about ideal gases, the following assumptions are taken into consideration:

  1. The ideal gases are made up of molecules which are in constant motion in random directions.
  2. The molecules of an ideal gas behave as rigid spheres.
  3. All the collisions are elastic.
  4. The temperature of the gas is directly proportional to the average kinetic energy of the molecules.
  5. Pressure occurs due to the collision between the molecules with the walls of the container.

The ideal gas law:

Behavior of ideal gas 1

The gases which obey the three laws namely,

  1. Charles’ law – At constant pressure and number of moles, the volume of a gas is directly proportional to its temperature.

\(\begin{array}{l} V ∝ T \end{array} \)

  1. Boyle’s law – At constant temperature and number of moles, the volume of a gas is inversely proportional to its pressure.

\(\begin{array}{l} V ∝ \frac{1}{p} \end{array} \)

  1. Avogadro law – At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles.

\(\begin{array}{l} V ∝ n \end{array} \)

Combining all the three laws we get,

\(\begin{array}{l} V ∝ \frac{nT}{p} \end{array} \)

\(\begin{array}{l} V = R \frac{nT}{p} \end{array} \)

Here R is the constant of proportionality. On rearranging the above equations we get,

p V = n RT

R is known as the universal gas constant and is the same for all the gases. The above equation is called the ideal gas equation. So it can be said that at constant temperature and pressure n moles of any gas will have the same volume.

\(\begin{array}{l} V = \frac{n R T}{p} \end{array} \)

Here n, R, T, and p, all are constant so there will be a fixed volume for all the gases under these conditions. This equation is applicable to any gas which approaches the ideal behaviour. The ideal gas law is also known as the equation of the state because it determines the relation between the four variables and describes the state of a given gas.

If we consider a case in which the temperature, volume and pressure varies from T1, V1, p1 to T2, V2, p2 then the gas law can be written as:

\(\begin{array}{l} \frac{p_1 V_1}{T_1} = n R \end{array} \)


\(\begin{array}{l} \frac{p_1 V_1}{T_1} = n R\end{array} \)

\(\begin{array}{l} \Rightarrow \frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2} \end{array} \)

This is a very useful equation and is known as the combined gas law. If five values are known then the sixth value can be calculated.

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Ideal Gas Equation definitions, derivation

Frequently Asked Questions – FAQs


What is an ideal gas equation and derive it mathematically?

The ideal gas equation is formulated as PV = nRT. In this equation, P refers to the pressure of the ideal gas, V is the volume of the ideal gas, n is the total amount of ideal gas that is measured in terms of moles, R is the universal gas constant, and T is the temperature.

What is meant by the ideal gas equation?

An equation that equates the product of the pressure and the volume of one mole of gas to the product of its thermodynamic temperature and the gas constant. The equation is exact for an ideal gas and is a good approximation for real gases at low pressures. Also called: the ideal gas equation, ideal gas law.

What is an ideal gas example?

Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure.

What are ideal gas conditions?

For gas to be “ideal” there are four governing assumptions: The gas particles have negligible volume. The gas particles are equally sized and do not have intermolecular forces (attraction or repulsion) with other gas particles. The gas particles have perfect elastic collisions with no energy loss.

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