Question

derive an ideal gas equation

Answer 1

Gas laws such as Boyle’s law, Charles’s law, and Gay Lussac’s law give us an elementary idea of the change in the physical properties of gases with changes in state functions (pressure, temperature, and volume). A gas which follows these laws such as Boyle’s law, Charles’s law, Avogadro’s Law is known as ideal gas.



An ideal gas is generally hypothetical as it doesn’t consider the intermolecular forces between the gas molecules. Real gases also behave as ideal gases but under certain specific conditions when gaseous molecules have negligible forces of interaction between them. A general equation has been derived with the help of gas laws for the ideal gases. This equation is better known as an ideal gas equation. The ideal gas equation helps us to co-relate values of pressure, temperature, volume and number of moles. A general derivation

The ideal gas equation helps us to co-relate values of pressure, temperature, volume and number of moles. A general derivation of the ideal gas equation with the help of gas laws is discussed below:

According to the Boyle’s Law, at a constant temperature, for a fixed number of moles of a gas the volume of a gas varies inversely with its pressure.

\(V ~∝~ \frac{1}{P}\) ————— (1)

Where,
\(V\)= volume
\(P\) = pressure

According to the Charles’ Law, at constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature.

\(V ~∝~ T\) — ———————- (2)

Where, \(T\)= temperature

According to the Avogadro’s Law, at same temperature and pressure, an equal volume of gases contain an equal number of molecules.

\(V~ ∝~ n\) ———————— (3)

Where, \(n\) = number of moles of gases

From equation (1), (2) and (3), we can deduce that,

\(V ~∝ ~\frac{nT}{P}\)

\(\Rightarrow~V\) = \(R \frac{nT}{P}\)

Where, \(R\) is known as a universal gas constant. The above equation is commonly known as an ideal gas equation. Value of \(R\) can be calculated at \(STP\) (standard temperature pressure) for one mol of gas as:
Volume at STP = 22.710981 L/mol
Pressure at STP = 1 bar = 105 Pa
Temperature at STP = 273.15

Answer 2

Answer

V= k g r

Where k is constant