Question

what is ideal equation and prove it.

Answer 1

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gasesunder many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law and Avogadro's law.[1] The ideal gas law is often written as

{\displaystyle PV=nRT,}

where:

{\displaystyle P} is the pressure of the gas,{\displaystyle V} is the volume of the gas,{\displaystyle n} is the amount of substance of gas (in moles),{\displaystyle R} is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,{\displaystyle T} is the absolute temperature of the gas.

It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently) by August Krönig in 1856[2]and Rudolf Clausius in 1857.[3]

Answer 2

In simple terms,
A gas which follows 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 considers 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.

Now the ideal gas equation,
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 ∝ 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 ∝ nT/P
⇒ V = RnT/P
Where, R is known as a universal gas constant.
Thus, the equation becomes,
PV = nRT. (answer)


Hope it helps you.
Thank you.