Question

Is ideal gas law direct or inverse.

Answer 1

To answer this question, we must know Ideal gas law and its derivation. The ideal gas law equation shows the relation between pressure, volume, number of moles and temperature of a gas. 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 behaviour of many gases under many conditions, although it has several limitations.

Complete answer:
The ideal gas law is given by,
$PV = nRT$
Where,
$P$ is the pressure of the gas.
$V$ is the volume,
$n$ is the number of moles of the gas,
$R$ is the gas constant and
$T$ is the temperature in Kelvin.
Let us consider an ideal gas which is at pressure, $P$ and let its volume be $V$ . The gas is kept at temperature, $T$ and the number of moles of the gas is $n$ .
According to Boyle's law, at constant temperature and number of moles of the gas, the volume is inversely proportional to the pressure. Therefore,
$V \propto \dfrac{1}{P}$ -----(1)
According to the Charles law, at constant pressure and number of moles of the gas, the volume is directly proportional to the temperature. Therefore,
$V \propto {\rm T}$ -----(2)
According to Avogadro's law, at constant pressure and temperature, the volume of the gas is directly proportional to the number of moles. Therefore,
$V \propto n$ -----(3)
Now, from equation (1), (2) and (3) we can say,
$V \propto \dfrac{{nT}}{P}$
Now removing sign of proportionality,
$V = R\dfrac{{nT}}{P} \\\ \Rightarrow PV = nRT$
This is the equation of ideal gas law.
Now from this we can conclude that the ideal gas law is both direct and inverse because the volume of a gas is inversely proportional to its pressure and directly proportional to its temperature and the amount of gas.

Note:
The ideal gas law assumes that gases behave ideally, meaning they adhere to the following characteristics:
(1) The collisions occurring between molecules are elastic and their motion is frictionless, meaning that the molecules do not lose energy.
(2) The total volume of the individual molecules is magnitudes smaller than the volume that the gas occupies.
(3) There are no intermolecular forces acting between the molecules or their surroundings.
(4) The molecules are constantly in motion, and the distance between two molecules is significantly larger than the size of an individual molecule.