JEE Main Class 11 Syllabus 2025 PDF for Paper 1 and 2

The Gas Laws - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

Gas laws(I) is considered one of the most asked concept.
12 Questions around this concept.

Solve by difficulty

A gas expands obeying the relation as shown in the $\mathrm{P / V}$ diagram. The maximum temperature in this process is equal to

$\mathrm{\frac{P_0 V_0}{R}}$

$\mathrm{\frac{3 P_0 V_0}{R}}$

$\mathrm{\frac{9 P_0 V_0}{8 R}}$

None of these

View Solution

Concepts Covered - 3

Gas laws(I)

BOYLE'S LAW

Boyle’s law : It states that, for a given mass of an ideal gas at constant temperature, the volume of a gas is inversely proportional to its pressure.

$\ \ \ \ \ \ \ V \propto \frac{1}{P} \quad \\ \\ \text { or, } \quad P.V=\text { constant }$

$\Rightarrow P_{1} V_{1}=P_{2}V_{2}$

We can also write the above equation as,

$P V=P\left(\frac{m}{\rho}\right)=\text { constant }$

So, $\Rightarrow \quad \frac{P}{\rho}=\text { constant or } \frac{P_{1}}{\rho_{1}}=\frac{P_{2}}{\rho_{2}}$

We can represent the Boyle's law through the various graph, which is shown as -

CHARLE'S LAW -

Charle's law : It states that, if the pressure remaining constant, the volume of the given mass of a gas is directly proportional to its absolute temperature.

From the above statement we can conclude the following equations -

$\boldsymbol{V\ \propto \ T}$

So, $\\ \frac{V}{T} = Constant \\ \\ \\ \frac{V_1}{T_1} = \frac{V_2}{T_2}$

This equation can also be written in terms of density and temperature as -

$\\ {\text { } \frac{V}{T}=\frac{m}{\rho T}=\text { constant }\left(\text { As volume } V=\frac{m}{\rho}\right)} \\ \\ \\ {\text { or, } \quad \rho T=\text { constant } \\ \\ \mathbf{\Rightarrow \rho_{1} T_{1}=\rho_{2} T_{2}}}$

We can represent the Charle's law through the various graph, which is shown as -

Gas laws(II)

Gay-Lussac’s law -

Gay-Lussac’s law or pressure law : If the volume remains constant, then the pressure of a given mass of a gas is directly proportional to its absolute temperature.

So, We can conclude the above statement in the following equation -

$P \propto T \text { or } \frac{P}{T}=\text { constant } \Rightarrow \frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}$

The graphical representation of Gay-Lussac's law is -

AVAGADRO'S LAW -

Avogadro’s law : Equal volume of all the gases under similar conditions of temperature and pressure contain equal number of molecules. It implies that -

$N_1 = N_2$
N = Number of molecules in a particular gas.

Gas laws(III)

GRAHAM’S LAW OF DIFFUSION

Graham’s law of diffusion: It states that when any two gases at the same pressure and temperature are allowed to diffuse into each other, then the rate of diffusion of each gas is inversely proportional to the square root of the density of the gas.

So we can say that,

$r \propto \frac{1}{\sqrt{\rho}} \propto \frac{1}{\sqrt{M}} \ \alpha \ V_{rms}$

Where, r = rate of diffusion of gas

$\rho$ = Density of the gas

M = Molecular weight of the gas

$V_{rms}$ = Root mean square velocity

Now, from the above equation we can write,

$\frac{r_{1}}{r_{2}}=\sqrt{\frac{\rho_{2}}{\rho_{1}}}=\sqrt{\frac{M_{2}}{M_{1}}}$

DALTON'S LAW OF PARTIAL PRESSURE -

Dalton’s law of partial pressure :It states that the total pressure exerted by a mixture of non-reacting gases occupying a vessel is equal to the sum of the individual pressures which each gases exert if it alone occupied the same volume at a given temperature.

Now, let us have a mixture of 'n' gases, so from the above statement we can conclude that -

$\text { For } n \text { gases } P=P_{1}+P_{2}+P_{3}+\ldots . . P_{n}$