The Gas Laws - Practice Questions & MCQ

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.

$
\begin{aligned}
V & \propto \frac{1}{P} \\
\text { or, } \quad P . V & =\text { constant } \\
\Rightarrow P_1 V_1 & =P_2 V_2
\end{aligned}
$

We can also write the above equation as,

$
\begin{aligned}
P V & =P\left(\frac{m}{\rho}\right)=\text { constant } \\
\Rightarrow \quad \frac{P}{\rho} & =\text { constant or } \frac{P_1}{\rho_1}=\frac{P_2}{\rho_2}
\end{aligned}
$

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 - 

$
\begin{aligned}
\boldsymbol{V} & \propto \boldsymbol{T} \\
\frac{V}{T} & =\text { Constant } \\
\frac{V_1}{T_1} & =\frac{V_2}{T_2}
\end{aligned}
$

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

$
\frac{V}{T}=\frac{m}{\rho T}=\text { constant }\left(\text { As volume } V=\frac{m}{\rho}\right)
$

or, $\quad \rho T=$ constant $\Rightarrow \rho_1 \mathbf{T}_1=\rho_2 \mathbf{T}_2$

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

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 - 

                                                 $P \propto T$ or $\frac{P}{T}=$ 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.

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, 

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

Where, $r=$ rate of diffusion of gas

$$
\begin{aligned}
& \rho=\text { Density of the gas } \\
& \mathrm{M}=\text { Molecular weight of the gas } \\
& V_{r m s}=\text { Root mean square velocity }
\end{aligned}
$$

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 -

$$
\text { For } n \text { gases } P=P_1+P_2+P_3+\ldots \ldots P_n
$$

Here, $\mathrm{P}=$ Pressure exerted by the mixture of gases

$$
P_1, P_2 \ldots \ldots P_n=\text { Partial pressure of the component gases. }
$$