An empty $LPG$ cylinder weighs $14.8 \ kg$. When full,it weighs $29.0 \ kg$ and shows a pressure of $3.47 \ atm$. In the course of use at ambient temperature,the mass of the cylinder is reduced to $23.0 \ kg$. The final pressure inside of the cylinder is $....... \ atm$. (Nearest integer)
(Assume $LPG$ to be an ideal gas)

Why is it necessary for chemists to understand the laws that govern the physical states of matter?

$1 \text{ mole}$ of gas $A$ and $1 \text{ mole}$ of gas $B$ at $27^{\circ} C$ were pumped into a $24.6 \ L$ volume pre-evacuated isolated flask. The catalyst coated inside the flask catalyses the following reaction $A_{(g)} + B_{(g)} \longrightarrow 2 D_{(g)}$. The kinetic energy of $D$ is $98.03 \ L \ atm$. Calculate the pressure realized at the end of the reaction. (in $atm$)

For one mole of an ideal gas,increasing the temperature from $10^{\circ} C$ to $20^{\circ} C$:

$A$ container contains a mixture of $He$ and $Ne$ gases at a certain temperature. $He$ is $20 \%$ by mass of the mixture. What is the ratio of the partial pressure of $He$ to $Ne$?

Two gases $X$ and $Y$ are taken in equal molar proportions. The ratio of their rates of diffusion is $1 : 2$. What will be the mole fraction of $X$ in a mixture containing $2 \ g$ of $X$ and $3 \ g$ of $Y$?