What is the density of one mole of $He$ (molar mass $= 4 \ g \ mol^{-1}$) at $300 \ K$ and a pressure of $0.82 \ atm$? $(R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1})$

Match the laws given in List-$I$ with their mathematical forms given in List-$II$.

List-$I$	List-$II$
$(1)$ Boyle's Law	$(A)$ $p \propto T$
$(2)$ Charles's Law	$(B)$ $V \propto n$
$(3)$ Gay-Lussac's Law	$(C)$ $p \propto \frac{1}{V}$
$(4)$ Avogadro's Law	$(D)$ $pV = nRT$
$(5)$ Ideal Gas Equation	$(E)$ $V = k_2T$

At $0\, ^\circ C$ and $1\, \text{atm}$ pressure,a gas occupies $100\, \text{cc}$. If the pressure is increased to $1.5$ times and the temperature is increased by one-third of its absolute temperature,then the final volume of the gas will be :- $cc$

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is $0.0050 \ cm$ and the air inside contains $14$ per cent oxygen. Assuming that the pressure in the alveoli is $1.0 \ atm$ and the temperature is $37 \ ^oC$,calculate the number of oxygen molecules in one of the alveoli.

For an ideal gas,Boyle's law is best described by which of the following graphs?

Which of the following represents the correct relationship between the change in density of an ideal gas and the change in temperature?