Which of the following is true of a sample of hydrogen gas whose mass is \(4.00 g\) under a pressure of \(2 atm\) and a temperature of \(27^{\circ} C\) ? \(\left( H =1, R =0.082\right.\) lit atm. \(Mol ^{-1}\) \(\operatorname{deg}-1\) )
A. its volume is \(24.6\) litres B. it contains \(6.02 \times 10^{23}\) molecules C. it exists as atoms because of temperature D. none of the above
Correct Answer: A
Explanation
The molar mass \(\left( H _{2}\right) 2 \times 1=2 g / mol\) No of mole of \(H _{2}\) \begin{aligned} &=\frac{\text { mass of } H _{2}}{ m . \text { mass of } H _{2}} \\ &=\frac{4.00 g }{2.000 g / mol }=2.0 mol \\ \text { From } P V=n R T \\ V &=\frac{n R T}{P} \\ &=\frac{2.0 \times 0.082 \times(27+273)}{2} \\ &=24.6 \text { litre } \end{aligned} \(\therefore\) its volume is \(24.6\) litre.ut, No of \(mol =\frac{\text { no of molecules }}{6.02 \times 10^{23}}\) \(\therefore\) no of molecule = no of mole \(6.02 \times 10^{23}\) \(=2.0 mol \times 6.02 \times 10^{23}=12.04 \times 10^{23}\) i.e. it contains \(12.04 \times 10^{23}\) molecules and not \(6.02 \times 10^{23}\) molecules