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# Under the same conditions of temperature and pressure you collect 2 litres of carbon dioxide, 3 litres of chlorine, 5 litres of hydrogen, 4 litres of nitrogen and 1 litre of sulphur dioxide. In which gas sample will there be: (a) The greatest number of molecules. (b) The least number of molecules. Justify your answer.

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## (a) According to Avogadro's law, at same temperature and pressure conditions, equal number of molecules of any gas occupy equal volumes. Hence, higher the volume of a gas, larger will be the number of molecules of the gas. Therefore, five litres of hydrogen gas will have the greatest number of molecules. Alternatively, Number of molecules of a gas = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{gas}}{\mathrm{Molar}\mathrm{volume}\mathrm{of}\mathrm{gas}}×\mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{number}$ = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{gas}\left(\mathrm{L}\right)}{22.4\mathrm{L}}×6.023×{10}^{23}$ Volume of different gas Number of molecules 2 L of CO2 $\frac{2}{22.4\mathrm{L}}×6.023×{10}^{23}=0.54×{10}^{23}$ 3 L of Cl2 $\frac{3}{22.4\mathrm{L}}×6.023×{10}^{23}=0.81×{10}^{23}$ 5 L of H2 $\frac{5}{22.4\mathrm{L}}×6.023×{10}^{23}=1.34×{10}^{23}$ 4 L of N2 $\frac{4}{22.4\mathrm{L}}×6.023×{10}^{23}=1.07×{10}^{23}$ 1 L of SO2 $\frac{1}{22.4\mathrm{L}}×6.023×{10}^{23}=0.27×{10}^{23}$ It is evident from the table that five litres of H2 has largest number of molecules, which is 1.34$×$1023. (b) As can be seen in the table above, the gas having the lowest volume will contain least number of molecules. So, one litre of SO2 will have the least number of molecules, which is 0.26$×$1023.  Suggest Corrections  1      Similar questions  Related Videos   Concentration Terms
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