Which gas sample contains the fewest molecules?
A
$$1.00{dm}^{3}$$ of carbon dioxide at $${27}^{o}C$$ and $$2.0kPa$$
B
$$1.00{dm}^{3}$$ of hydrogen at $${100}^{o}C$$ and $$2.0kPa$$
C
$$1.00{dm}^{3}$$ of nitrogen at $${300}^{o}C$$ and $$4.0kPa$$
D
$$1.00{dm}^{3}$$ of oxygen at $${250}^{o}C$$ and $$3.0kPa$$
Correct option is B. $$1.00{dm}^{3}$$ of hydrogen at $${100}^{o}C$$ and $$2.0kPa$$
PV = nRT
n = moles = PV/RT..
P, V, R, and T are all constant right? 1 atm, 1.0 L , R, and 273 K?
so "n" is constant. ie they all have the same number of moles of molecules. ie they all have the same number of molecules.
in fact,
n = 1 atm x 1.0 L / (0.0821 Latm/moleK x 273K) = 0.0446 moles
and
0.0446 moles x (6.022x10^23 molecules / mole ) = 2.69x10^22 molecules
as the molecular mass of the hydrogen is least among all of these and mole=given mass/molar mass
hence hydrogen gas contains the fewest molecules