Answer:
247 molecules
Explanation:
This problem can be solved by using the ideal gas equation:
[tex]pV=nRT[/tex]
where in this case we have
[tex]p=10^{-12}N/m^2 = 10^{-12} Pa[/tex] is the lowest pressure attainable
[tex]V=1 cm^3 = 1\cdot 10^{-6}m^2[/tex] is the volume we are considering
n is the number of moles
R is the gas constant
[tex]T=19^{\circ}+273=292 K[/tex] is the absolute temperature
Solving the equation for n, we find
[tex]n=\frac{pV}{RT}=\frac{(10^{-12} Pa)(1\cdot 10^{-6}m^3)}{(8.314 J/mol K)(292 K)}=4.1\cdot 10^{-22}mol[/tex]
And since the number of molecules in 1 mole of gas is
[tex]N_A = 6.022\cdot 10^{23}[/tex] (avogadro number)
The number of molecules present here is
[tex]N=n N_A = (4.1\cdot 10^{-22}mol)(6.022 \cdot 10^{23} mol^{-1})=246.9 \sim 247[/tex]
so, there are approximately 247 molecules.
