In this question, we have to use the ideal gas law, which can be written as:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature (in K).
In this question, P = 1 x 10^-15 mm Hg
1 atm of pressure is equal to 760 mm Hg. Thus the given pressure can also be converted to the units of atm.
Thus, P = 1 x 10^-15 mm Hg x 1 atm / 760 mm = 1.3158 x 10^-18 atm
V = 1 l
T = 22 degrees C = 22 + 273 K = 295 K
and R: universal gas constant = 0.0821 l atm/mol/K
Substituting all the values in the equation, we get:
1.3158 x 10^-18 atm x 1 l = n x 0.0821 l atm/mol/K x 295 K
or, n = 5.378 x 10^-20 moles
Since each mole of a substance contains 6.023 x 10^23 molecules, the number of molecules in the current case are:
Number of molecules = 5.378 x 10^-20 x 6.023 x 10^23
= 3.24 x 10^4 molecules or 32,392 molecules.
Hope this helps.