Physics
posted by Chris on .
A container of volume 19.4 cm3 is initially filled with air. The container is then evacuated at 0oC to a pressure of 6.0 mPa. How many molecules are in the container after evacuation if we assume that air is an ideal gas?

Since the gas is ideal, we can use the Ideal Gas Law:
PV = nRT
where
P = pressure in atm
V = volume in L
n = number of moles of air
R = universal gas constant = 0.0821 Latm/molK
T = temperature in K
We first convert the given in the appropriate units:
V = 19.4 cm^3
cm^3 is also equal to mL. Thus there are 1000 cm^3 for every 1 L, or
V = 19.4 / 1000 = 0.0194 L
P = 6 mPa
The conversion is: 101325 Pa = 1 atm, thus
P = (6 / 1000) / 101325 =
T = 0 C
We just add 273 to make it Kelvin:
T = 0 + 273 = 273 K
Substituting to the equation:
PV = nRT
n = PV/RT
n = (5.92 10^8)(0.0194) / (0.0821)(273)
n = 5.125 * 10^11 moles
Note that this is only the moles. To get the number of molecules, note that 1 mol = 6.022 * 10^23 representative particles. Thus,
5.125 * 10^11 * 5.125 * 10^11
= 3.087 * 10^13 molecules
Check the significant figures.
Hope this helps :3 
*lol sorry, in the last calculation that should be
5.125 * 10^11 * 6.022 * 10^23
but the answer is still the same. :)