Posted by **Chris** on Tuesday, October 29, 2013 at 11:23am.

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?

- Physics -
**Jai**, Tuesday, October 29, 2013 at 12:18pm
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 L-atm/mol-K

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

- Physics -
**Jai**, Tuesday, October 29, 2013 at 12:37pm
*lol sorry, in the last calculation that should be

5.125 * 10^-11 * 6.022 * 10^23

but the answer is still the same. :)

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