How Many Molecules Exist in a Cubic Centimeter at 10^-15 atm and 20°C?

[bse]

How many molecules exist in one cubic centimeter of space at a pressure of 10^-15 atm and temperature of 20 degrees C?

 

[mgb_phys]

PV = nRT
Where P pressure, V volume, T absolute temperature, n number of moles and R is a constant
You can find the units and value of R in the tetbook or wiki.

 

[Moetasim]

At standard temperature and pressure, one mole of any gas occupies 22.4 liters of volume. Using the ideal gas law, we can calculate the number of molecules in one cubic centimeter (0.000001 liters) at a pressure of 10^-15 atm and temperature of 20 degrees C.

n = PV/RT
n = (10^-15 atm)(0.000001 L) / (0.0821 L atm/mol K)(293 K)
n = 4.26 x 10^-28 moles

One mole of any substance contains 6.022 x 10^23 molecules, so in one cubic centimeter of space at these conditions, there would be approximately 2.56 x 10^-4 molecules. This is an incredibly small number, highlighting the vastness of space and the emptiness of a vacuum.