Question

How many atoms are contained in 16.80 L of Xe at STP?

Answer 1

The answer is `4.52 * 10^23` atoms.

This problem can be solved either by using the ideal gas law, `PV = nRT`, or by using the molar volume of an ideal gas at STP.

If one were to use the ideal gas law, it is important to know that STP means a pressure of 1.00 atm and a temperature of 273.15K. In order to determine the number of atoms, we need to first determine the number of moles

`PV = nRT -> n = (PV)/(RT) = (1.00atm * 16.80 L)/(0.082 (L*atm)/(mol*K) * 273.15K) = 0.750 mol es`

Since 1 mole of any substance has exactly `6.022 * 10^23` atoms (or molecules - this is known as Avogadro's number), we can determine the number of atoms by

`0.750mol es * (6.022 * 10^23at oms)/(1 mol e) = 4.52 * 10^23at oms`

The second method uses the fact that 1 mole of any ideal gas occupies `22.4L` at STP. We could determine the number of moles by

`n = V/V_(molar) = (16.80L)/(22.4L) = 0.750mol es`

And, once again

`0.750mol es * (6.022 * 10^23at oms)/(1 mol e) = 4.52 * 10^23at oms`