Chemistry gas pressure moles

Question

Which of the following sets of gas variables describes the largest number of molecules?

1.00 L of Ar at 0 °C and 1.00 atm

1.00 L of CH₄ at 0 °C and 1.25 atm

1.00 L of CO₂ at 20 °C and 1.00 atm

1.00 L of CO at 50 °C and 1.25 atm

Answer 1

The question is essentially asking which one has the greatest number of moles of gas.

From the ideal gas equation PV = nRT and rearranging for moles (n) we have..

n = moles = PV/RT and in all cases, volume (V) is 1.00 L so that is constant. R is the gas constant so it, too can be ignored. That leaves us with

n = moles = P/T (recall T is in Kelvin)

1) 1 atm / 273 = 0.00367

2) 1.25 atm / 273 = 0.00458

3) 1 atm / 293 = 0.00341

4) 1.25 atm / 323 = 0.00389

So greatest number of moles is found in 1.00 L of CH₄ at 0 °C and 1.25 atm

(note: it doesn't matter what the gas is (CO, Ar, CO2 or CH4) since 1 mole of any gas has the same number of molecules. Also note that you don't have any molecules of Ar, but rather you have atoms)