In the movie "santa claus is coming to town", the mayor burgermeister meisterburger outlaws toys after tripping on a rubber duck. to make rubber ducks un-crushable while being delivered by santa, the ducks are filled with an inert, harmless gas. a 2.5 gram sample of the gas fills a 5 liter container. if the pressure in the container is 1.2 atmospheres at a temperature of 27 degrees celsius, what is the molecular weight of the gas in grams per mole?

 PM = 2,254 g / mol

Explanation:

We must assume that the gas behaves like an ideal gas, in this case we can use the state equation

         PV = n RT

Where P is the pressure, V is the volume, n is the number of moles, R the gas constant worth 8,134 J/mol K, the absolute temperature (degrees Kelvin)

let's start reducing everything to the international system of SI units

       m = 2.5 g (1 kg / 1000g) = 2.5 10⁻³ kg

       V = 5 liters (1 m3 / 1000 liter) = 5 10⁻³ m3

       P = 1.2 atm (1,013 105 Pa / 1 atm) = 1.2 10⁵ Pa

       T = 27 + 273 = 300K

Let's calculate the number of moles

      n = PV / RT

      n = 1.2 10⁵  5 10⁻³ / (8.134  300)

      n = 0.246 mol

To calculate the molecular weight we use a direct rule of proportions

      PM = mass / n

      PM = 2.5 10⁻³ / 0.246

      PM = 2,254 kg / mol

      PM = 2,254 g / mol

this is poiselle's equation from fluid mechanic in physics. mech eng