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