Answer:
Molar mass of the unknown gas is 64.6 g/mol
Step-by-step explanation:
Let's think this excersise with the Ideal Gases Law.
We start from the N₂. At STP conditions we know that 1 mol of anything occupies 22.4L.
We apply: P . V = n . R . T
5 atm . V = 1 mol . 0.082 . 325K
V = (1 mol . 0.082 . 325K) / 5 atm = 5.33 L
It is reasonable to say that, if we have more pressure, we may have less volume.
As this is the volume for 1 mol of N₂, our mass is 28 g. Then, the density of the nitrogen and the unknown gas is 28 g/5.33L = 5.25 g/L
Our unknown gas has, this density at 27°C and 2 atm.
If we star from this, again: 1 mol of any gas occupy 22.4L at STP, we can calculate the volume for 1 mol at those conditions:
P₁ . V₁ / T₁ = P₂ . V₂ / T₂
1 atm . 22,4L / 273K = 2 atm . V₂ / 300K
Remember that the value for T° is Absolute (T°C + 273)
[ (1 atm . 22.4L / 273K) . 300K] / 2 atm = V₂ → 12.3L
This is the volume for 1 mol of the unknown gas at 2 atm and 27°C
We use density to determine the mass: 12.3 L . 5.25 g/L = 64.6 g
That's the molar mass: 64.6 g/mol