Calculate the volume occupied by 2 mole of N₂ at 200K & 8.21 atm pressure, if P_CV_C / RT_C = 3/8 and P_rV_r / T_r .

First, we will calculate the volume occupied by two moles of nitrogen at STP. We know that one mole of every gas occupies a volume of 22.4 litres at STP. Therefore volume occupied by 2 moles of nitrogen at STP will be 2 X 22.4 = 44.8 litres. 

STP stands for standard temperature and pressure. For STP conditions, the temperature is 273.15K (0⁰ C) and pressure is 1 bar (10⁵ Pascals or 0.987 atm).

we will now use the relation

 P₁V₁ / T₁ = P₂V₂ / T₂

Here P₁ = 0.987 atm, V₁ = 44.8 litres, T₁ = 273.15 K, P₂ = 8.21 atm, T₂ = 200K and V2 has to be calculated. Substituting these values in the above expression, we get

 [0.987 X 44.8] / 273.15 = [8.21 X V₂] / 273.15

 This gives us V₂ = 3.94 Litres