A vessel of volume 20L contains a mixture of hydrogen and helium at temperature of 27^ C and pressure 2 atm. The mass of mixture is 5 ~g . Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the given mixture will be

Step-by-step solution

Let there are n ₁ moles of hydrogen and n ₂ moles of helium in the given mixture. As Pv = nRT Then the pressure of the mixture array r P= n ₁ RT V + n ₂ RT V = ( n ₁+ n ₂ ) RT V 2 101.3 10³= ( n ₁+ n ₂ ) (8.3 300) 20 10⁻³ array or, array l ( n ₁+ n ₂ )= 2 101.3 10³ 20 10⁻³ (8.3)(300) or, n ₁+ n ₂=1.62 array The mass of the mixture is (in grams) array l n ₁ 2+ n ₂ 4=5 ( n ₁+2 n ₂ )=2.5 array Solving the eqns. (1) and (2), we get n ₁=0.74 and n ₂=0.88 Hence, m _ H m _ He = 0.74 2 0.88 4 = 1.48 3.52 = 2 5