One litre of oxygen at a pressure of 1 atm and two litres of nitrogen at a pressure of 0.5 atm, are introduced into a vessel of volume 1 L . If there is no change in temperature, the final pressure of the mixture of gas (in atm ) is

Step-by-step solution

Ideal gas equation is given by P V = n R T ...(i) For oxygen, P = 1 atm, V = 1 L, n = n O 2 Therefore, Eq. (i) becomes ∴ 1 × 1 = n O 2 R T n O 2 = 1 R T For nitrogen P = 0.5 atm, V = 2 L, n = n N 2 ∴ 0.5 × 2 = n N 2 R T ⇒ n N 2 = 1 R T For mixture of gas P mix V m i x = n m i x R T Here, n m i x = n O 2 + n N 2 ∴ P m i x V m i x R T = 1 R T + 1 R T P m i x V m i x = 2 V m i x = 1