A rigid vessel contains a non-reactive mixture of SO ₂( g ) and O ₂( g ) at a total pressure of 130 kPa initially. The partial pressure of O ₂( g ) is 30 kPa . A catalyst is introduced and the gases are allowed to react completely to form SO ₃( g ) at a constant temperature. Find the final total pressure in the vessel in kPa.

Step-by-step solution

Initial total pressure, P_ total = 130 kPa Initial partial pressure of O ₂ , P_ O ₂ = 30 kPa Initial partial pressure of SO ₂ , P_ SO ₂ = 130 - 30 = 100 kPa The balanced chemical equation for the reaction is: 2 SO ₂( g ) + O ₂( g ) 2 SO ₃( g ) At constant volume and temperature, partial pressure is directly proportional to the number of moles. From the stoichiometry, 1 mole of O ₂ reacts with 2 moles of SO ₂ . So, 30 kPa of O ₂ will react with 2 30 = 60 kPa of SO ₂ . Since 100 kPa of SO ₂ is available, O ₂ is the l