Consider the equilibrium reaction: 2 SO ₃( g ) 2 SO ₂( g ) + O ₂( g ) Initially, pure SO ₃ is taken and its degree of dissociation ' a ' is very small ( a 1 ). The system reaches equilibrium at a total pressure P₁ . If the equilibrium is re-established at the same temperature but at a new total pressure P₂ = P₁ 8 , the new degree of dissociation ' a_ new ' in terms of ' a ' will be:

Step-by-step solution

For the reaction: 2 SO ₃( g ) 2 SO ₂( g ) + O ₂( g ) Let the initial moles of SO ₃ be 1 . At equilibrium, moles of SO ₃ = 1 - a Moles of SO ₂ = a Moles of O ₂ = a 2 Total moles at equilibrium = 1 - a + a + a 2 = 1 + a 2 Since a is very small, 1 + a 2 1 and 1 - a 1 . Partial pressures at equilibrium: p_ SO ₃ = 1 1 P = P p_ SO ₂ = a 1 P = aP p_ O ₂ = a/2 1 P = aP 2 The equilibrium constant K_p is: K_p = (p_ SO ₂ )^2 (p_ O ₂ ) (p_ SO ₃ )^2 = (aP)^2 ( aP 2 ) P^2 = a^3 P 2 Since K_p depends only on temperature, it remai