For the synthesis of sulphur trioxide gas represented by the equation 2 SO ₂( g ) + O ₂( g ) 2 SO ₃( g ) , the forward reaction rate constant is 1.5 10^3 and the backward reaction rate constant is 3.0 10^2 at 300 K . [Given: R = 1 12 L atm K ⁻¹ mol ⁻¹ ] The value of K _ p for this reaction at 300 K is:

Step-by-step solution

The equilibrium constant in terms of concentration, K _ c , is the ratio of the forward rate constant to the backward rate constant: K _ c = k _ f k _ b = 1.5 10^3 3.0 10^2 = 5 For the reaction 2 SO ₂( g ) + O ₂( g ) 2 SO ₃( g ) , the change in the number of moles of gaseous species is: n _ g = moles of gaseous products - moles of gaseous reactants n _ g = 2 - (2 + 1) = -1 The relationship between K _ p and K _ c is: K _ p = K _ c ( RT )^ n _ g Substituting the given values: RT = 1 12 300 = 25 K _ p = 5 (25)⁻¹ = 5