Suppose that a 1.0-L reaction vessel initially contains 1.0 mol of O3 and 1.0 mol of O2. What fraction of the O3 will have reacted when the rate falls to one-half of its initial value?

given reaction

2O₃ ⇄ 3O₂

initial 1 1

final 1-x 1 + 1.5x

rate of reaction = k [ O₃ ]² / [ O₂ ]

initial rate = k. 1² / 1 = k

final rate = k (1-x) ² / (1 + 1.5x) = k/2

(1-x) ² / (1 + 1.5x) = 1/2

2x² - 5.5 x + 1 = 0

x = 0.196

So fraction of ozone reacted =.196