The following data was recorded for the decomposition of XY compound at 750K [XY] mol / L Rate of decomposition of XY mol / L s 0.4 5.5 10⁻⁷ 0.8 22.0 10⁻⁷ 1.2 49.5 10⁻⁷ What is the order of reaction with respect to decomposition of XY?

Step-by-step solution

The rate law for the decomposition of XY is given by Rate = k[XY]^ n , where n is the order of the reaction. Using the data from the table: For [XY]₁ = 0.4 mol/L, Rate₁ = 5.5 10⁻⁷ mol/L s. For [XY]₂ = 0.8 mol/L, Rate₂ = 22.0 10⁻⁷ mol/L s. Taking the ratio of the rates: Rate₂ Rate₁ = ( [XY]₂ [XY]₁ )^ n 22.0 10⁻⁷ 5.5 10⁻⁷ = ( 0.8 0.4 )^ n 4 = 2^ n Since 4 = 2² , we have n = 2 . Verifying with the third data point: For [XY]₃ = 1.2 mol/L, Rate₃ = 49.5 10⁻⁷ mol/L s. Rate₃ Rate₁ = ( 1.2 0.4 )² = 3² = 9 . 49.5 10⁻⁷ 5.5 10