During a chemical reaction X Y , the rates of reaction starting with initial concentrations of X as 4.0 10⁻³ M and 2.0 10⁻³ M are 4.8 10⁻⁴ ~mol ~L ⁻¹ / s and 1.2 10⁻⁴ ~mol ~L ⁻¹ / s respectively. What is the order of reaction with respect to X ?

Step-by-step solution

The rate law for the reaction X Y is given by r = k[X]^ n , where n is the order of the reaction. For the first condition: 4.8 10⁻⁴ = k(4.0 10⁻³)^ n (Equation 1) For the second condition: 1.2 10⁻⁴ = k(2.0 10⁻³)^ n (Equation 2) Dividing Equation 1 by Equation 2: 4.8 10⁻⁴ 1.2 10⁻⁴ = k(4.0 10⁻³)^ n k(2.0 10⁻³)^ n 4 = ( 4.0 10⁻³ 2.0 10⁻³ )^ n 4 = (2)^ n Since 4 = 2² , we have n = 2 . Answer: 2