The decomposition of nitrous oxide, 2 N ₂ O (g) 2 N ₂(g) + O ₂(g) , follows zero-order kinetics. If the initial concentration of N ₂ O is 0.5 M and the rate constant k is 1.25 10⁻³ M s ⁻¹ , what is the exact time taken for the reaction to reach 100 % completion?

Step-by-step solution

For the zero-order reaction 2 N ₂ O 2 N ₂ + O ₂ , the rate of reaction is expressed as: Rate = - 1 2 d[ N ₂ O ] dt = k - d[ N ₂ O ] dt = 2k The integrated rate law is: [ N ₂ O ]₀ - [ N ₂ O ]_t = 2kt For 100 % completion, the final concentration of the reactant is zero ( [ N ₂ O ]_t = 0 ). Substituting the given values ( [ N ₂ O ]₀ = 0.5 M, k = 1.25 10⁻³ M s ⁻¹ ): 0.5 - 0 = 2 (1.25 10⁻³) t 0.5 = 2.5 10⁻³ t t = 0.5 2.5 10⁻³ = 500 2.5 = 200 s Omitting the stoichiometric factor of 2 in the rate equation leads to the in