For the reaction 2 ~N ₂ O ₅ 4 NO ₂+ O ₂ , rate constant k is 4.48 10⁻⁵ ~s ⁻¹ and the initial pressure is 600 ~atm . After 10 ~min , determine the final pressure of N ₂ O ₅ .

Step-by-step solution

The reaction is 2 N ₂ O ₅ 4 NO ₂ + O ₂ . Since the rate constant k has units of s ⁻¹ , the reaction is a first-order reaction. The integrated rate law for a first-order reaction is given by P_ t = P₀ e^ -kt , where P_ t is the pressure of the reactant at time t , P₀ is the initial pressure, k is the rate constant, and t is the time. Given values are P₀ = 600 ~atm , k = 4.48 10⁻⁵ ~s ⁻¹ , and t = 10 ~min = 600 ~s . Substituting these values into the equation: P_ t = 600 e^ -(4.48 10⁻⁵ ~s ⁻¹) (600 ~s ) P_ t = 600 e^ -