The decomposition of O ₃(g) follows first order kinetics and is given by O ₃(9) O ₂(9)+ O (9) The rate constant for this reaction is 1.0 10⁻³ ~s ⁻¹ . The initial pressure of O ₃(g) is 100 ~atm . What will be the partial pressure (in atm) of O ₃, O ₂, O respectively after 38.38 minutes?

Step-by-step solution

Decomposition of O ₃ , O ₃(g) O ₂(g)+ O (g) Initial pressure 100 ~atm 0 0 Partial pressure 100-x x x after 38.38 ~m in aligned p_i( initial pressure ) & =100 ~atm .p_f (final pressure ) & after 38.38 ~m . & =100-x aligned From first order reaction, Given, k=1 10⁻³ ~s ⁻¹, t=38.38 ~m . aligned k & = 2.303 t p_i p_f 1 10⁻³ ~s ⁻¹ & = 2.303 38.38 60 100( ~atm ) 100-x( ~atm ) 100 100-x & = 1 10⁻³ ~s ⁻¹ 38.38 60 2.303 aligned x=90 ~atm Pressure of O ₃ after 38.38 ~m . p o ₃=p_f=100-x=100-90 ~atm =10 ~atm Pressure of O ₂(g