Chapter 12, Problem 30E

The annual production of HNO₃ in 2013 was 60 million metric tons Most of that was prepared by the following sequence of reactions, each run in a separate reaction vessel.

(a) $4{\text{NH}}_3\left(g\right)+5{\text{O}}_2\left(g\right)\to 4\text{NO}\left(g\right)+6{\text{H}}_2\text{O}\left(g\right)$

(b) $2\text{NO}\left(g\right)+{\text{O}}_2\left(g\right)\to 2{\text{NO}}_2\left(g\right)$

(C) $3{\text{NO}}_2\left(g\right)+{\text{H}}_2\text{O}\left(l\right)\to 2{\text{HNO}}_3\left(aq\right)+\text{NO}\left(g\right)$

The first reaction is run by burning ammonia in air over a platinum catalyst. This reaction is fast. The reaction in equation (c) is also fast. The second reaction limits the rate at which nitric acid can be prepared from ammonia. If equation (b) is second order in NO and first order in O₂, what is the rate of formation of NO₂ when the oxygen concentration is 0.50 M and the nitric oxide concentration is 0.75 M? The rate constant for the reaction is $5.8\times {10}^{-6}$ L²/mol²/s.