Question

The mechanism for the reaction of carbon monoxide with nitrogen dioxide is given bellow
$2{NO}_2\left(g\right)\to {NO}_3\left(g\right)+NO\left(g\right)\left(slow\right)$
${NO}_3\left(g\right)+CO\left(g\right)\to {NO}_2\left(g\right)+{CO}_2\left(g\right)\left(fast\right)$
Which of the following could be the rate law for this reaction?

• A. Rate = $k\left[{NO}_2\right]$
• B. Rate = ${k\left[{NO}_2\right]}^2$
• C. Rate = $k\left[{NO}_3\right]\left[CO\right]$
• D. Rate = $k\left[{NO}_3\right]\left[CO\right]{\left[{NO}_2\right]}^2$
• E. Rate = $k\left[NO\right]\left[{NO}_3\right]/{\left[{NO}_2\right]}^2$

Answer 1

The correct option is B Rate = ${k\left[{NO}_2\right]}^2$

The following could be the rate law for this reaction,
$Rate={k\left[{NO}_2\right]}^2$
It is based on the slow step of the reaction which is,
$2{NO}_2\left(g\right)\to {NO}_3\left(g\right)+NO\left(g\right)\left(slow\right)$
It involves 2 molecules of ${NO}_2$, hence, it is of second order in ${NO}_2$.
Hence, in the rate law for this reaction, the concentration of ${NO}_2$ is raised to power 2.