Question

How will each of the following affect the rate of the reaction:

\({\bf{CO}}\left( {\bf{g}} \right){\bf{ + \;N}}{{\bf{O}}_{\bf{2}}}\left( {\bf{g}} \right) \to {{\bf{O}}_{\bf{2}}}{\bf{\;}}\left( {\bf{g}} \right){\bf{ + NO}}\left( {\bf{g}} \right)\) if the rate law for the reaction is rate = \({\bf{k(NO}}{}_{\bf{2}}{\bf{)(CO)}}\)?

1. Increasing the pressure of \({\bf{NO}}{}_{\bf{2}}\) from 0.1 atm to 0.3 atm
2. Increasing the concentration of CO from 0.02 M to 0.06 M.

Short answer

1. Increasing the pressure of \({\bf{NO}}{}_{\bf{2}}\) from 0.1 atm to 0.3 atm, the rate of reaction increases by factor 3
2. Increasing the concentration of CO from 0.02 M to 0.06 M the rate of reaction increases by factor 3

Step-by-step solution

Rate law 

The rate law for a chemical reaction is an expression that provides a relationship between the rate of the reaction and the concentration of the reactants participating in it.

General rate law for the given reaction is represented as follow

\({\bf{rate = k}}\,{\bf{(N}}{{\bf{O}}_{\bf{2}}}{\bf{)}}\,{\bf{(CO)}}\)

Effect of increasing pressure

The rate of reaction at0.02M concentrationofCOand pressure of NO₂ is represented as

\({\bf{rat}}{{\bf{e}}_{\bf{1}}}{\bf{ = k}}\,{\bf{(}}\,{\bf{0}}{\bf{.1}}\,\,{\bf{atm}}\,{\bf{)}}\,{\bf{(}}\,{\bf{0}}{\bf{.02}}\,{\bf{M}}\,{\bf{)}}\)

When the concentration ofCOis 0.02Mand pressure of NO₂ increases from 0.1 atm to 0.3atm, the rate of reaction becomes

\({\bf{rat}}{{\bf{e}}_{\bf{2}}}{\bf{ = k}}\,{\bf{(}}\,{\bf{0}}{\bf{.3}}\,{\bf{atm}}\,{\bf{)}}\,{\bf{(}}\,{\bf{0}}{\bf{.02}}\,{\bf{M}}\,{\bf{)}}\)

Rate of reaction after increasing pressure of NO₂ is calculated as

\(\begin{aligned}{}\frac{{{\bf{rat}}{{\bf{e}}_{\bf{2}}}}}{{{\bf{rat}}{{\bf{e}}_{\bf{1}}}}}{\bf{ = }}\frac{{{\bf{k}}\,{\bf{(}}\,{\bf{NO}}{}_{\bf{2}}{\bf{)}}\,{\bf{(}}\,{\bf{CO}}\,{\bf{)}}}}{{{\bf{k}}\,{\bf{(}}\,{\bf{NO}}{}_{\bf{2}}{\bf{)}}\,{\bf{(}}\,{\bf{CO}}\,{\bf{)}}}}\\\;\;\;\;\;\;\;\;\;\;\;\;\;{\bf{ = }}\frac{{{\bf{k}}\,{\bf{(}}\,{\bf{0}}{\bf{.3}}\,{\bf{atm}}\,{\bf{)}}\,{\bf{(}}\,{\bf{0}}{\bf{.02}}\,{\bf{M}}\,{\bf{)}}}}{{{\bf{k}}\,{\bf{(}}\,{\bf{0}}{\bf{.1}}\,{\bf{atm}}\,{\bf{)}}\,{\bf{(}}\,{\bf{0}}{\bf{.02}}\,{\bf{M}}\,{\bf{)}}}}\\{\bf{ = 3}}\end{aligned}\)

After increasing pressure of \({\bf{NO}}{}_{\bf{2}}\), the rate of reaction increases by factor 3.

Effect of CO concentration  

The rate of reaction at 0.02M concentration of COand 0.1atm pressure of NO₂ is represented as

\({\bf{rat}}{{\bf{e}}_{\bf{1}}}{\bf{ = k}}\,{\bf{(0}}{\bf{.1atm)}}\,\,{\bf{(0}}{\bf{.02}}\,{\bf{M)}}\)

When the concentration ofCOincreases from0.02M to 0.06M and pressure isNO₂ remains 0.1atm. the rate of reaction becomes

\({\bf{rat}}{{\bf{e}}_{\bf{2}}}{\bf{ = k(0}}{\bf{.1atm)(0}}{\bf{.06M)}}\)

The rate of reaction after increasing concentration can be calculated as

\(\begin{aligned}{}\frac{{{\bf{rat}}{{\bf{e}}_{\bf{2}}}}}{{{\bf{rat}}{{\bf{e}}_{\bf{1}}}}}{\bf{ = }}\frac{{{\bf{k(0}}{\bf{.1atm)(0}}{\bf{.06M)}}}}{{{\bf{k(0}}{\bf{.1atm)(0}}{\bf{.02M)}}}}\\{\bf{ = 3}}\end{aligned}\)

After increasing concentration, the rate of reaction changes by factor 3.