# Lecture 30: Fast and Slow Steps to Reactions and Catalysts

### Reactions Where First Reaction is Fast and Second Slow

Example 1

﻿$2H_{2(g)}+2NO_{(g)}\rightarrow 2H_{2}O_{(g)}+N_{2(g)}$﻿

1. ﻿$2NO_{(g)}\rightleftharpoons N_{2}O_{2(g)}$﻿ (Fast)
2. ﻿$H_{2(g)}+N_{2}O_{2(g)}\rightarrow H_{2}O_{(g)}+N_{2}O_{(g)}$﻿ (Slow) ﻿$K_{2}\left [ H_{2} \right ]\left [ N_{2}O_{2} \right ]$﻿ (Intermediate)
3. ﻿$H_{2(G)}+N_{2}O_{2(g)}\rightarrow H_{2}O_{(g)}+N_{2(g)}$﻿ (Fast)

﻿$2H_{2(g)}+2NO_{(g)}\rightarrow 2H_{2}O_{(g)}+N_{2}$﻿

For Step 1 Rate﻿$_{Forward}$﻿ = Rate﻿$_{reverse}$﻿

﻿$K_{1}\left [ NO \right ]^{2}=K_{-1}\left [ N_{2}O_{2} \right ]$﻿

﻿$\left [N_{2}O_{2} \right ]=\frac{K_{1}}{K_{-1}}\left [ NO \right ]^{2}$﻿

﻿$Rate_{ons}= K\left [ H_{2} \right ]\left [ NO \right ]^{2}$﻿

﻿$Rate= K_{2}\left [ H_{2} \right ]\left [ N_{2}O_{2} \right ]$﻿

﻿$Rate=K_{2}\left [ H_{2} \right ]\frac{K_{1}}{K_{-1}}\left [ NO \right ]^{2}$﻿

﻿$Rate=\frac{K_{2}K_{1}}{K_{-1}}\left [ H_{2} \right ]\left [ NO \right ]^{2}$﻿

First Reaction is at equilibrium so Rate of K﻿$_{1}$﻿ = Rate of K﻿$_{-1}$﻿

#### Why is First Reaction Assumed to be reversible and at Equilibrium?

Goes back and forth because the second step is slow

Example 2

﻿$NO_{(g)}+Br_{2(g)}\rightarrow NOBr_{2(g)}$﻿ (Very Fast)

﻿$NOBr_{2(g)}+ NO_{(g)}\rightarrow 2NOBr_{(g)}$﻿ (Very Slow)

﻿$NO_{(g)}+Br_{2(g)}+NO_{(g)}\rightarrow 2NOBr_{(g)}$﻿

﻿$2NO_{(g)}+Br_{2(g)}\rightarrow 2NOBr_{(g)}$﻿

﻿$K_{1}\left [ NO \right ]\left [ Br_{2} \right ]=K_{-1}\left [ NOBr_{2} \right ]\Rightarrow \left [ NOBr_{2} \right ]=\frac{K_{1}}{K_{2}}\left [ NO \right ]\left [ Br_{2} \right ]$﻿

Step 2 (slow) Rate = ﻿$K_{2}\left [ NOBr_{2} \right ]\left [ NO \right ]$﻿

﻿$Rate = \frac{K_{1}K_{2}}{K_{-1}}\left [ NO \right ]\left [ Br_{2} \right ]\left [ NO \right ]$﻿

﻿$Rate = K \left [ NO \right ]^{2} \left [ Br_{2} \right ]$﻿

### Catalysts

• Speed up a reaction
• Give the reaction an alternative mechanism for the reaction (with a lower activation energy)

Heterogeneous Catalysts - hold one reactant molecule in proper orientation for reaction to occur when the collision takes place (and sometimes also help to start breaking bonds). Catalysts and reactant are in the same phase.

Homogeneous Catalysts - reacts with one of the reactant molecules to form a more stable activated complex with a lower activation energy. Catalyst in a different phase.

The proton is the most pervasive homogeneous catalyst because water is the most common solvent. Water forms protons by the process of self-ionization of water. In an illustrative case, acid accelerate (catalyst) the hydrolysis of ester.

Heterogeneous

Absorption ﻿$\rightarrow$﻿ Diffusion ﻿$\rightarrow$﻿ reaction ﻿$\rightarrow$﻿ Desorption.

﻿$H_{2}C= CH_{2}+H_{2}\rightarrow CH_{3}CH_{3}$﻿ (Addition reaction)