B2. Multi-Step Reactions
- Page ID
- 5071
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
Reversible First Order Reactions
\[ A \underset{k_2} {\overset{k_1}{\rightleftharpoons}} P \]
A differential equation can be written for this reaction:
\[ v = \dfrac{d[A]}{dt} = -k_1[A] + k_2[P] \label{7}\]
This can be solved through integration to give the following equations:
Graphs of A and P vs t for this reaction at two different sets of values of k1 and k2 are shown below.
Figure: Reversible First Order Reactions: A <=> P
Xcel Spread Sheet: Reversible First Order Reactions -
Go to the following spread sheet and change the values of k1 and k2. Note the changes in the graphs. Remember from our discussion of macromolecule:ligand binding, the dissociation constant, Kd, was related to the rate constants by the formula Kd = k2/k1. Note that if the first order rate constants for a reversible chemical reaction are equal, Keq (and its inverse) equal 1, and the equilibrium concentrations of A and P are equal.
4/26/13Wolfram Mathematica CDF Player - Reversible First Order Reactions ([A] blue, [B] red) (free plugin required)
Consecutive First Order Reactions
For these reactions:
Graphs of A, B, and C vs t for these reaction at two different sets of values of k1 and k2 are shown below.
Figure: Consecutive Irreversible First Order Reactions: A --> B --> C
Xcel Spread Sheet: Consecutive Reactions -
Change the values of k1 and k2. Note the changes in the graphs.
4/26/13Wolfram Mathematica CDF Player - Irreversible Consecutive First Order Reactions ([A] blue, [B] red, [C] orange (free plugin required)
Reaction Appliets:
- Reactions Kinetics: Java Applet - Zero, First, and Second Order Reactions
- Consecutive reactions
- Graphical determination of reaction order from initial rates