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Biology LibreTexts

B2. Multi-Step Reactions

  • Page ID
    5071
  • [ "article:topic", "authorname:jjakubowskih", "license:ccbyncsa" ]

    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)

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