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الموضوع: Second Order Reaction Second Order Reaction

  1. #1
    عضو ذهبي الصورة الرمزية اسراء
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    Aug 2011
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    افتراضي Second Order Reaction Second Order Reaction

    Second Order Reaction

    The rate of a second order reaction is proportional to either the concentration of a reactant squared, or the product of concentrations of two reactants.

    For the general case of a reaction between A and B, such that



    the rate of reaction will be given by
    1. Initial concentrations of the two reactants are equal:

    Equation (1) can be written as:Separating the variables and integrating


    gives
    Provided that [ A ] = [ A ] o at t = 0, the constant of integration C becomes equal to 1 / [ A ] o.

    Thus the second order integrated rate equation is


    A plot of 1 / [ A ] vs t produces a straight line with slope k and intercept 1 / [ A ]o. The plot should be linear up to a conversion of about 50 %.


    2. Starting concentrations of the two reactants are different:


    If [ A ] o and [ B ] o are different the variable x is used.

    Noting that d[ A ] = - dx, the general rate equation (1) can be expressed by


    where [ A ] o - x = [ A ], [ B ] o - x = [ B ] and x is the decrease in the concentration of A and B respectively.

    In order to integrate the left-hand side of equation (6), it is necessary to perform a partial fraction expansion. The fraction on the left hand-side of equation below is splitted into a sum of simple fractions on the right hand-side.


    c' and c'' are two constants. Putting them back over a common denominator



    leads to

    Provided that - x (c' + c'') = 0

    The equations above allow to determine the factors c' and c'':



    Using c', c'' notation equation (6) becomes the form


    whose integration

    results in

    where C is the constant of integration.

    Using the condition that x = 0, when t = 0, the value of C can be found:



    and equation (15) becomes
    If [ A ] o > [ B ] o, then a plot of

    against t will have a positive slope, equal ([ A ] o - [ B ] o) · k.

    Because equivalent amounts of A and B are reacting, [ A ] can be expressed in terms of [ B ]:

    If the experimental method yields reactant concentrations rather than x, the equivalent form of equation (17) is




    The rate constant can be determined using equation (20), provided that the initial concentration of A is twice the initial concentration of B (see Kinetic equations - Reaction Second Order - Download PDF file):


    where xo = [ B ] o and x = [ B ] .

    Summary
    Reaction Order Differential Rate Law Integrated Rate Law Linear Plot Slope of
    Linear Plot
    Units of
    Rate Constant
    0 - d [A] / dt = k [ A ] = [ A ] o - kt [ A ] versus t - k mol · L -1 · s -1
    1 - d [ A ] / dt = k [ A ] [ A ] = [ A ] o · e - kt ln [ A ] versus t - k s -1
    2 - d [ A ] / dt = k [A] 2 1 / [ A ] = 1 / [ A ] o + kt 1 / [ A ] versus t k L · mol -1 · s -1

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  2. #2
    مراقب عام الصورة الرمزية Eiman
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    افتراضي رد: Second Order Reaction Second Order Reaction

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  3. #3
    عضو ذهبي الصورة الرمزية Raed
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    افتراضي رد: Second Order Reaction Second Order Reaction

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  4. #4
    مشرفة الاقسام الاكاديمية الصورة الرمزية تمارا احمد
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    افتراضي رد: Second Order Reaction Second Order Reaction

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  5. #5
    عضو مميز الصورة الرمزية قمر بلحاج
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    افتراضي رد: Second Order Reaction Second Order Reaction

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