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    Chemical Kinetic Note 03

    Uploaded by

    Nurul Izzanie Adnan
    Here are the steps to solve this problem: 1) The reaction is second order if a plot of 1/[A] vs time is linear. 2) Plot 1/[A] vs time using the data given. This will give a straight line, indicating the reaction is second order. 3) For a second order reaction, the rate law is: Rate = -d[A]/dt = k[A]2 4) Integrate the rate law between time 0 and t: ∫1/[A] dt = ∫ k dt 1/[A]t - 1/[A]0 = kt 5) Plot 1/[A] vs t and determine the slope,

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    Chemical Kinetic Note 03

    Uploaded by

    Nurul Izzanie Adnan
    315 views28 pages
    Here are the steps to solve this problem: 1) The reaction is second order if a plot of 1/[A] vs time is linear. 2) Plot 1/[A] vs time using the data given. This will give a straight line, indicating the reaction is second order. 3) For a second order reaction, the rate law is: Rate = -d[A]/dt = k[A]2 4) Integrate the rate law between time 0 and t: ∫1/[A] dt = ∫ k dt 1/[A]t - 1/[A]0 = kt 5) Plot 1/[A] vs t and determine the slope,

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    Here are the steps to solve this problem: 1) The reaction is second order if a plot of 1/[A] vs time is linear. 2) Plot 1/[A] vs time using the data given. This will give a straight line, indicating the reaction is second order. 3) For a second order reaction, the rate law is: Rate = -d[A]/dt = k[A]2 4) Integrate the rate law between time 0 and t: ∫1/[A] dt = ∫ k dt 1/[A]t - 1/[A]0 = kt 5) Plot 1/[A] vs t and determine the slope,

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    315 views28 pages

    Chemical Kinetic Note 03

    Uploaded by

    Nurul Izzanie Adnan
    Here are the steps to solve this problem: 1) The reaction is second order if a plot of 1/[A] vs time is linear. 2) Plot 1/[A] vs time using the data given. This will give a straight line, indicating the reaction is second order. 3) For a second order reaction, the rate law is: Rate = -d[A]/dt = k[A]2 4) Integrate the rate law between time 0 and t: ∫1/[A] dt = ∫ k dt 1/[A]t - 1/[A]0 = kt 5) Plot 1/[A] vs t and determine the slope,

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 28
    At a glance
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    The document discusses chemical kinetics and rate laws, including zero, first and second order reactions.

    The rate law is rate = k[H2O2][I-], with the reaction being first order with respect to H2O2 and I- and zero order with respect to H+.

    The reaction is first order with respect to H2O2 and I- and zero order with respect to H+.

    CHEMICAL KINETICS

    SSC 2453 CHEMICAL KINETICS AND ELECTROCHEMISTRY

    The concentrations of N2O5 are 1.24e-2 and 0.93e-2 M at 600 and 1200 s after the reactants are mixed at the appropriate temperature. Evaluate the reaction rates for 2 N2O5 4 NO2 + O2

    DIFFERENTIAL RATE LAWS


    Dependence of reaction rate on the concentrations of reactants is called the rate law, which is unique for each reaction. For a general reaction,

    a A + b B + c C products
    order wrt A, B, and C, determined experimentally

    the rate law has the general form reaction rate = k [A]X [B]Y [C]Z the rate constant For example, the rate law is rate = k [Br-] [BrO3-] [H+] for 5 Br- + BrO3- + 6 H+ 3Br2 + 3 H2O

    Use differentials to express rates

    The reaction is 1st order wrt all three reactants, total order 3.
    3

    VARIATION OF REACTION RATES AND ORDER 2nd order, rate = k [A]


    2

    rate First order, rate = k [A] k = rate, 0th order

    [A] = ___?

    [A]

    The variation of reaction rates as functions of concentration for various order is interesting. Mathematical analysis is an important scientific tool, worth noticing.
    4

    DIFFERENTIAL RATE LAW DETERMINATION


    Estimate the orders and rate constant k from the results observed for the reaction? What is the rate when [H2O2] = [I-] = [H+] = 1.0 M? H2O2 + 3 I- + 2 H+ I3- + 2 H2O Exprmt [H2O2] 1 0.010 2 0.020 3 0.010 4 0.010 [I-] 0.010 0.010 0.020 0.010 [H+] 0.0050 0.0050 0.0050 0.0100 Initial rate M s-1 1.15e-6 2.30e-6 2.30e-6 1.15e-6

    Learn the strategy to determine the rate law from this example. Figure out the answer without writing down anything.
    5

    DIFFERENTIAL RATE LAW DETERMINATION


    Estimate the orders from the results observed for the reaction H2O2 + 3 I- + 2 H+ I3- + 2 H2O

    Exprmt [H2O2] 1 0.010 2 0.020 3 0.010 4 0.010

    [I-] 0.010 0.010 0.020 0.010

    [H+] 0.0050 0.0050 0.0050 0.0100

    Initial rate M s-1 1.15e-6 2.30e-6 1 for H2O2 2.30e-6 1 for I1.15e-6 0 for H+

    1.15e-6 = k [H2O2]x [I-]y [H+]z 1.15e-6 k (0.010)x(0.010)y(0.0050)z exprmt 1 ----------- = ------------------------------------2.30e-6 k (0.020)x(0.010)y(0.0050)z exprmt 2 x=1 1 1 ---- = --- x 2 2

    ( )

    DIFFERENTIAL RATE LAW DETERMINATION


    Other orders are determined in a similar way as shown before. Now, lets find k and the rate

    Thurs, rate = 1.15e-6 = k (0.010)(0.010) from exprmt 1


    k = 1.15e-6 M s-1 / (0.010)(0.010) M3 = 0.0115 M-1 s-1 And the rate law is therefore,

    d [H2O2] k rate == 0.0115 [H2O2] [I-] a differential rate law dt total order 2
    The rate when [H2O2] = [I-] = [H+] = 1.0 M: The rate is the same as the rate constant k, when concentrations of reactants are all unity (exactly 1), doesnt matter what the orders are.

    DIFFERENTIAL RATE LAW DETERMINATION

    The reaction rate d[H2O2]/dt = 0.0115 [H2O2] [I], for H2O2 + 3 I- + 2 H+ I3- + 2 H2O What is d[I]/dt when [H2O2] = [I] = 0.5?

    Note the reaction rate expression and the 15 Chemical Kinetics of equation. stoichiometry

    DIFFERENTIAL RATE LAW DETERMINATION

    The reaction rate d[H2O2]/dt = 0.0115 [H2O2] [I], for H2O2 + 3 I- + 2 H+ I3- + 2 H2O What is d[I]/dt when [H2O2] = [I] = 0.5? Solution: Please note the stoichiometry of equation and how the rate changes. d[I]/dt = 3 d[H2O2]/dt = 3* 0.0115 [H2O2] [I] = 0.0345 * 0.5 * 0.5 = 0.0086 M s-1 In order to get a unique rate constant k, we evaluate k for the reaction a A + b B product this way rate = -1/a d[A]/dt = -1/b d[B]/dt = k [A]x [B]y

    Note the reaction rate expression and the 15 Chemical Kinetics of equation. stoichiometry

    DIFFERENTIAL RATE LAW DETERMINATION


    From the following reaction rates observed in 4 experiments, derive the rate law for the reaction A + B + C products where reaction rates are measured as soon as the reactants are mixed. Expt [A]o [B]o [C]o rate 1 0.100 0.100 0.100 0.100 2 0.200 0.100 0.100 0.800 3 0.200 0.300 0.100 7.200 4 0.100 0.100 0.400 0.400

    This example illustrates the strategy to determine, and a reliable method to solve rate-law experimentally.

    10

    DIFFERENTIAL RATE LAW DETERMINATION


    From the following reaction rates, derive the rate law for the reaction A + B + C products where reaction rates are measured as soon as the reactants are mixed.

    Expt [A]o [B]o [C]o rate

    1 0.100 0.100 0.100 0.100

    2 0.200 0.100 0.100 0.800

    3 0.200 0.300 0.100 7.200

    4 0.100 0.100 0.400 0.400

    order 3 from expt 1 & 2 2 expt 1, 2 & 3 1 expt 1 & 4

    Assume rate = k [A]x[B]y[C]z Therefore 8 = 2x log 8 = x log 2 x = log 8 / log 2 =3 0.800 k 0.2x 0.1y 0.1z ----- = ---------------------0.100 k 0.1x 0.1y 0.1z

    11

    CONCENTRATIONS AS FUNCTIONS OF TIME


    One reactant A decomposes in 1st or 2nd order rate law.
    Differential rate law d[A] / dt = k Integrated rate law [A] = [A]o k t [A] = [A]o e k t or ln [A] = ln [A]o k t 1 1 = k t [A] [A]o [A] conc at t [A]o conc at t = 0
    12

    INTEGRATED RATE LAWS

    d[A] = k [A] dt
    d[A] = k [A]2 dt

    Describe, derive and apply the integrated rate laws Learn the strategy to determine rate-law 15 Chemical Kinetics

    CONCENTRATION AND TIME OF 1ST ORDER REACTION


    Describe the features of plot of [A] vs. t and ln[A] vs. t for 1st order reactions. Apply the technique to evaluate k or [A] at various times.
    ln[A ] [A] = [A]o e k t ln [A] = ln [A]o k t

    [A]

    t
    13

    HALF LIFE & K OF FIRST ORDER DECOMPOSITION


    The time required for half of A to decompose is called half life t1/2. Since = ln [A]o k t When [A] = [A]o e k t t = t1/2, [A] = [A]o or ln [A]

    Thus

    ln [A]o = ln [A]o k t1/2


    ln 2 = k t1/2 k t1/2 = ln 2 = 0.693
    relationship between k

    and t1/2

    Radioactive decay usually follow 1st order kinetics, and half life of an isotope is used to indicate its stability.
    Evaluate t from k or k from t
    14

    1ST ORDER REACTION CALCULATION


    N2O5 decomposes according to 1st order kinetics, and 10% of it decomposed in 30 s. Estimate k, t and percent decomposed in 500 s.

    If the rate-law is known, what are the key parameters?

    Solution next
    15

    1ST ORDER REACTION CALCULATION


    N2O5 decomposes according to 1st order kinetics, and 10% of it decomposed in 30 s. Estimate k, t and percent decomposed in 500 s. Solution: Assume [A]o = [N2O5]o = 1.0, then [A] = 0.9 at t = 30 s or 0.9 = 1.0 e k t apply [A]o = [A] e k t ln 0.9 = ln 1.0 k 30 s 0.1054 = 0 k * 30 k = 0.00351 s 1 t = 0.693 / k = 197 s apply k t = ln 2 [A] = 1.0 e 0.00351*500 = 0.173 Percent decomposed: 1.0 0.173 = 0.827 or 82.7 %
    After 2 t (2*197=394 s), [A] = ()2 =, 75% decomposed. After 3 t (3*197=591 s), [A] = ()3 =1/8, 87.5% decomposed.
    Apply integrated15 Chemical Kinetics rate law to solve problems
    16

    TYPICAL PROBLEM : 1ST ORDER REACTION


    The decomposition of A is first order, and [A] is monitored. The following data are recorded: t / min 0 [A]/[M] 0.100 2 0.0905 4 0.0819 8 0.0670

    Calculate k (What is the rate constant? Calculate the half life (What is the half life? Calculate [A] when t = 5 min. Calculate t when [A] = 0.0100. (Estimate the time required for 90% of A to decompose.)
    Work out all the answers
    17

    TYPICAL PROBLEM WRT 1ST ORDER REACTION


    The decomposition of A is first order, and [A] is monitored. The following data are recorded: t / min 0 [A]/[M] 0.100 2 0.0905 4 0.0819 8 0.0670

    Calculate k (What is the rate constant? k = 0.0499) Calculate the half life (What is the half life? Half life = 13.89) Calculate [A] when t = 5 min. (What is the concentration when t = 5 min?) Calculate t when [A] = 0.0100.

    Work out all the answers


    18

    A 2ND ORDER EXAMPLE


    Dimerization of butadiene is second order:
    2 C4H6(g) C8H12(g). The rate constant k at some temperature is 0.100 /min. The initial concentration of butadiene [B] is 2.0 M.

    Calculate the time required for [B] = 1.0 and 0.5 M


    Calculate concentration of butadiene when t = 1, 5, 10, and 30.

    If the rate-law is known, what are the key parameters?


    Apply the right model and work out all the parameters. Solution next
    19

    A 2ND ORDER EXAMPLE


    Dimerization of butadiene is second order: 2 C4H6(g) = C8H12(g). The rate constant k at some temperature is 0.100 /min. The initial concentration of butadiene [B] is 2.0 M. Calculate the time t required for [B] = 1.0 and 0.5 M Calculate concentration of butadiene when t = 1, 5, 10, and 30.

    1 1 [B] [B]o

    =kt

    1 1 [B] [B]o t = k [B]o [B] = [B]o k t + 1

    t=
    Work out the formulas and then evaluate values

    10

    15

    30
    0.29

    35
    0.25
    20

    [B] = 1.67 1.0 0.67 0.50

    HALF LIFE OF 2ND ORDER CHEMICAL KINETICS


    4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

    1/[B]

    t=

    10

    15

    30
    0.29

    35
    0.25
    21

    [B] = 1.67 1.0 0.67 0.50

    How does half life vary in 2nd orderChemical Kinetics reactions? 15

    PLOT OF [B] VS. T & 1/[B] VS. T FOR 2ND ORDER REACTIONS
    t=
    [B]

    1
    [B]

    10

    15

    30 0.29

    35 0.25

    [B] = 1.67 1.0 0.67 0.50 1 [B]o [B] = [B]o k t + 1

    1 [B]

    1 = k t [B]o

    t
    22

    What kind of plot is linear for 1st and 2nd reactions? 15 Chemical Kinetics

    EXERCISES

    The decomposition of N2O5 is an important process in tropospheric chemistry. The half-life for the first order decomposition of this compound is 2.05 x 104 s.
    How long will it take for a sample of N2O5 to decay to 60% of its initial value?

    EXERCISES

    Carbon-14 is a radioactive nucleus with a half-life of 5760 years. Living matter exchanges carbon with its surroundings (for example, through CO2) so that a constant level of 14C is maintained, corresponding to 15.3 decay events per minute. Once living matter has died, carbon contained in the matter is not exchanged with the surroundings, and the amount of 14C that remains in the dead material decreases with time due to radioactive decay. Consider a piece of fossilized wood that demonstrates 2.4 14C decay per minute. How old is the wood?

    EXERCISES

    Consider the experiment where the concentration of products are given in the following table: Time (minutes): 0 4 6 10 15 20 (a-x) (M): 8.04 5.30 4.58 3.50 2.74 2.22 (i) Prove that the reaction is second order (ii) Determine the rate constant
    Assume (a-x) = [A]t

    EXERCISES

    Consider the dimerization reaction: 2C4H6(g) C8H12(g) The concentration of C4H6 at time intervals, t was determined as follows: [C4H6] (M) Time (s) 0.01000 0 0.00625 1000 0.00476 1800 0.00370 2800 0.00313 3600 0.00270 4400 0.00241 5200 0.00208 6200 (i) Using graphical method, determine the order of the reaction (ii) What is the value of the rate constant? (iii) What is the half-life of the reaction?

    METHOD OF INITIAL RATES


    Establishing the Order of a reaction by the Method of Initial Rates. Use the data provided establish the order of the reaction with respect to HgCl2 and C2O22- and also the overall order of the reaction

    Notice that concentration changes between reactions are by a factor of 2. Write and take ratios of rate laws taking this into account.

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