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Understanding Reaction Rates: A Comprehensive Analysis of Kinetics

This document delves into the concept of reaction rates in chemical kinetics. It explains how reactants transform into products over time, emphasizing the importance of calculating the rate of reaction. By using differential rate laws and experimental data, we determine the reaction order and rate constant. The document includes examples, including a case study of phenolphthalein's reaction in a basic environment, and guides the reader on graphing concentration against time to derive rate constants. Through practical examples, the order of reactants is explored, illustrating how concentration changes affect reaction rates.

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Understanding Reaction Rates: A Comprehensive Analysis of Kinetics

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  1. Kinetics • Until now, we have considered that reactions occur: Reactants form products and conservation of mass is used to find amounts of these • Now, we investigate how fast products are formed (or how fast reactants disappear): THE RATE of REACTION • We will use differential rate laws to determine order of reaction and rate constant from experimental data 

  2. Rate of Reaction • Rate = Δ[concentration] or d [product] Δ time dt • Rate of appearance of a product = rate of disappearance of a reactant • Rate of change for any species is inversely proportional to its coefficient in a balanced equation.

  3. Rate of Reaction • Assumes nonreversible forward reaction • Rate of change for any species is inversely proportional to its coefficient in a balanced equation. • 2N2O5 4NO2 + O2 • Rate of reaction = -Δ[N2O5] = Δ[NO2] = Δ[O2] 2 Δt 4 Δt Δt where [x] is concentration of x (M) and t is time (s)

  4. Reaction of phenolphthalein in excess base • Use the data in the table to calculate the rate at which phenolphthalein reacts with the OH- ion during each of the following periods: • (a) During the first time interval, when the phenolphthalein concentration falls from 0.0050 M to 0.0045 M. • (b) During the second interval, when the concentration falls from 0.0045 M to 0.0040 M. • (c) During the third interval, when the concentration falls from 0.0040 M to 0.0035 M.

  5. Reactant Concentration by Time

  6. Finding k given time and concentration • Create a graph with time on x-axis. • Plot each vs. time to determine the graph that gives the best line: • [A] • ln[A] • 1/[A] • (Use LinReg and find the r value closest to 1) • k is detemined by the slope of best line (“a” in the linear regression equation on TI-83) • 1st order (ln[A] vs. t): k is –slope • 2nd order (1/[A] vs t: k is slope)

  7. Rate Law Expression • As concentrations of reactants change at constant temperature, the rate of reaction changes. According to this expression. Rate = k[A]x[B]y… • Where k is an experimentally determined rate constant, [ ] is concentration of product and x and y are orders related to the concentration of A and B, respectively. These are determined by looking at measured rate values to determine the order of the reaction.

  8. same 2x 2x Finding Order of a Reactant - Example2ClO2 + 2OH- ClO3- + ClO2- + H2O • Start with a table of experimental values: • To find effect of [OH-] compare change in rate to change in concentration. • When [OH-] doubles, rate doubles. Order is the power: 2x = 2. x is 1. This is 1st order for [OH-].

  9. 9x Finding Order of a Reactant - Example2ClO2 + 2OH- ClO3- + ClO2- + H2O • Start with a table of experimental values: • To find effect of [ClO2] compare change in rate to change in concentration. • When [ClO2] triples, rate increases 9 times. Order is the power: 3y = 9. y is 2. This is 2nd order for [ClO2]. same 3x

  10. Finding Order of a Reactant - Example2ClO2 + 2OH- ClO3- + ClO2- + H2O • Can use algebraic method instead. This is useful when there are not constant concentrations of one or more reactants. This example assumes you found that reaction is first order for [OH-] . 6.00 x 10-4=k(0.010)x(.030)1 1.08 x 10-2 = k (0.030)x(.060)1 0.0556 = .333x(.5) For [ClO2]x , x = 2

  11. Rate Law:2ClO2 + 2OH- ClO3- + ClO2- + H2O Rate = k[ClO2]2[OH-] To find k, substitute in any one set of experimental data from the table. For example, using the first row: k = rate/[ClO2]2[OH-] k = 6.00x10-4Ms-1 = 200 M-2s-1 [0.010M]2[0.030M] Overall reaction order is 2+1=3. Note units of k.

  12. Determining units for k given overall reaction order Rate(M/s) = k[A]x x = overall order of reaction [A] = the reactant concentration (M)

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