C16 - Kinetics II

Reaction rate

• Measures the speed of a chemical change

  • How quickly reactants are used up or products are formed

  • Is defined as the change in amount of reactants or products per unit time

• Mol dm^-3 s^-1

Measuring gas volume

• If gas is produced, it can be collected in a gas syringe

• Record the volume of gas at regular intervals

• Convert gas volume to moles using ideal gas equation

• Determine reactant concentration using stoichiometry

Measuring mass change

• If gas is released, reaction system will lose mass

• Measure the mass at regular intervals using a balance

• Calculate moles of gas lost and remaining reactant concentration using mole calculations

Tracking colour change

• Colorimeter measures the absorbance of solution

• More concentrated coloured solution have higher absorbance

• Create a calibration curve by plotting conc against absorbance

• During reaction, measure absorbance of samples at regular intervals

• Use calibration curve

Monitoring pH changes

• If H+ ions are produced or consumed, the pH of the solution will change

• Measure pH at regular intervals and calculate [H+]

  • pH = -log[H+]

Performing titrations

• Take small samples of the reaction mixture at regular intervals

• Titrate each sample with a standard solution

• Calculate reactant or product concentration from titration data

Measuring electrical conductivity

• Changes in the number of ions in solution affect electrical conductivity

• Measure conductivity at regular intervals

Rate equations

• Relate reaction rate to reactant concentration

• For general reaction A + B ---> C + D

  • Rate reaction is k[A]^m[B]ⁿ

  • Rate is in Mol dm^-3 s^-1

  • K is rate constant

  • [A] and [B] are concentrations of reactants A and B (Mol dm^-3)

  • M and n are the orders of reaction with respect to A and B

Reaction orders

• Values of m and n are reaction orders with respect to each reactant

Zero, first and second order

• Zero order

  • M or n = 0

  • Rate is independent of the reactant concentration

  • Doubling or tripling the concentration has no effect on the rate

• First order

  • M or n = 1

  • Rate is directly proportional to the reactant concentration

• Second order

  • M or n = 2

  • Rate is proportional to the square of reactant concentration

  • Doubling the conc. Quadruples the rate

• Overall order of reaction is the sum of m and n

  • Do NOT come from balanced chemical equations

Rate constant

• Relates rate of reaction to concentration at specific temperature

• Larger value of k

  • Faster rate of reaction

• Constant value of k

  • Fixed temperature

• Increasing temperature exponentially

  • Increases the value of k

  • Collisions between reactant molecules are more frequent and more energetic

• Units

  • Depend on the overall order of the reaction

Rate-conc graphs

• Can reveal the reaction order with respect to a particular reactants

• Graph

  • Begin with a concentration-time graph for the reactant of interest

  • Calculate the rate (gradient) at various points along curve

  • Plot the rate y-axis against concentration

  • Fit a smooth curve or line through data points

  • 
    

Rate-conc graphs - orders

• Zero order

  • Rate = k

  • Horizontal line shows rate is independent of reactant concentration

• First order

  • Rate = k[X]

  • Straight line passes through origin signifies that the reaction rate is directly proportional to the reactant concentration

• Second order

  • Rate = k[X]²

  • Curved plot indicates that it is proportional to the square

Half-life in first order reaction

• Half life is time taken for concentration of a reactant to decrease to half of its initial value

• First order reactions

  • Half-life independent of the initial concentration

  • Each successive half-life is the same duration

  • Half-life can be read directly from concentration time graph

• Rate constant

  • K = ln(2) / half-life

Graph for half-life

• Determine half-life

  • 
    

  • So half life is 100s

• Use equation and substitution

  

Performing rate experiments to determine reaction orders

• To determine rate

  • Initial rates method

    • Involves measuring how the initial rate changes when you alter the initial concentration of the reactant in the question

  • Continuous

    • Tracking the change in concentration of the reactant over time

    • Plot a rate-concentration graph

Initial rates method

• Initial rate of a reaction refers to rate at the beginning

• Can be calculates by the gradient of the tangent to concentration-time graph at t=0

• Steps

  • Perform the reaction several times

    • Change the initial concentration of one reactant while keeping the others the same

  • Calculate the initial rate from the c-t data for each experiment

  • Analyse how the initial rates change with varying initial conc

    • Deduce the order of reaction with respect to each reactant

Simplifying initial rate experiment with clock reactions

• Clock reactions

  • Time taken to produce a fixed amount of product

    • Measured as initial concentrations of reactants are variable

  • Clear observable change

  • Faster the clock reaction finishes, higher the initial rate

• Assumes

  • Reaction concentrations do not change over the timescale

  • Temperature remains constant

• Initial rate is inversely proportional to time taken for colour change

Iodine clock reaction

• H₂O₂(aq) + 2I-(aq) + 2H+(aq) ➔ 2H₂O(l) + I₂(aq)

• Small quantity of sodium thiosulfate and starch indicator is added to excess hydrogen peroxide and acidified iodide

• Sodium thiosulfate

  • Rapidly consumes any iodine produced

  • 2S₂O₃2-(aq) + I₂(aq) ➔ S₄O₆2-(aq) + 2I-(aq)

• Initially

  • All iodine generated in the first reaction is immediately consumed by the second

  • Once all the thiosulfate is exhausted, iodine accumulates

    • Triggers a sudden blue-black colour change

• Varying concentration

  • Done with iodide and hydrogen peroxide

  • Change endpoint time and therefore reflect the reaction rate

Continuous monitoring methods

• Measuring volume of gas evolved

• Measuring the mass loss as a gas escapes

• Measuring pH changes

• Using colorimetry to quantify colour changes

Rate determining step

Slowest step in a multi-step reaction mechanism

Rate equation and RDS

• Helps to identify which reactants are involved in the rate-determining step

• Key points

  • If a reactant appears in the rate equation, it must be involved in the RDS

  • Conversely, if reactant is absent from rate equation, it does not participate in the RDS

  • RDS is not always the first step in the mechanism

  • Reaction mechanism usually cannot be deduced solely from the balanced equation

Predicting rate equation from mechanism

• Order of reaction with respect to a particular reactant shows how many moles of that reactant are involved

  • If a reaction is second-order with respect to X, then two moles of X present in RDS

Using rate equation to deduce mechanism

• Knowledge of which reactants feature in RDS can help deduce the mechanism

• Substitution of Cl in chloromethane by the OH- nucleophile

  • Two mechanisms:

    • 1 step

      • 
        

    • 2 step

      • C-Cl bond breaks, forming carbocation intermediate (slow)

      • Positively charged carbocation rapidly reacts with the negatively charged OH- nucleophile to form final product (fast)

    • Rate is k[CH₃Cl] which shows that it must be the 2 step reaction

Intermediate in RDS

• In some cases the RDS may involve an intermediate that is formed and consumed

• Proceeds via a two-step mechanism

  • Step 1: 2NO ➔ N2O2

  • Step 2: N2O2 + O2 ➔ 2NO2

  • Rate = k[NO]2[O₂]

• RDS must involve 2 NO and 1 O₂

  • 1 cannot be RDS as no O₂

  • While 2 doesn’t have NO it has N₂O₂ which is derived from NO

  • Step 2 is the RDS

SN1 and SN2

• Nucleophilic substitution reactions of halogenoalkanes can proceed via two mechanisms

  • SN1

    • Two molecules are involved in RDS

    • Only secondary and tertiary haloalkanes

  • SN2

    • One molecule involved in RDS

    • Only primary and secondary haloalkanes

SN2

• Primary haloalkanes

• Consider reaction of iodoethane with hydroxide ions

  • CH₃CH₂I + OH- ---> CH₃CH₂OH + I-

  • Reaction occurs in single step

  • 
    

  • Rate equation therefore is k[CH₃CH₂I][OH-]

  • Shows that the reaction rate depends on the concentration of both reactants

  • Indicates that one molecule of each reactant is involved in the RDS

• Primary halogenoalkanes favour this mechanism because there is enough space around the carbon atom for nucleophile to approach

SN1

• Tertiary haloalkanes

  • Favour this mechanism because carbon atom is surrounded by alkyl groups

  • Make it harder for direct nucleophilic attack

  • Carbocation intermediate is also stabilised by the surrounding alkyl groups

• k[(CH₃)₃Cl]

• 
  

Arrhenius equation

• Ae ^{(-Ea / RT )} = k

  • K = rate constant

  • A = Arrhenius constant

  • Ea = activation energy (J mol-1)

  • E = natural logarithm base

  • R = gas constant (8.31)

  • T = temperature (K)

Influence of activation energy on reaction rate

• Activation energy

  • Higher Ea, lower rate constant becomes

  • A high activation energy means fewer reactant molecules have enough KE to react successfully

  • Therefore higher Ea means slower rate

Influence of temperature on reaction rate

• Increase in temperature leads to an exponential increase in rate constant (k)

• At higher temperatures, reactant molecules move faster

  • Results in more frequent collisions

• Higher temp provides greater KE for reactant molecules

  • Higher proportion to exceed activation energy barrier

• Both contribute to increased reaction rate when temperature increases

Calculating rate constant using a graph

• Ln(k) = -Ea / RT   +    ln(A)

• Y = ln(k)

• X = 1/T

• Gradient = -Ea / R

• Y - intercept = ln(A)