Title: Lesson 3 Rate Law and Reaction Order Learning Objectives: – Know that rate law can only be derived from experimental data – Understand the concept of reaction order – Identify reaction order from appropriate graphs – Complete an experiment to determine the order of a reaction with respect to the concentration of acid.

Main Menu Recap  On the same axes, sketch the Maxwell-Boltzmann distribution for a lower and a higher temperature, and use this to explain why increasing the temperature increases the rate of reaction.

Main Menu Recap  Excess magnesium, was added to a beaker of aqueous hydrochloric acid. A graph of the mass of the beaker and contents was plotted against time (line 1).  What change in the experiment could give line 2? A. The same mass of magnesium in smaller pieces B. The same volume of a more concentrated solution of hydrochloric acid C. A lower temperature D. A more accurate instrument to measure the time

Main Menu Recap  Which quantities in the enthalpy level diagram are altered by the use of a catalyst?  A.I and II only  B.I and III only  C.II and III only  D.I, II and III  Which statement is true about using sulfuric acid as a catalyst in the following reaction? CH 3 –CO–CH 3 (aq) + I 2 (aq)  CH 3 –CO–CH 2 –I(aq) + HI(aq) I. The catalyst increases the rate of reaction. II. The catalyst lowers the activation energy for the reaction. III. The catalyst has been consumed at the end of the chemical reaction. A. I and II only B. I and III only C. II and III only D. I, II and III

Finding the rate Ch 1.1 A2 How do you find reaction rates? In this reaction, the concentration of butyl chloride, C 4 H 9 Cl, was measured at various times, t. C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq)

Finding the rate Ch 1.1 A2 How do you find reaction rates? The average rate of the reaction over each interval is the change in concentration divided by the change in time: C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq)

Finding the rate Ch 1.1 A2 How do you find reaction rates?

Finding the rate Ch 1.1 A2 How do you find reaction rates? The average rate decreases as the reaction proceeds. What do you notice about the average rate? Why? As the reaction goes forward, there are fewer collisions between reactant molecules.

Example Ch 1.1 A2 How do you find reaction rates? Given the following data, what is the average rate of the following reaction over the time interval from 54.0 min to min? CH 3 OH (aq) + HCl (aq) → CH 3 Cl (aq) + H 2 O (l) Time (min)[HCl] (M)

Finding the rate Ch 1.1 A2 How do you find reaction rates? Given: [HCl] 54 min = 1.58 M [HCl] 215 min = 1.02 M Find: avg. rate of disappearance of HCl Given: [HCl] 54 min = 1.58 M [HCl] 215 min = 1.02 M Find: avg. rate of disappearance of HCl Avg. rate = -  [HCl]  t = - (1.02 M M) 215 min - 54 min = M / min Avg. rate = -  [HCl]  t = - (1.02 M M) 215 min - 54 min = M / min

Finding the rate Ch 1.1 A2 How do you find reaction rates? A plot of concentration vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. A plot of concentration vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq)

Finding the rate Ch 1.1 A2 How do you find reaction rates? Rate laws for the reaction must be determined experimentally. Measure the instantaneous reaction rate at the start of the reaction (i.e. at t = 0) for various concentrations of reactants. You CANNOT determine the rate law for the reaction by looking at the coefficients in the balanced chemical equation!

Main Menu Now look at this example...  An oxidised buckminsterfullerene, C 60 O 3 decomposes into C 60 O, releasing O 2 :  The reaction can be measured by change of absorbance of light of a certain wavelength.  Absorption ∝ [C 60 O 3 ] Remember: Rate is expressed as a positive value!

Main Menu  Rate calculated as a function of time:  Rate of reaction plotted against the absorbance of C 60 O 3 : Rate decreases over time, slowing as the concentration of C 60 O 3 decreases. This mirrors the absorbance graph on the previous slide! Rate must be related to concentration at each time The straight line graph of rate against absorbance confirms: Reaction rate ∝ [C 60 O 3 ]

Main Menu Rate expression or Rate law  Reaction rate ∝ [C 60 O 3 ]  This proportional relationship is converted into an equation by introducing a constant.  Reaction rate = k[C 60 O 3 ]k = rate constant  This expression is a first order expression because the concentration is raised to the power one.  In general, the rate is proportional to the product of the concentrations of the reactants, each raised to a power. m and n, are known as the orders of the reaction with respect to reactants A and B. Overall order is the SUM of the individual orders.

Main Menu The table below gives some examples of some reaction equations. There is no predictable relationship between the co-efficients in the equation and the values for the order of reaction with respect to the reactants. ORDERS OF REACTION CAN ONLY BE OBTAINED BY EXPERIMENTAL DATA!

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Solutions

Main Menu What is reaction order?  Reaction order describes how changes to the concentration of reactants affect the rate of a reaction  Assuming temperature and pressure are fixed 0 th Order (0 o ) Changing the concentration does not affect the rate [R] doubled  rate same [R] halved  rate same [R] trebled  rate same 1 st Order (1 o ) [R] doubled  rate doubled [R] halved  rate halved [R] trebled  rate trebled 2 nd Order (2 o ) [R] doubled  rate quadrupled [R] halved  rate quartered [R] trebled  rate x 9

Main Menu For example:  The reaction is 0 th order w.r.t reactant A  Comparing Runs 2 and 3:  [A] doubles but [B] remains fixed  Rate unchanged  The reaction is 1 st order w.r.t reactant B  Comparing Runs 1 and 2:  [B] doubles but [A] remains fixed  Rate doubles  Overall the reaction is 1 st order Run #Initial [A] ([A] 0 ) Initial [B] ([B] 0 ) Initial Rate (v 0 ) M 1.25 x M/s M2.00 M2.5 x M/s M 2.5 x M/s

Main Menu Another example: ExperimentInitial [NO] / mol dm –3 Initial [H 2 ] / mol dm –3 Initial rate / mol (N 2 ) dm –3 s – ×10 – ×10 – ×10 – ×10 –5  The reaction is 1 st order w.r.t reactant H 2  Comparing Runs 1 and 2:  [H 2 ] doubles but [NO] remains fixed  Rate doubles  The reaction is 2 nd order w.r.t reactant NO  Comparing Runs 1 and 3:  [NO] doubles but [H 2 ] remains fixed  Rate quadruples  Overall the reaction is 3 rd order (1 st order + 2 nd order = 3 rd order)

First Order Reactions Ch 1.1 A2 How do you find reaction rates? Expt[A] (M)Rate (M/s) x2 As [A] doubles, the rate doubles [A]  rate As [A] doubles, the rate doubles [A]  rate First Order Reaction – Overall reaction order = 1 – Rate = k[A] First Order Reaction – Overall reaction order = 1 – Rate = k[A]

Second Order Reactions Ch 1.1 A2 How do you find reaction rates? Expt Initial [A] (M) Initial [B] (M ) Rate (mol dm -3 s -1 ) x x x x1 x2 [A] stays the same [B] doubles [A] stays the same [B] doubles x2 x1 x4 the rate doubles [B]  rate [A] doubles [B] stays the same [A] doubles [B] stays the same the rate is x4 [A] 2  rate

Second Order Reactions Ch 1.1 A2 How do you find reaction rates? [A] doubles [B] stays the same [A] doubles [B] stays the same [A] stays the same [B] doubles [A] stays the same [B] doubles the rate doubles [B]  rate the rate is x4 [A] 2  rate What is the rate equation for this reaction? Rate = k[A] 2 [B] The reaction is second order in respect of A and first order in respect of B. The overall reaction order is 3.

Initial [X]/MInitial [Y]/MInitial [Z] / MInitial rate/ mol dm -3 s x x x x Second Order Reactions Ch 1.1 A2 How do you find reaction rates? x1 x3 [Z] triples [X] &[Y] stay the same [Z] triples [X] &[Y] stay the same X0.5 x1 the rate trebles [Z]  rate [X] halves [Y] & [Z] stay the same [X] halves [Y] & [Z] stay the same the rate is the same [X] 0  rate NE x1 [Y] quadruples [X] & [Z] stay the same [Y] quadruples [X] & [Z] stay the same the rate goes up by 16 (ie 4 2 ) [Y] 2  rate x1 x4 x1

Second Order Reactions Ch 1.1 A2 How do you find reaction rates? What is the rate equation for this reaction? Rate = k[Y] 2 [Z] The reaction is second order in respect of Y and first order in respect of Z. The overall reaction order is 3. [X] halves [Y] & [Z] stay the same [X] halves [Y] & [Z] stay the same [Z] triples [X] &[Y] stay the same [Z] triples [X] &[Y] stay the same the rate trebles [Z]  rate the rate is the same [X] 0  rate [Y] quadruples [X] & [Z] stay the same [Y] quadruples [X] & [Z] stay the same the rate goes up by 16 (ie 4 2 ) [Y] 2  rate

Main Menu Determination of the order of reaction Initial rates method  This involves carrying out separate experiments with different starting concentrations of A, with other reactants held constant  effect on [A] can be observed. This can then be repeated for reactant B.

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Solutions

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Graphical representation of reaction kinetics  Zero order reaction  Concentration of reactant A does not affect the reaction

Main Menu Graphical representation of reaction kinetics  First-order reaction  Rate is directly proportional to the concentration A

Main Menu Graphical representation of reaction kinetics  Second-order reaction  Rate is directly proportional to the square of concentration A Note: The concentration – time graph is steeper at the start and levels off more (when compared to first-order graph) Parabola shape – characteristic of the square function

Main Menu Summary

Main Menu Rate-Concentration Graphs 0 th Order  No effect  Gradient 0 1 st Order  Direct proportion  Gradient positive and constant 2 nd Order  Squared relationship  Gradient positive and increasing

Main Menu 0 th Order Half-life decreases Concentration-Time Graphs 1 st Order Half-life constant 2 nd Order Half-life increases t 1/2

Main Menu Constant half life is a feature of only first order reactions Constant half life can be used to establish that a reaction is first order w.r.t that reactant. The shorter the half life, the faster the reaction.

Main Menu Rate Graphs in Practice  In the experiment you will follow the progress of a reaction using a data logger with pH probe  Follow the instructions here.instructions here  This will collect so much data that the only realistic way to analyse it will be by spreadsheet. There is an example here.There is an example here  Information about R 2 values can be found here:  How to do line equations here:

Main Menu Review  The order of a reaction tells us the effect on the rate of changing the concentration of the reactants.  Order can be determined by:  Directly comparing experimental data  The gradient of a rate-concentration graph  The shape of a concentration-time graph