43 RATE EQUATIONS, ORDERS & CONSTANTS

C hem F actsheet January 2003

Number 43

Rate Equations, Orders & Constants To succeed with this topic you need to:  Know Know and and under understa stand nd the the AS AS mater material ial on kinet kinetics ics collision theory ♦ activation energy ♦ Maxwell-Boltzman graph ♦ ♦ Factors affecting rates of reaction ♦ Catalysts and energy profiles covered in Factsheet No. 10 (Kinetics I)

Finding the orders from experimental data This following worked example is typical of what will be expected of you in an examination question. The reaction: 2C + D + 2E → 3F + 2G products the following data experiment number

After working through the Factsheet you will be able to: • unders understan tand d the parts parts making making up the the rate equati equation on (or expre expressi ssion) on);; • be able able to find the the orders orders for for a particu particular lar chemi chemical cal reacti reaction on from from the data given for it; • be able able to perf perform orm calcu calculat lation ionss based based on the the rate rate equati equation; on; • be able able to work work out the units units for for the the rate rate constant constant,, k .

1 2 3 4

Rate expressions (equations)

A + B + 2C

→

2 8 16 16

rate constant

[A]

×

[B]

∝

is the

[C] (NB. the rate constant, When [C] doubles, doubles, the rate doubles rate = k [C] i.e.directly i.e.directly proportional so is first k enables the ‘=’ sign to be put in). order. order.

[ ] = concentration i.e. mol dm -3 2

Answer

For C compare experiments 2 and 3 Rate ∝ [C] (NB. proportional sign) because only C changes.

2D + E

The rate expression (or equation) works out to be

−1

1. 0 1. 0 1.0 2.0

Working Out

Let us consider a reaction of substances A, B and C where the equa tion is

units of mol dm -3 s

1.0 2.0 2.0 2.0

Hint the process involves looking at the experiments for C ,D and E and selecting two where only one of C, D or E changes - compare changes in concentration with the effect on the rate.

The rate expression can only be w orked out from the data provided by reaction rate experiments.

×

0.5 0.5 1.0 1.0

initial rate / mol dm -3s-1

(a) What are the the orders with respect respect to C, D and E? (b) Write the the rate equation equation for this reaction reaction..

The balanced chemical equation (the stoichiometric equation) can tell you nothing about the rate expression.

rate = k 

concentrations / mol dm-3 [C] [D] [E]

For D compare experiments 1 and 2. rate

1

'orders'

∝

[D]2

doubles, the rate goes up rate = k [D] when [D] doubles, [D]2 2 nd 4 times i.e. 4 = 2 , so 2 order

In words: The reaction is 2nd order with respect to A and 1 st order with respect to B. Overall, the reaction is 3rd order (2 + 1)

For E compare experiments 3 and 4 rate

Note the following points about this example: (1) We would mormally mormally write [B], [B], not [B]1. The 1 is put in to make it clear (2) C does not appear appear in the rate expression expression – it is ‘0 order’ order’ and if shown 0 would look like this [C] (3) the expression expression would would normally be shown shown as

∝

[E]0

when [E] doubles, doubles , the rate is rate = k [E] [E]0 unchanged i.e. no effect so is zero order Combine the answers in (a)

rate = k [A] [A]2 [B]

(b)

rate = k [C][D] [C][D] 2 or rate = k [C][D] [C][D]2[E]0

with the ‘×’ symbol removed. Summary 0 order order changin changing g the the concent concentrati ration on has has no effect effect on the rate rate

1

1st order order -

directl directly y proport proportion ional al relatio relationsh nship ip e.g. e.g. half concen concentra tratio tion n and half rate, triple concentration and triple the rate.

2nd order -

‘squared ‘squared factor factor’’ involved involved e.g. e.g. triple triple concent concentratio ration n and rate rate increases 9×, double concentration and rate increases 4×.

Rate Equations, Orders & Constants

Chem Factsheet

Questions

Exam Hint -  The

initial rate data is a common place for questions to  catch out candidates by using ‘powers of 10’ (standard form). Look at this data:  rate  2 x 10 -3  8 x 10 -3  3.2 x 10 -2  6.4 x 10 -2  Comparing these is a problem! 

1. For the the reaction reaction between between A, B and and C the followi following ng results results were were obtained: obtained: expe experi rime ment nt 1 2 3 4

Now do this conversion to 10 -3  for all figures:  rate  2 x 10 -3  E x 4  comparison  8 x 10 -3  E x 4  are  3.2 x 10 -2  = 32 x 10 -1 x 10 -2 = 32 x 10 -3  E 6.4 x 10 -2  = 64 x 10 -1 x 10 -2 = 64 x 10 -3  x 2  now possible  (check conversions on your calculator if you are unsure) 

1 2 3

[ ] = mol mol dm dm-3 rate = mol dm-3 s-1

Powers • Anythi Anything ng witho without ut a number number by it it is to the the powe powerr 1. • Multiply ⇒ add powers. • Dividing ⇒ subtract powers. • Powers Powers on on the botto bottom m change change sign sign when when you bring bring them them to the the top. top. • If you you are find finding ing a "powe "powerr of a power power"" you mult multiply iply.. e.g. (mol dm-3)3 = mol1 3dm-3 3 = mol3dm-9 • You can can only only simpli simplify fy power powerss of the same same thin thing g e.g. mol2 × mol = mol3, but mol dm-3 can't be simplified.

k =

rate [A][B]

Example 2 k =

rate [C]2[D]

expe experi rime ment nt 1 2 3 4

×

=

mol dm-3s-1 mol dm-3mol dm-3

s-1 mol dm-3

=

mol-1dm3s-1

conc concen entr trat atio ion n / mol mol dm-3 [E] [F] [G] 1 1 0.5 1 2 0.5 2 2 0.5 2 2 1.5

initial rate / mol dm-3s-1 7.0 × 10-3 1.4 × 10-2 1.4 × 10-2 4.2 × 10-2

(a) Write the the rate expression expression for for this reaction. reaction. (b) Calculate Calculate the the value value for for k and state its units.

1. (a) rate = k [A] [A]1 rate = k [B] [B]0 (b) (b) rate rate = k  [A][C]2 rate (c) k  = [A][C]2 use experiment 1: 2.0 × 104 = 1 × 12 = 2.0 × 10-4

rate = k [C] [C]2[D] mol dm-3s-1 (mol dm-3)3

2.5 × 10-4 2.5 × 10-4 5.0 × 10-4

Answers

mol dm-3s-1 = mol dm-3 × mol dm-3

=

rate / mol dm-3s-1

3. The following following results results were obtained obtained for for the reaction reaction between between E, F and G:

rate = k [A][B] [A][B]

=

conc concen entr trat atio ion n / mol mol dm-3[C] [D] 0.01 0.1 0.01 0.2 0.02 0.3

(a) Write the the rate expression expression for for this reaction. reaction. (b) Calculate Calculate the the value value for for k and give its units.

(2) be able to rearrange rearrange the the rate equation equation (3) Know how how to combine powers

Example 1

2.0 × 10-4 4.0 × 10-4 2.0 × 10-4 1.6 × 10-3

2. For the reactio reaction n between C and D the followi following ng results results were obtained obtained::

 k Finding the units of  k

×

initial rate / mol dm-3s-1

(a) What are the the orders orders with respect respect to A, B and and C? (b) What is the rate expression expression for for this reaction? reaction? (c) (c) Calcul Calculate ate the the value value for k . What are its units?

expe experi rime ment nt

To do this you need to (1) (1) reme rememb mber er the the uni units ts of :

conc concen entr trat atio ion n / mol mol dm-3[A] [B] [C] 1 1 1 2 1 1 1 2 1 2 1 2

=

= mol dm-3 s-1 mol-3 dm9 =

mol dm-3 s-1 mol3 dm-9

Units: =

mol-2dm-6s-1

=

rate = k [C] [C]2

mol dm-3 s-1 mol dm-3 (mol dm-3)2 mol-2 dm6 s-1

 k Finding the value of  k This is a relatively straightforward procedure: 1. choose the values values for any one of the experiments experiments in in the data data table 2. substitute substitute these these values values for [ ] and rate rate into into the rate rate expression expression 3. rearra rearrange nge the the equati equation on and calcu calculat latee k .

2. (a) rate = k [C] [C] 2.5 × 10-4 (b) k  = 0.01 = 2.5 × 10-2s-1

You will find examples of this calculation in the questions at the end of this Factsheet.

3. (a) rate = k [F][G] [F][G] (b) k  = 1.4 × 10-2 mol-1dm3s-1

 Acknowledgeme  Acknowledgements: nts: This Factsheet was researched and written by Sam Goodman Curriculum Press, Unit 305B, The Big Peg, 120 Vyse Vyse Street, Birmingham, B18 6NF ChemistryFactsheets may be copied free of charge by teaching staff or students, provided that  their school is a registered subscriber.  No part part of these these Factsh Factsheets eets may be reprod reproduced uced,, stored stored in a retrieva retrievall system, system, or trans transmitte mitted, d, in any 1351-5136  other form or by any other means, without the prior permission of the publisher. ISSN publisher. ISSN 1351-5136 

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