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Unit 4,Topic 3: How Fast? Exam Questions 1. In an experiment designed to find the mechanism of the reaction between a halogenoalkane, RX, and hydroxide ions, the following data were obtained at constant temperature. In itial co n cen tratio n o f R X /m ol dm 0.01 0.01 0.005 In itial co n cen tratio n o f OH /m ol dm 0.04 0.02 0.04 8 10 4 10 4 10 –6 –6 –6 –3 –3 In itial rate /m ol dm s –3 –1 (i) Deduce the order with respect to RX and OHand hence write the rate equation for the reaction. (ii) Calculate a value for the rate constant for the reaction. (4) 2. This question is about the reaction between bromomethane and aqueous hydroxide ions CH 3 Br + OH CH 3 OH + Br . (a) An increase in temperature increases the rate of this reaction. Explain the increase by referring to the collision frequency and the collision energy of the molecules. ............................................................ ........................................................ ................ ............................................................ ........................................................ ................ NT Exampro 1

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Unit 4,Topic 3: How Fast? Exam Questions1. In an experiment designed to find the mechanism of the reaction between a halogenoalkane, RX, and hydroxide ions, the following data were obtained at constant temperature. I n i t i a l c o n c e I nn ti rt ai a t il o c n o no cf e n R X / m 3 o l d m O H / m 3 o l d m 0 0 0 (i) . 0 . 0 . 0 1 1 0 5 0 0 0 . 0 . 0 . 0 4 2 4 t I r n a i t t i i o a n l ro a f t e / m o l 3 d1 m s 8 4 4 6 6 6

1 1 1

0 0 0

Deduce the order with respect to RX and OH and hence write the rate equation for the reaction.

(ii)

Calculate a value for the rate constant for the reaction.

(4)

2.

This question is about the reaction between bromomethane and aqueous hydroxide ions CH3Br + OH CH3OH + Br . (a) An increase in temperature increases the rate of this reaction. Explain the increase by referring to the collision frequency and the collision energy of the molecules. .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(3)

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(b)

By sketching the energy distribution of the molecules at a given temperature, T, show how the presence of a catalyst will increase the rate of the reaction.

(3)

(c)

Define the following terms used in reaction kinetics. (i) Overall order of reaction .......................................................................................................................... ..........................................................................................................................(1)

(ii)

Rate constant .......................................................................................................................... ..........................................................................................................................(1)

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(d)

In the reaction between bromomethane and aqueous hydroxide ions at constant temperature the concentration of bromomethane at various times is given in the table.t i m [ C3

e / m H B

i n0 r 3 ] 0 / .m 1

1

0

2

0

3

0

4

0

5

0

6

0

7

0 1 4

0o0 0l . 0 d 70 m 4. 0

50 7. 0

40 3. 0

3 0 3. 0

20 5. 0

10 9 . 0

(i)

Plot a graph to show that the reaction is first order with respect to bromomethane.

(4)

(ii)

If the concentration of the hydroxide ion doubles, all other factors remaining constant, the rate of the reaction doubles. What is the order of reaction with respect to the hydroxide ion? ..........................................................................................................................(1)

(iii)

Hence write a rate equation for this reaction. ..........................................................................................................................(1)

(iv)

Based on the kinetic information obtained above write the mechanism for the reaction between CH3Br and aqueous OH- ions.(3) (Total 17 marks)

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3.

Thioethanamide reacts with sodium hydroxide as follows: CH3CSNH2 + 2OH CH3CO2 + HS + NH3 The reaction is first order with respect to both thioethanamide and hydroxide ions. (i) Write the rate equation for this reaction. .(1)

(ii)

What is the overall order of the reaction? .(1)

(iii)

Given that the reaction occurs in two stages and the rate determining step is: CH3CSNH2 + OH CH3CONH2 + HS Write an equation for the second step in the reaction. .(1) (Total 3 marks)

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CH4. This question concerns 2-bromo-2-methylbutane, C H3

3

CH

2

C CH3

B r which reacts with

aqueous potassium hydroxide solution via an SN1 mechanism. (a) (b)

Show this mechanism and identify the rate determining step.(4)

If the conditions are altered potassium hydroxide will react to give an elimination reaction with the same halogenoalkane.

Draw the structural formula and give the name of an organic product of this elimination reaction, showing all the covalent bonds.(2)

(c)

The product in (b) can be polymerised. (i) (ii) Write the formula for this polymer showing the structure of the repeating unit.(2)

Suggest why, in terms of the nature of the bonds in such polymers, they are persistent in the environment but are not particularly hazardous.(2)

(d)

The rate equation for the substitution reaction in part (a) is rate = k[2-bromo-2-methylbutane] (i) State the order of the reaction. (1)

(ii)

If the same halogenoalkane is reacted with cyanide ions instead of hydroxide ions, and all other conditions remain the same, state with reasons whether the rate of the reaction would alter. (3)

(e)

Reaction rates generally increase with an increase in temperature for two reasons. (i) State what these reasons are. (2)

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(ii)

The distribution of molecular energies at a given temperature T1 is shown below. Sketch on the same axes a graph appropriate to a higher temperature T2, and hence explain why the rate increases.

N um ber of m o le c u le s w ith a g iv e n e n e rg y

E n e rg y (4)

(iii)

By using the graph, or otherwise, explain the effect of a catalyst on the rate of a reaction. (2) (Total 22 marks)

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5.

Iodine reacts with propanone in the presence of an acid catalyst according to the equation:

C H 3C O C H

3

+ I2

H +

C H 3C O C H 2I + H I

Data concerning an experiment to determine the rate equation for this reaction are given in the following table: R e la tiv e c o n c e n tr a tio n s [C H 3 C O C H 3] 1 1 2 1 (a) (i) [I 2 ] 1 2 1 1 [H +] 1 1 1 2 2 2 4 4 R e la t iv e r a te

State why a rate equation cannot be written from a knowledge only of the chemical equation representing the reaction. ........................................................... ...........................................................(2)

(ii)

Use the data to deduce the order of reaction with respect to propanone . Iodine .. hydrogen ions .(3)

(iii)

What does the value for iodine tell you about the part that iodine plays in the rate determining step of the reaction? ...........................................................(1)

(iv)

Write the rate equation for the reaction. ...........................................................(1)

(b)

(i)

Use the bond enthalpies given, in kJ mol1, to calculate the enthalpy change for the iodination of propanone: CH +413 11 +151 C1 +228 H1 +298(2)

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(ii)

Draw an enthalpy level diagram for the reaction, showing on it both catalysed and uncatalysed pathways.

(3) (Total 12 marks)

6.

(a)

The kinetics of the hydrolysis of the halogenoalkane RCH2Cl with aqueous sodium hydroxide (where R is an alkyl group) was studied at 50 C. The following results were obtained: Experiment 1 2 3 (i) [RCH2Cl] 0.050 0.15 0.10 [OH] 0.10 0.10 0.20 Initial rate/mol dm3 s1 4.0 104 1.2 103 1.6 103

Deduce the order of reaction with respect to the halogenoalkane, RCH2Cl, and with respect to the hydroxide ion, OH, giving reasons for your answers. ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ......................................................................................................................(4)

(ii)

Hence write the rate equation for the reaction. ......................................................................................................................(1)

(iii)

Calculate the value of the rate constant with its units for this reaction at 50 C.

(2)

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(iv)

Using your answer to part (ii), write the mechanism for this reaction.

(3)

(b)

(i)

Write the equation for the reaction of concentrated sulphuric acid with solid sodium chloride. ......................................................................................................................(1)

(ii)

When concentrated sulphuric acid is added to solid sodium bromide a different type of reaction occurs. Explain why the reactions are different. Identify the gases produced with sodium bromide and write an equation to show the formation of these gases. ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ......................................................................................................................(4) (Total 15 marks)

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7.

In an experiment to determine the rate of the reaction between persulphate ions and iodide ions in aqueous solution2 S2O 8 + 2I 2SO 2 + I2 4

the following data were obtained:

C o n c e n tra tio n /m o l d m S2O2 8

3

I 0 .1 0 0 0 .1 0 0 0 .2 0 0

In itia l ra te /m o l d m 3 s 1 0 .3 6 0 .7 2 1 .4 4

0 .1 0 0 0 .2 0 0 0 .2 0 0(a) (i)

Deduce the order of reaction with respect to each of the reagents and hence write the rate equation for the reaction. ............................................................................................................................ ............................................................................................................................ ............................................................................................................................(3)

(ii)

With reference to this reaction state what is meant by the overall order of a reaction. ............................................................................................................................ ............................................................................................................................(1)

(iii)

Calculate the rate constant including units.

(2)

(iv)

Explain why the rate equation cannot be written directly from the stoichiometric equation for the reaction. ............................................................................................................................ ............................................................................................................................(1)

(b)

(i)

Suggest a suitable experimental technique that would enable you to determine the rate of the reaction given opposite. ............................................................................................................................ ............................................................................................................................(1)

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(ii)

Suggest a necessary condition that would help to ensure accurate results. ............................................................................................................................(1)

(iii)

Suggest one advantage or disadvantage of your chosen experimental method. ............................................................................................................................ ............................................................................................................................(1) (Total 10 marks)

8.

(a)

(i)

Explain what is meant by the following terms. Rate of reaction ....... ....... Overall order of a reaction ................................................................................ ....... .......(2)

(ii)

Explain why the order of reaction cannot be deduced from the stoichiometric equation for a reaction. ....... ....... .......(1)

(b)

Substitution reactions of halogenoalkanes, can proceed via an SN1 or SN2 mechanism. When 1-bromobutane, CH3CH2CH2CH2Br, 2-bromobutane, CH3CH2CHBrCH3, and 2-bromo-2-methylpropane, (CH3)3CBr, are reacted separately with aqueous sodium hydroxide solution each gives the corresponding alcohol. (i) Give the mechanism for the SN1 reaction between 2-bromobutane and hydroxide ions.

(3)

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(ii)

Explain why the product mixture is not optically active. ....... ....... .......(2)

(iii)

In an experiment designed to find the mechanism of the reaction between 2-bromo2-methylpropane and hydroxide ions the following data were obtained at constant temperature. Initial concentration of 2-bromo-2-methylpropane /mol dm3 0.10 0.20 0.30 Initial concentration of OH / mol dm3 0.10 0.10 0.20 Initial rate of reaction /mol dm3 s1 1.2 102 2.4 102 3.6 102

Use the data to deduce the rate equation for the reaction of 2-bromo-2methylpropane with sodium hydroxide solution. ....... ....... .......(3)

(c)

Suggest, in outline, a method you could use to follow the progress of the reaction between a bromoalkane and aqueous sodium hydroxide. ....... ....... ....... ....... ....... .......(3) (Total 14 marks)

9.

(a)

In a rate of reaction experiment between two substances, A and B, the overall order of the reaction was found to be 2. Write three possible rate equations for such a second order reaction between A and B. ............................................................................................................................... ...............................................................................................................................

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...............................................................................................................................(3)

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(b)

At a certain temperature the rate of reaction between nitrogen monoxide, NO, and hydrogen, H2, was investigated. The following data were obtained. [NO]/mol dm3 1.0 1.0 3.0 (i) [H2]/mol dm3 1.0 3.0 1.0 Rate/mol dm3 s1 0.02 0.06 0.18

Use the data above to deduce the rate equation for this reaction.

(3)

(ii)

Use your answer to (b)(i) above to calculate the value of the rate constant, with units.

(2)

(c)

The investigation described in part (b), above, was repeated, but at a higher temperature, and the rate of the reactions increased. Explain, in terms of particles, why an increase in temperature increases the rate of a reaction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(3)

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(d)

State the effect of an increase in temperature on the value of the rate constant, k. ...............................................................................................................................(1)

(e)

Explain the effect of a catalyst on the rate of a reaction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(3) (Total 15 marks)

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ANSWERS 1. In an experiment designed to find the mechanism of the reaction between a halogenoalkane, RX, and hydroxide ions, the following data were obtained at constant temperature. I n i t i a l c o n c e I nn ti rt ai a t il o c n o no cf e n R X / m 3 o l d m O H / m 3 o l d m 0 0 0 (i) . 0 . 0 . 0 1 1 0 5 0 0 0 . 0 . 0 . 0 4 2 4 t I r n a i t t i i o a n l ro a f t e / m o l 3 d1 m s 8 4 4 6 6 6

1 1 1

0 0 0

Deduce the order with respect to RX and OH and hence write the rate equation for the reaction.(halving [RX] halves rate ) 1st order wrt RX (1) (halving [OH-] halves rate ) 1st order wrt OH (1) explanation of either of statements in brackets (1) rate = k[RX][OH-] (1)

(ii)

Calculate a value for the rate constant for the reaction.

rate 8 10 6 OR 0.02 (1) k= = [RX][0H - ] 0.01 0.04mol-4 dm3 s-1 (1) (4)

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2.

This question is about the reaction between bromomethane and aqueous hydroxide ions CH3Br + OH (a) An increase in temperature increases the rate of this reaction. Explain the increase by referring to the collision frequency and the collision energy of the molecules.collision frequency () as molecules move faster () collision energy () as mole have higher momentum/greater kinetic energy () proportion of colls. energy > Ea rises or more successful/effective collisions (1) (3)

(b)

By sketching the energy distribution of the molecules at a given temperature, T show how the presence of a catalyst will increase the rate of the reaction.

n

o

.

o

f

m

o

l s .

i f t w d r a w

o nm

g

r a p h s ta h x e n1 (

a r e )

e n

e r g

yE

a

( c a t )

E

a

general form of graph (1) must be skewed to the left (no bell shapes) Ea shown (1) Ea cat (1) (this mark can still be awarded if speed on x-axis) Eacat mark can not be awarded if it is to the LHS of the hump (3)

(c)

Define the following terms used in reaction kinetics. (i) Overall order of reactionsum of powers to which concentration terms are raised (in rate equation) (1) sum of individual orders () only (1)

(ii)

Rate constant(proportionality) constant in rate equation (1) or defined K = Ae E/RT (1)

(d)

In the reaction between bromomethane and aqueous hydroxide ions at constant temperature the concentration of bromomethane at various times is given in the table.t i m [ C3

e / m H B

i n0 r 3 ] 0 / .m 1

1

0

2

0

3

0

4

0

5

0

6

0

7

0 1 4

0o0 0l . 0 d 70 m 4. 0

50 7. 0

40 3. 0

3 0 3. 0

20 5. 0

10 9 . 0

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graph of [CH3Br] vs t (2) ie correct points (1) correct line smooth curve (1) if a plot of [CH3Br] vs 1/t (0) or in [CH3Br] vs t (2) penalise () if one or both of the axes are less than half the size of the grid given show constant half-life using 2 values (2) if one value of half-life is given and say it is 1st order (1) only if just state constant half-life with no value used or state . 1st order (0) (or constant t from constant slope / straight line = 1st order if log plot used (2))

(ii)

Plot a graph to show that the reaction is first order with respect to bromomethane.one (1) (4)

(iii)

If the concentration of the hydroxide ion doubles, all other factors remaining constant, the rate of the reaction doubles. What is the order of reaction with respect of the hydroxide ion?rate = k [CH3Br] [OH-] (1) consequential on answer to (d)(ii) (1)

(iv)

Hence write a rate equation for this reaction. H O H C H BH r O H H H C H O CB H rH H + B r

H

C

B

mr

a y

b

e

+ s C h Bo

wr

n

a s

arrows must not come from the charge drawing of the lone pair is not essential intermediate must be ve if (d)(iii) is correct but a correct SN1 mechanism is given here (1) max for (d)(iv) if in (d)(iii) rate = k [CH3Br) ie 1st order is given but a correct SN 1 mechanism is given here (3) for (d)(iv) if (d)(iii) is incorrect but a correct SN2 mechanism is given here (1) max for (d)(iv) if no answer to (d)(iii) and a correct SN1 or SN2 mechanism is given here then (1) max for (d)(iv) (1)

(v)

Based on the kinetic information obtained above write the mechanism for the reaction between CH3Br and aqueous OH ions.(3) (Total 17 marks)

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3.

Thioethanamide reacts with sodium hydroxide as follows: CH3CSNH2 2OH CH3CO2 + HS + NH3 The reaction is first order with respect to both thioethanamide and hydroxide ions. (i) Write the rate equation for this reaction.rate = k[CH3CSNH2] [OH] (1) (1)

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(ii)

What is the overall order of the reaction?2 (1) (1)

(iii)

Given that the reaction occurs in two stages and the rate determining step is:CH3CSNH2 + OH CH3CONH2 + HS

Write an equation for the second step in the reaction.CH3CONH2 + OH CH3CO2 + NH3 (1) (1) (Total 3 marks)

4.

(a)(1 )

C H C 2H5

3

(1 )

C C H3

B r

r.d .s .

(1 )

(1 ) C H

3

O H +

C 2H

5

C

+3

Br

CH

1st arrow

:

it must start on the bond and not go past the Br do not allow [ ]+ it need not come from lone pair but it must not come from the negative charge

intermediate : 2nd arrow :

C H do not penalise if mechanism all correct but C H sticks or R3

3

C C H3

B r used instead accept

lone pair not required on the OH but if no negative charge penalise (1) if fully correct SN2 mechanism given then (max 2) 4 (b) C 2H5

C CH3

CH

2

(1)

2methylbut1ene (1)

CH H

3

C H C C C H

3

3

(1)

(2) methylbut2ene 2

must show hydrogens in the structure and skeletal formulae not acceptable

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(c)

(i) C 2H C C H3 5

H C H n or

C H C H

3

C H C C H

3

s tru c tu re o f o n e re p e a t u n it (1 ) f o r lin e s e ith e r s id e ( ) n fo r n o u ts id e b ra c k e ts ( )

3

n

If more than one correct repeat unit is given then (max 1) ie () for lines () for n outside brackets mark consequentially on the answer to (b) as long as it is a 5 carbon alkene (ii) 2

saturated compounds very unreactive or (covalent/) bonds strong/stable/hard to break/ unreactive (1) no poisonous/toxic breakdown products or nontoxic in themselves or any reference to toxicity of materials (1) it is unreactive (0) or it is stable (0) 2 1 (1) not 1st w.r.t. halogenoalkane rate of reaction same (1) SN1 r.d.s. is ionisation of halogenoalkane or hydroxide ions not in r.d.s. (1) independent of the nature of the nucleophile or zero order w.r.t nucleophile or hydroxide/cyanide (1) 1

(d)

(i) (ii)

3

(e)

(i) & (ii) mark parts (i) and (ii) together and the marks are for : increase (kinetic) energy (1) collision frequency increases / more collisions (1) not faster collisions not more effective collisions more molecules have enough energy to react / more molecules have energy greater than activation energy (1) E no of m o lsA cat

E

A

e n e rg y T2: lower peak (1) shifted to right (1) EA shown to right of both humps or stated (1) (e)(i) & (ii) (6) (iii) any real absurdity (1) 6

EA catalysed < EAuncatalysed (1) (can be shown on graph in (ii) but neither line should be left of peaks) comment about number of molecules which then have enough energy to react or catalyst provides an alternative route (1)

2[22]

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5.

(a)

(i)

kinetics depends on species or molecules in ratelimiting step or slowest step (1); NOT order can only be found by experiment; this depends on mechanism or some recognition that a multistage process may be involved in the reaction (1) 2 1, 0, 1 Not involved in ratelimiting step (1) consequential on (ii) rate = k [CH3COCH3] [ H+] (1) could show [I2]0 but this is not required Answers to (iii) and (iv) consequential on answer to (ii), and must be consistent throughout (H = D(I I) + D(C H) D(C I) D(H I) = (+151) + (+413) (+228) (+298) = +38 kJ mol1 (1) Correct answer with no working (1); 38 scores 0; ignore units 3 1

(ii) (iii) (iv)

1

(b)

(i)

2

(1 ) (1 ) e n th a lp y io d o p ro p a n o n e + H I

p ro p an o n e + io d in e

(1 ) S e e n o te s b e lo w

re a c tio n c o o rd in a te (ii) Relative positions of products and reactants which need not be identified(1) Correct profile uncatalysed (1) could show a transition state Correct profile catalysed (1) must show intermediate Consequential on b(i) for full marks but if b(i) is correct but diagram is shown as EXOTHERMIC, maximum 2 marks for profiles.[12]

3

6.

(a)

(i)

Experiments 1 & 2, [RCH2Cl] 3, Rate 3 (1) 1st order w.r.t. [RCH2Cl] (1) Experiments 1 & 3, [RCH2Cl] and [OH] 2, rate 4 (1) 1st order w.r.t. [OH] (1) Rate = k [RCH2Cl] [OH] consequential on (i)

4 1

(ii)

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(iii)

k=

rate 4.0 10 4 mol dm 3s 1 = = 0.080 (1) mol1 dm3 s1 (1) [RCH 2 Cl][OH ] 0.050 0.10 mol 2 dm 6 2

(iv)

(SN2)

R H O

R C l H (1 ) H O H C Cl H (1 )

R H O H C H3

C H (1 )

+ C l

Note SN1: allow if first order deduced from parts (1) and (ii) for full marks. (b) (i) NaCl + H2SO4 HCl + NaHSO4 (ignore any state symbols) 2NaCl + H2SO4 2HCl + Na2SO4 Gases are : sulphur dioxide / SO2 and bromine / Br2 (1) Bromide reduces H2SO4 / HBr produced in first step is strong enough reducing agent to reduce conc sulphuric (1) because Br larger than Cl (1) H2SO4 + 2HBr 2H2O + SO2 + Br2 (1)

1

(ii)

4[15]

7.

(a)

(i)

Working to show first order with respect to [S2O82] (1) Working to show first order with respect to [l] (1) overall equation (1) 3 Consequential

(ii)

Sum of power of the concentration terms (for thio and iodide) in rate equation / number of each species involved up to and including or, in, the ratedetermining step in the reaction mechanism / Sum of the partial / individual orders / general equation of the form [thio]m[iodide]n overall order = m + n (1) 1

(iii)

36 (1) dm3mol 1s1 (1) 2 Consequential on part (i)

(iv)

Rate equation depends on mechanism / rate equation only involves those species in the rate determining step / slowest step (1) 1

(b)

(i)

Colorimetry / conductivity / remove samples and titrate with (standard) sodium thiosulphate solution (1)23

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1 (ii) Constant temperature (1) 1 (iii) Colorimeter / conductivity adv that monitoring is continuous / does not need removal of samples or disadv of titration is problems with timing (1) 1[10]

8.

(a)

(i)

(ii)

Rate of reaction - Rate of decrease / change in concentration of reactants (1) Overall order of a reaction - sum of the powers to which concentration terms are raised in the overall rate equation (1) (The stoichiometric equation includes all the reactants ) the rate equation only includes those species involved in the rate determining step / rate depends on mechanism (1)

2 1

H C 2H5

H C H (1 ) In te rm e d ia te (1 ) H C 2H5 3

C B r

C 2H

5

C

+

C H

3

+

B r

:O H

(b)

(i)

(1 )

3

C O H

CH

3

(ii)

The reaction goes through a planar intermediate and this can be attacked from either side (1) producing an equal mixture of the two optical isomers /racemic mixture / 50-50 mixture (1) Double conc. bromo compound rate double power 1 (1) Treble conc of bromo compound and double cone OH rate only up three times thus not dependant on conc of OH (1) Rate = rate constant [bromoalkane] (1) Must show use of data

2

(iii)

3 3

(c)

After given time remove sample (1) neutralise with nitric acid / quench / stop by adding specified reagent (1) add silver nitrate and observe extent of ppt. / as above and titrate solution with silver nitrate / titrate with specified reagent (1) Allow 1 mark for continuous method based on conductivity or pH

[14]

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9.

(a)

rate = k[A][B] (1) or any other where m+n = 2 rate = k[A] (1) rate = k[B] (1) 3

(b)

(i)

Working to show first order with respect to H2 (1) Working to show second order with respect to NO (1) Overall rate equation (must be consequential) rate k [H2] [NO]2 (1) 3

(ii)

0.02 = k (1.0)(1.0) or correct use of either of the other two rows of data k = 0.02 /1.0 = 0.02 (1) mol-2dm6s1 (1) 2 Consequential on (b)(i)

(c)

Molecules move faster/have more kinetic energy (1) More molecules / collisions have at least Eact (1) Greater proportion/fraction of collisions are successful OR more of the collisions are successful (1) 3

(d) (e)

k increases 1 Catalyst provides an alternative route (1) With a lower activation energy (consequential on first mark) (1) Rate increases because more collisions have enough energy to overcome the lower activation energy (1) [Accept argument based on Arrhenius equation for third mark] 3[15]

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