Rates, Orders & Arrhenius (OCR A Level Chemistry)

Exam Questions

3 hours30 questions
1a3 marks

The rate equation for the reaction between reactants X, Y and Z is shown below.

rate = k [X]2 [Y]

State the orders with respect to X, Y and Z.

1b1 mark

What is the overall order of this reaction?

1c
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3 marks

The rate of reaction is 3.72 x 10-5 mol dm-3 s-1 when the

  • concentration of X is 0.01 mol dm-3
  • concentration of Y is 0.02 mol dm-3
  • concentration of Z is 0.04 mol dm-3

Calculate the rate constant, k, for this reaction, including the units.

1d
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2 marks

The experiment was repeated but the initial concentration of X was doubled, all other concentrations remained the same.

State what the effect would be on the rate of reaction.

Explain your answer.

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2a1 mark

Bromide ions and bromate(V) ions react in acidic conditions to form aqueous bromine in the following equation.

5Br (aq) + BrO3 (aq) + 6H+ (aq) → 3Br2 (aq) + 3H2O (l)

A series of experiments was carried out at a given temperature to find the rate equation for the reaction.

The results from experiments using different hydrogen ion concentrations are shown in the graph below.

reaction-rate-h

Use the information in the graph to determine the order of reaction with respect to hydrogen ions.

2b1 mark

Experiments using different bromide concentrations showed that the order of reaction with respect to bromide ions was first order. 

On the graph below, sketch a graph to show how the concentration of bromide ions would change during the course of a reaction.

conc-time-graph-br--blank

2c2 marks

Overall, the reaction between bromide ions and bromate(V) ions in acidic conditions is fourth order.

i)
Deduce the order with respect to bromate(V) ions.

ii)
Using your answer to part (a), write the rate equation for the reaction.
2d2 marks

Bromide ions and bromate(V) ions react in acidic conditions to form aqueous bromine in the following equation.

5Br (aq) + BrO3 (aq) + 6H+ (aq) → 3Br2 (aq) + 3H2O (l)

i)
Using your answer to part (c), write an expression for the rate constant for the reaction between bromide ions and bromate(V) ions in acidic conditions.

ii)
Suggest suitable units for the rate constant.

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3a1 mark

Hydrogen peroxide, H2O2, is a colourless liquid. It is widely used in cosmetic and medical products. It is an effective disinfectant and bleaching agent.

Hydrogen peroxide is unstable and will decompose slowly to form water and oxygen. The rate of decomposition can be increased using manganese(IV) oxide as a catalyst.



2H2O2 (aq) → 2H2O (l) + O2 (g)

The graph below shows how hydrogen peroxide decomposes in the presence of manganese(IV) oxide.

5-1_q3a-ocr-a-as--a-level-easy-sq

What is meant by the half-life of a reaction?

3b
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3 marks

Use the graph to show that this reaction is first order with respect to hydrogen peroxide. 

Deduce the rate equation of the reaction.

3c
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4 marks

Using the graph, determine

i)
the rate of reaction, in mol dm-3 s-1, at 100 seconds.

ii)
the rate constant for this reaction. State the units.

Your answer must show full working on the graph.
3d1 mark

If the initial concentration of hydrogen peroxide was halved, what would be the effect on the half-life of this reaction?

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4a1 mark

In the presence of an acid, aqueous bromate(V) ions, BrO3- (aq), react with aqueous bromide ions, Br- (aq), to produce bromine, Br2 (aq).

5Br- (aq) + BrO3- (aq) + 6H+ (aq) → 3Br2 (aq) + 3H2O (l)

A student carried out an initial rates investigation on the reaction.

What is meant by the initial rate of reaction? 

4b3 marks

The rate equation for the reaction is

rate = k [Br- (aq)]2 [BrO3- (aq)] [H+ (aq)]2 

i)
What is the overall order of the reaction?

ii)
Suggest two reasons why it is unlikely that this reaction would take place in one step?
4c1 mark

A proposed rate-determining step for the reaction is shown below. 

2Br- (aq) + BrO3- (aq) + 2H+ (aq) → Br2 (aq) + H2O (l) + BrO2 (aq) 

Why is this not correct?

4d1 mark

Aqueous bromine is an orange solution and bromide ions are colourless in solution.

Suggest a suitable method of how the rate of reaction could be investigated.

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5a4 marks

The rate constant can be calculated using the Arrhenius equation, shown below.

                    k space equals space A e to the power of bevelled fraction numerator negative E subscript a over denominator R T end fraction end exponent

State what each of the following terms represents. Include units if appropriate.

  • A
  • Ea
  • T

5b1 mark

Rearrange the Arrhenius equation as shown in part (a) to calculate A.

5c3 marks

The Arrhenius equation can also be expressed in a logarithmic form as shown by the equation below.

ln space k space equals space ln space A space minus space fraction numerator E subscript a over denominator R T end fraction

When ln k is plotted against 1 over T, a downward straight line graph is produced which obeys the equation y = mx + c.

Complete the table below to show how the terms from the logarithmic Arrhenius equation relate to the equation of a straight line.

Straight line equation term Arrhenius equation term
y ln k
m  
x  
c  

5d3 marks

A graph of ln k against 1 over T is shown below.

in-k-v-t-1

i)
Calculate the gradient of the straight line.

ii)

Calculate the activation energy, Ea

The gas constant R = 8.314 J K-1 mol-1

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1a4 marks

Two compounds, X and Y, were reacted together. 

The initial rate of reaction when compound X and compound Y were reacted together was measured in a series of experiments. 

The temperature was kept constant and the results of the experiments are shown below.

Expt.

Initial [X] / mol dm-3

Initial [Y] / mol dm-3

Initial rate / mol dm-3 s-1

1

0.030

0.040

4.0 x 10-4

2

0.045

0.040

6.0 x 10-4

3

0.045

0.060

9.0 x 10-4

4

0.060

0.120

2.4 × 10-3

i)
Use the data in the table to deduce the order of reaction with respect to X.

ii)
State the order of the reaction with respect to Y.

iii)
Determine the overall order of the reaction.

iv)
Write the rate equation for the reaction.
1b
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5 marks

The results from three different experiments, carried out at a constant temperature, to investigate the rate of reaction between compounds A and B in a different chemical reaction are shown. 

A + B → Products 

Expt. 

Initial concentration of A / mol dm-3

Initial concentration of B / mol dm-3

Initial rate / mol dm-3 s-1

1

0.50

0.30

7.6 x 10-4

2

0.25

0.30

1.9 x 10-4

3

0.25

0.60

3.8 x 10-4

Use the data to calculate a value for the rate constant, k.

1c2 marks

An overall rate equation is given below.

Rate = k[P][Q]2 

i)
State what the units would be of the rate constant, k, in this reaction.

ii)
State the overall order of the reaction above.
1d
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3 marks

Chemists measured the rate of a chemical reaction in a series of experiments between compounds C and D at a fixed temperature as shown below.

Experiment

Initial concentration of C / mol dm-3

Initial concentration of D / mol dm-3

Initial rate
/ mol dm-3 s-1

1

0.13

0.12

0.32 x 10-3

2

0.39

0.12

2.88 x 10-3

3

0.78

0.24

11.52 x 10-3

i)
Deduce the order of the reaction with respect to C.

ii)
Deduce the order of the reaction with respect to D.

iii)
Write the overall rate equation for this reaction.

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2a
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5 marks

Chemists can use kinetic studies to help suggest mechanisms for reactions. 

The following data was obtained by reacting compounds A and B together in a series of experiments at a constant temperature.

Experiment

Initial [A]

 / mol dm-3

Initial [B] 

/ mol dm-3

Initial rate 

/ mol dm-3 s-1

1

0.14

0.22

0.26 x 10-3

2

0.42

0.22

2.34 x 10-3

3

0.84

0.44

9.36 x 10-3

i)
Show how the data in the table can be used to deduce that the reaction is second-order with respect to A.

ii)
Deduce the order with respect to B.

iii)
Calculate the value for the rate constant, k. State units in your answer.
2b
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4 marks

The set of data below was obtained from a series of experiments reacting compounds X and Y together at a fixed temperature. The rate equation for this reaction is:

Rate = k [X]2 [Y]

Experiment

Initial concentration of X / mol dm-3

Initial concentration of Y / mol dm-3

Initial rate 

/ mol dm-3 s-1

1

0.85

1.70

9.30 x 10-5

2

0.30

0.15

To be calculated

i)
Use the data from experiment 1 to calculate the value for the rate constant, k and state the units.

ii)
Using the rate constant k from part (i), calculate the initial rate of the reaction for experiment 2. 

(If you have been unable to calculate and answer for (i), you may assume a value of 6.10 x 10-5. This is not the correct answer.)

2c
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4 marks

The rate of reaction data between nitrogen monoxide (NO) and oxygen (O2) was obtained across a series of experiments at a constant temperature, as shown below. 

The rate equation for this reaction is:

Rate = k [NO]2[O2]

Experiment

Initial concentration of O2 / mol dm-3

Initial concentration of NO / mol dm-3

Initial rate 

/ mol dm-3 s-1

1

1.0 x 10-2

5.0 x 10-2

6.5 x 10-4

2

3.4 x 10-2

6.4 x 10-2

To be calculated

i)
Use the data for Experiment 1, calculate the value for the rate constant k at this temperature and state its units.

ii)
Calculate the value for the initial rate in Experiment 2.
2d
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5 marks

Nitrogen dioxide reacts with carbon monoxide at 100 ℃ to form nitrogen monoxide and carbon dioxide, as shown in the equation below.

2NO2 (g) + CO (g) → NO (g) + CO2 (g)

The initial rate of reaction was measured in a series of experiments at a constant pressure. The rate equation below was determined.

Rate = k [NO2]2

An incomplete table of data for the reaction between NO2 and CO is shown.

Experiment

Initial concentration of NO2 / mol dm-3

Initial concentration of CO / mol dm-3

Initial rate 

/ mol dm-3 s-1

1

4.1 x 10-2

2.8  x 10-3

3.3  x 10-5

2

7.8  x 10-3

2.8  x 10-3

 

3

 

5.6  x 10-3

1.8  x 10-4

i)
Use the data from Experiment 1 to calculate a value for the rate constant, k, at this temperature. State its units.

ii)
Use your value of k from (i) to complete the table for the reaction between NO2 and CO. (If you have been unable to calculate and answer for (i), you may assume a value of 2.3. This is not the correct answer.)

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3a2 marks

For this question look at Figure below.

rate-constant-and-temp-relationship

i)
Identify which of the graphs A, B, C or D shows how the rate constant, k, varies with temperature.

ii)
State the effect, if any, increasing the concentration of a reactant would have on the value of the rate constant, k.
3b3 marks

Compound X and Y react together in the following equation.

X + 4Y → XY4

The rate equation for this reaction is below.

rate = k[X][Y]2

A possible mechanism for this reaction is

   Step 1    X + 2Y → XY2

   Step 2    XY2 + Y → XY3

   Step 3    XY3 + Y → XY4

i)
State the overall order for this reaction.

ii)
Deduce which one of the three steps is the rate determining step. Give reasons for your answer.
3c5 marks

Chemists studied the rate of reaction of ethanal dimerises in dilute alkaline solution to form 3-hydroxybutanal in the following equation at a constant temperature of 298K.

2CH3CHO → CH3CH(OH)CH2CHO      Rate = k[CH3CHO][:OH]

Initial concentration of ethanal / mol dm-3

Initial concentration of sodium hydroxide / mol dm-3

Initial rate / mol dm-3 s-1

0.15

0.025

2.7 x 10-3

i)
Use the data from the table to calculate a value for the rate constant k and state its units.

The following three step mechanism for this reaction has been suggested.

    1. CH3CHO + :OH → :CH2CHO + H2O
    2. CH3CHO + :CH2CHO → CH3CH(O:)CH2CHO
    3. CH3CH(O:)CH2CHO + H2O → CH3CH(OH)CH2CHO + :OH
ii)
Using the rate equation, predict which of these steps is the rate-determining step and explain why.
3d4 marks

Iodide ions, I-, react with S2O82- ions as shown in the equation below.

2I-(aq) + S2O82- (aq) → I2(aq) + 2SO42-(aq)

A student investigates the rate of this reaction using the initial rates method.

The student measures the time taken for a certain amount of iodine to be produced.

Outline a series of experiments that the student could have carried out using the initial rates method.

How could the results be used to show the reaction is first order with respect to both I- and S2O82- ? In your answer you should make clear how the results are related to the initial rates.

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4a3 marks

The Arrhenius equation can be represented as kA e to the power of negative fraction numerator E subscript a over denominator R T end fraction end exponent  in its exponential form. 

State the effect on k of an increase in;

i)
The Arrhenius constant, A, (frequency factor)

ii)
Activation energy, Ea

iii)
Temperature, T
4b
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2 marks

Hydrogen peroxide decomposes to form water and oxygen as shown in the equation below.

2H2O2 (aq) → 2H2O (l) + O2 (g)

The table  below shows the value of the rate constant at different temperatures for a reaction.

Rate constant k / s-1

ln k

Temperature / K

1 over T

0.000493

 

295

 

0.000656

 

298

 

0.001400

 

305

 

0.002360

 

310

 

0.006120

 

320

 

Complete the table by calculating the values of ln k and 1 over italic Tat each temperature.

4c
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6 marks

The Arrhenius equation when expressed as a logarithmic relationship is as follows: 

ln space k space equals space minus fraction numerator E subscript a over denominator R T end fraction space plus space ln A

i)
Using your results from part (b) plot a graph of ln k against 1 over italic T

ii)

Use your graph to calculate a value for the activation energy, in kJ mol−1, for this reaction. To gain full marks you must show all of your working.

The gas constant R = 8.31 J K−1 mol−1

blank-arrhenius-plot

4d
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7 marks

The table below shows a series of experiments carried out to investigate how temperature affects the rate of reaction

Rate constant k / s-1

ln k

Temperature / K

1 over T

3.1 x 10-5

-10.4

278

0.00360

4.7 x 10-4

-7.7

298

0.00336

1.7 x 10-3

-6.4

308

0.00325

5.2 x 10-3

-5.3

318

0.00314

The logarithmic form of the Arrhenius equation is:

ln k =-(Ea / RT) + ln A

i)
Use the completed set of results above, to plot a labelled graph of ln k against 1 over italic T

ii)
Use your graph to calculate a value for the activation energy, in kJ mol−1, for this reaction. The gas constant R = 8.31 J K−1 mol−1. 

blank-plot

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5a3 marks

Methanoic acid and bromine react as in the equation below.

Br2(aq) + HCOOH(aq) → 2H+(aq) + 2Br-(aq) + CO2(g)

A student investigates the rate of this reaction by monitoring the concentration of bromine over time. The student uses a large excess of HCOOH to ensure that the order with respect to HCOOH will be effectively zero.

From the experimental results, the student plots the graph below.

q5a-in-question

i)
Suggest how the concentration of bromine could have been monitored.

ii)
Suggest a different experimental method that would allow the rate of this reaction to be followed over time.

iii)
Why would use of excess HCOOH ensure that the order of reaction with respect to HCOOH is effectively zero.
5b
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6 marks

Using the graph, determine

i)
the initial rate of reaction

ii)
the rate constant.


Your answer must show full working using the graph and the lines below as appropriate.

5c
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3 marks

A student investigates the reaction between iodine, I2, and propanone (CH3)2CO,  in the presence of aqueous hydrochloric acid, HCl(aq).

The results of the investigation are shown below.

Rate concentration graph

rate-concentration-graph-for-iodine

Results of initial rates experiments

Experiment

[(CH3)2CO (aq)] / mol dm-3 [HCl (aq)] / mol dm-3 initial rate / mol dm-3 s-1
1` 1.50 x 10-3 2.00 x 10-2 2.1 x 10-9
2 3.00 x 10-3 2.00 x 10-2 4.2 x 10-9
3 3.00 x 10-3 5.00 x 10-2 1.05 x 10-8

Determine the orders with respect to I2,  (CH3)2CO and HCl.

You must explain your reasoning.

5d2 marks

The student then investigates the reaction of hydrogen, H2 and iodine monochloride, ICl.

The equation for this reaction is shown below.

H2 (g) + 2ICl (g) → 2HCl (g) + I2 (g)

The rate equation for this reaction is shown below.

rate = k [H2 (g)] [ICl (g)]

Predict a possible two step mechanism for this reaction. The first step should be the rate determining step.

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1a
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4 marks

In the presence of acid, H+(aq), chlorine and propanone react together:

CH3COCH3 (aq) + Cl2 (aq) → CH3COCH2Cl (aq) + HCl (aq)

A student carried out an investigation into the kinetics of this reaction.

The student investigated how different concentrations of chlorine affect the initial rate of the reaction. A graph of [Cl2 (aq)] against time is shown below:

5-1_q1a-ocr-a-as--a-level-hard-sq

The student then investigated how different concentrations of propanone and H+(aq) affect the initial rate of reaction.

Their results are shown below.

Experiment  [Cl2 (aq)]
/ mol dm-3
 [CH3COCH3 (aq)]
/ mol dm-3
 [H+(aq)]
/ mol dm-3
Inital rate
/ mol dm-3 s-1
1 0.003 0.75 0.05 0.18 x 10-5
2 0.003 1.50 0.15 1.08 x 10-5
3 0.003 1.50 0.30 2.16 x 10-5

Use the student's results to determine the reaction orders. Explain your answer.

1b
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4 marks

Deduce the rate equation and calculate the rate constant for this reaction, including the units.

1c
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1 mark

The student varied the concentrations of the reactants in another experiment and they found the rate to be 0.26 x 10-5 mol dm-3 s-1. They also used a pH probe and found that the reaction mixture had a pH of 2.

What would the initial rate of the reaction mixture be if the amount of acid added was altered to give a pH of 1?

Assume the temperature and the initial concentrations of the other reactants remained the same.

1d2 marks

The experiment was repeated at a lower temperature. What would be the effect, if any, of this change on the rate and the rate constant of the reaction?

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2a1 mark

Clock reactions can be used to obtain the initial rate of a reaction by taking a single measurement instead of continuous measurements.

The time taken for a visual change to occur is timed and the initial rate is taken to be proportional to begin mathsize 14px style 1 over t end style.

What assumption is made so that the initial rate can be taken to be proportional to begin mathsize 14px style 1 over t end style?

2b2 marks

A student investigates the reaction of hydrogen peroxide, H2O2, and iodide ions in the presence of an acid.

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

Thiosulfate ions, S2O32-, are added to the reaction which react with iodine forming tetrathionate ions, S4O62-.

2S2O32- (aq) + I2 (aq) → S4O62- (aq) + 2I- (aq)

Starch solution is also added.

Explain how the addition of thiosulfate ions and starch solution enables a measurement of the time taken for a colour change to occur.

2c
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4 marks

A student carried out a series of experiments to investigate the reaction of hydrogen peroxide with iodide ions in the presence of an acid.

In the first series of experiments, the students varied the concentration of hydrogen peroxide with the same concentrations and volumes of iodide ions and acid. Their results are shown in the table below.

[H2O2 (aq)] / mol dm-3 s-1 Time / s begin mathsize 14px style 1 over t end style / s-1
0.020 259  
0.040 125  
0.060 78  
0.080 59  
0.100 48  

Complete the table and use the data to plot a graph of 1 over t against concentration of hydrogen peroxide on the graph below using the results in the table. You should draw a line of best fit.

5-1-q2d-blank-graph

2d3 marks

In the second series of experiments, different concentration of iodide ions were used with the same concentrations and volumes of hydrogen peroxide and acid.

In the final series of experiments, different concentrations of acid were used with the same concentrations and volumes of hydrogen peroxide and iodide ions.

Graphs of begin mathsize 14px style 1 over t end style against concentration are plotted for these two series of experiments below.


5-1_q2d-ocr-a-as--a-level-hard-sq

Use your graph from part (c) and the two graphs above to deduce the rate equation for the reaction.

2e2 marks

Explain what evidence there is that the reaction takes place in more than one step.

2f3 marks

Deduce a possible three-step mechanism for this reaction. Assume the first step is the rate-determining step.

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3a1 mark

Nitrogen monoxide, NO, reacts with oxygen, O2. The rate equation for this reaction is shown below.

rate = k[NO(g)]2[O2(g)]

State what would happen to the rate of the reaction if the initial concentration of NO is tripled and the initial concentration of O2 is halved.

3b2 marks

Nitrogen monoxide is produced by combustion in car engines and released into the atmosphere. 

In the lower atmosphere, nitrogen monoxide is responsible for the formation of ozone in a series of reactions shown below.

NO (g) + ½O2 (g) → NO2 (g)

NO2 (g) → NO (g) + O (g)

O2 (g) + O (g) → O3 (g)

i)
What is the overall equation for this series of reactions?

ii)
Explain why NO is acting as a catalyst in this reaction.
3c3 marks

When nitrogen monoxide is present in the upper atmosphere, is it involved in the removal of ozone, O3. The overall equation for the reaction is shown below.

O (g) + O3 (g) → 2O2 (g)

The rate equation is:   rate = k[NO(g)][O3(g)]

i)
How does this show that the mechanism contains more than one step?

ii)
Deduce a possible two-step mechanism for this reaction.

3d2 marks

Ozone in the lower atmosphere can react with ethene to produce methanal, CH2O (g) which contributes to low-level smog. The equation is shown below.

O3 (g) + C2H4 (g) → 2CH2O (g) + ½O2 (g)

The order of the reaction with respect to both reactants is first order. The initial rate of formation of methanal was found to be 2.0 x 10-11 mol dm-3 s-1.

The initial concentration of ozone was doubled and the initial concentration of ethene was tripled.

Calculate the initial rate of oxygen formation.

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4a2 marks

Bromate(V) ions and bromide ions react in the presence of acid to form bromine and water.

Write the half equations and overall balanced symbol equation, including state symbols, for this reaction.

4b
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3 marks

A  student carried out a series of experiments to investigate how the rate of the reaction of bromate and bromide in the presence of an acid varies with temperature.

The time taken, t, was measured for a fixed amount of bromine to form at different temperatures. The results are shown in the table below.

Temperature (T ) / K bold 1 over bold T bold space bold cross times bold space bold 10 to the power of bold minus bold 3 end exponent / K-1 Time (t ) / s begin mathsize 14px style bold 1 over bold t end style / s-1 ln bold 1 over bold t
408 2.451 21.14 0.0473 -3.051
428   10.57 0.0946 -2.358
448 2.232 5.54    
468 2.137     -1.106
488 2.049 1.71 0.5851 -0.536

Calculate the missing values to complete the table above.

4c4 marks

The Arrhenius equation relates the rate constant, k, to the activation energy, Ea, and temperature, T.

ln k = ln Abegin mathsize 14px style fraction numerator negative E subscript straight a over denominator R T end fraction end style

In this experiment, the rate constant, k, is directly proportional to begin mathsize 14px style 1 over t end style. Therefore, 

ln space 1 over t space equals space ln space A space plus space fraction numerator negative E subscript straight a over denominator R T end fraction

Use your answers from part (b) to plot a graph of ln begin mathsize 14px style 1 over t end style against begin mathsize 14px style 1 over T end style x 10-3 on the graph below.

q4c_rate-equations_structured_hard_a_level_aqa_chemistry-2

4d
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4 marks

Use your graph and information from part (c) to calculate a value for the activation energy, in kJ mol–1, for this reaction. To gain full marks you must show all of your working. 

The value of the gas constant, R = 8.314 J K–1 mol–1

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5a3 marks

Three experiments were carried out at 20 oC to investigate the rate of the reaction between compounds F and G. The results are shown in the table below.

  Experiment 1 Experiment 2 Experiment 3
Initial concentration of F / mol dm-3 1.71 x 10-2 5.34 x 10-2 7.62 x 10-2
Initial concentration of G / mol dm-3 3.95 x 10-2 6.24 x 10-2 3.95 x 10-2
Initial rate / mol dm-3 s-1 3.76 x 10-3 1.85 x 10-2 1.68 x 10-2

Use the data in the table to deduce the rate equation for the reaction between F and G.

5b2 marks

F and G react together to form FG2 according to the following two step mechanism.

   Step 1: F + G → FG

   Step 2: FG + G → FG2

Using your answer to part (a), explain which step is the rate-determining step.

5c2 marks

Use the information in the table in part (a) to calculate a value for the rate constant, k, for this reaction between 0.0534 mol dm-3 F and 0.0624 mol dm-3 G

Give your answer to the appropriate number of significant figures.

State the units for k.

5d3 marks

The Arrhenius equation shows how the rate constant, k, for a reaction varies with temperature, T.

k = Ae-Ea/RT

For the reaction between 0.0534 mol dm-3 F and 0.0624 mol dm-3 G at 25 °C, the activation energy, Ea, is 16.7 kJ mol–1

Use your answer to part (c) to calculate a value for the Arrhenius constant, A, for this reaction. 

The gas constant R = 8.314 J K–1 mol–1Give your answer to the appropriate number of significant figures.

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