How Fast? The Rate of Chemical Change (HL IB Chemistry)

In any chemical reaction, the particles will all be moving around in different directions, at different speeds, with different amounts of energy.

A Maxwell-Boltzmann distribution is a graph which shows the distribution of energy amongst particles within a chemical reaction. 

Figure 1 below shows the Maxwell-Boltzmann distribution in a sample of a gas at a fixed temperature, T₁. 

Figure 1

State why a Maxwell-Boltzmann distribution curve always starts at the origin and what the area under the curve represents.

Chemical reactions take place at different speeds. For a chemical reaction to take place, particles must collide with each other in the correct orientation and with sufficient energy. 

Give one reason why a reaction may be slow at room temperature.

State the meaning of the term rate of reaction.

A group of students were completing a practical, investigating the factors which affect the rate of the chemical reaction shown below. 

A (s) + B (aq) → C (g)

The students collected the gas produced and plotted the graph shown in Figure 1. 

Figure 1

Explain why the gradient of the curve in part (b) decreases as the time of the reaction progresses.

Another way to increase the rate of reaction is to increase the temperature. 

Explain why a small increase in temperature has a large effect on the initial rate of a chemical reaction.  

The decomposition of hydrogen peroxide into water and oxygen is a very slow chemical reaction. 

Write the equation for the decomposition of hydrogen peroxide.

The rate of decomposition of hydrogen peroxide can be found by collecting and measuring the volume of gas formed at specific time intervals.

The decomposition of hydrogen peroxide is a slow reaction, so a catalyst is often added to speed up the rate of the reaction. Catalysts are used in many chemical reactions to increase the rate.

The following shows a two-step reaction mechanism of a chemical reaction, where a catalyst, X is used. 

STEP 1:                                  W + X  →  Y + Z

STEP 2:                                  Y + W → Z + A + X

OVERALL REACTION:         2W → 2Z + A

Give a reason, other than the rate of reaction increasing, why it can be deduced from the three equations above that X is a catalyst.

The graph shown below represents the decomposition of hydrogen peroxide.

Figure 1

The graph starts to level out as the reaction slows down.

State why the rate of the reaction slows down over time.  

During the following reaction, A and B react together to produce C. 

A  +  2B  ⇌  C

Figure 1 shows the production of C over time.   

Figure 1

In the reaction in part (a), large pieces of A were used.

Use collision theory to explain what would happen to the rate of the reaction if powdered A was used instead of large pieces.

In a different reaction, gaseous W and X were added together to produce Y and Z as shown in the equation below:

2W (g)  +  X (g)  →  Y (g)  + 2Z (g)

A catalyst was added to speed up the rate of reaction. 

Some changes were made individually to the experiment completed in part (c). 

Consider your Maxwell-Boltzmann distribution curve from part (c). For each of the changes in parts (i), (ii) and (iii) below, state and explain the effect that the change would have on:

• The area under the curve 
• The value of the most probable energy of the molecules (E_mp) 
• The proportion of molecules with energy greater than or equal to E_a
  

The number of molecules in the original reaction mixture is increased, but no other changes are made.

[2] 

A catalyst is added to the original reaction mixture, but no other changes are made.

[2]

Iodine reacts with propanone in an acid catalyzed reaction, according to reaction equation below.  

CH₃COCH₃ (aq) + I₂ (aq) → CH₃COCH₂I (aq) + H⁺ (aq) + I^- (aq)

Suggest how the change in concentration of iodine could be used to determine the rate of the above reaction.  

A group of students completed the iodination of propanone reaction using the same acid catalyst, but with different concentrations. The results achieved are shown in the table below:

Table 1

Use the table to state and explain the relationship between the concentration of acid used in the reaction and the rate.

Sodium thiosulfate and hydrochloric acid will react together readily, as shown by the equation below:

Na₂S₂O₃  +  2HCl  →  2NaCl  +  S  +  SO₂  +  H₂O

This reaction is often referred to as the ‘disappearing cross’ experiment. The cross disappears when viewed from above because the solution turns cloudy as a sulfur precipitate is formed, covering the cross.  

Figure 1

The speed of the reaction can be increased, by raising the temperature of the sodium thiosulfate solution in the reaction. The thiosulfate solution is heated to different temperatures before the acid is added, and the time it takes for the cross to disappear is recorded. The times can then be compared.

Suggest one reason why the value for the rate of reaction when a higher temperature was used may be less accurate than at a lower temperature.

Collision theory can be used to explain why different factors affect the rate of a chemical reaction.

Describe collision theory.

A student carried out a metal displacement reaction between zinc powder and copper(II) sulfate solution. The equation for the reaction is

Zn (s) + CuSO₄ (aq) → ZnSO₄ (aq) + Cu (s)

3.78 g of zinc powder was added to 50.0 cm³ of 0.250 moldm^-3 copper(II) sulfate solution.

Determine the limiting reagent showing your working.

The reaction between the zinc and copper sulfate was carried out in a polystyrene cup and the temperature change was measured using a temperature probe. The maximum temperature rise the student recorded was 8.5 ^oC. 

Using sections 1 and 2 of the data booklet, calculate the enthalpy change, ∆H, for the reaction, in kJ.

Assume that all the heat evolved was absorbed by the solution, and that the density and specific heat capacity of the copper(II) sulfate solution are the same as pure water.

State two further assumptions made in the calculation of ∆H.

Using Figure 1, sketch a graph of the concentration of zinc sulfate, ZnSO₄ (aq), versus time and show how the graph may be used to find the initial rate of reaction.

                                                                  Figure 1

A student investigated the rate of decomposition of hydrogen peroxide, H₂O₂, at a temperature of 45 ^o The decomposition reaction occurs in the presence of a catalyst, MnO₂.

The results she obtained are shown in Table 1 below.

Table 1

Plot a graph on the axes below in Figure 1 and from it determine the rate of reaction after 60 s.

Figure 1

On the same graph sketch the shape obtained if the student had carried out the same reaction at 60 ^oC. Explain the shape of the graph at 60 ^oC.

The decomposition of hydrogen peroxide can be investigated by measuring the volume of oxygen given off using the apparatus shown in Figure 2.

Figure 2

Two students decide to measure the rate of decomposition for H₂O₂ using the change in mass as oxygen escapes from the reaction container.

One student says that they should use a three decimal place rather than two decimal place balance because it will make their results more accurate. The second student disagrees and says it will make their results more precise, but not more accurate.

Which student is correct?

For the reaction below, consider the following experimental data.
 

X (aq) + Y (aq) → Z (aq)

Deduce the order of reaction with respect to X.

Deduce the order of the reaction with respect to Y.

Write the rate expression for the reaction between X and Y.

Determine the rate constant, k, correct to three significant figures and state its units, using data from Experiment 2. 

Explain why the reaction represented below is a redox reaction. 

2ClO₂ (aq) + 2NaOH (aq) → NaClO₃ (aq) + NaClO₂ (aq) + H₂O (l) 

For the reaction below, consider the following experimental data. 

2ClO₂ (aq) + 2OH^- (aq) → ClO₃^- (aq) + ClO₂^- (aq) + H₂O (l)

Deduce the rate expression.

Determine the rate constant, k, and state its units, using data from Experiment 3. 

Calculate the rate when [ClO₂ (aq)] = 3.10 x 10^-2 mol dm^-3 and [OH^- (aq)] = 1.50 x 10^-2 mol dm^-3.

Sketch a graph to show how the rate constant, k, varies with temperature.

The following mechanism is proposed for the reaction where ethanal dimerises in dilute alkaline solution to form 3-hydroxybutanal: 

Step 1: CH₃CHO + :OH^- → :CH₂CHO + H₂O 
Step 2: CH₃CHO + :CH₂CHO → CH₃CH(O:^-)CH₂CHO
Step 3: CH₃CH(O:^-)CH₂CHO + H₂O → CH₃CH(OH)CH₂CHO + :OH^- 

Classify OH^-, CH₂CHO and CH₃CH(O:^-)CH₂CHO as reactant, product, catalyst or intermediate, based on the proposed mechanism.

Using the following information about the proposed mechanism, deduce the rate expression. 

Step 1: CH₃CHO + :OH^- → :CH₂CHO + H₂O                                                slow step
Step 2: CH₃CHO + :CH₂CHO → CH₃CH(O:^-)CH₂CHO                                fast step
Step 3: CH₃CH(O:^-)CH₂CHO + H₂O → CH₃CH(OH)CH₂CHO + :OH^-         fast step

Calculate the initial rate of reaction for experiment 2, if measured under the same conditions.

State the effect, if any, increasing the concentration of a reactant would have on the value of the rate constant, k.

Nitrogen dioxide and carbon monoxide react according to the following equation. 

            NO₂ (g) + CO (g) → NO (g) + CO₂ (g) 

Using the following graph, what is the order with respect to NO₂?

 

The rate expression for the reaction of nitrogen dioxide and carbon monoxide at T < 227 ^OC is: 

            Rate = k [NO₂]² 

Sketch a labelled graph of concentration against time for carbon monoxide.

A student proposed the following single step mechanism for the reaction of nitrogen dioxide and carbon monoxide. 

NO₂ + CO → NO + CO₂         slow 

Rate = k [NO₂]² 

Justify whether the student’s proposed mechanism is correct.

Another student proposed the following mechanism for the reaction of nitrogen dioxide and carbon monoxide. 

Step 1:             NO₂ + NO₂ → NO + NO₃
   Step 2:             NO₃ + 2CO → NO + 2CO₂ 

Rate = k [NO₂]² 

Explain which of the student’s proposed mechanism steps is the rate determining step.

Nitrogen(II) oxide is oxidised according to the following equation. 

2NO (g) + O₂ (g) → 2NO₂ (g) 

The following mechanism is proposed for the two-step oxidation of nitrogen(II) oxide. 

Step 1:             NO (g) + NO (g) → N₂O₂ (g)
   Step 2:             N₂O₂ (g) + O₂ (g) → 2NO₂ (g) 

The potential energy profile for this two-step reaction is shown.

Explain which step is the rate determining step.

Energy profile diagrams give evidence for or against a proposed mechanism or proposed rate expression.

Explain why the following reaction between iodide ions and peroxodisulfate ions has a high activation energy. 

S₂O₈^2- (aq) + 2I^- (aq) → 2SO₄^2- (aq) + I₂ (aq)

Sketch the potential energy diagram for the reaction of iodide ions with peroxodisulfate ions catalysed by iron(II) ions according to the following mechanism. 

2Fe²⁺ (aq) + S₂O₈^2- (aq) → 2Fe³⁺ (aq) + 2SO₄^2- (aq)             slow
2Fe³⁺ (aq) + 2I^- (aq) → 2Fe²⁺ (aq) + I₂ (aq)                             fast

Deduce the rate expression for the reaction of iodide ions with peroxodisulfate ions catalysed by iron(II) ions according to the following mechanism. 

2Fe²⁺ (aq) + S₂O₈^2- (aq) → 2Fe³⁺ (aq) + 2SO₄^2- (aq)             slow
2Fe³⁺ (aq) + 2I^- (aq) → 2Fe²⁺ (aq) + I₂ (aq)                               fast

The decomposition of hydrogen peroxide into water and oxygen occurs at a slow rate with a rate constant of k = 6.62 x 10^-3 mol dm^-3 s^-1 and at a temperature of 290 K. 

Using Sections 1 and 2 of the Data Booklet, calculate the activation energy, E_a, correct to three significant figures and state its units.

The constant, A = 3.18 × 10¹¹ mol⁻¹ dm³.

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
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  at each temperature.

The results of the experiment can be used to calculate the activation energy, E_a. Use the results table to plot a graph of ln k against .

Using Sections 1 and 2 of the Data Booklet and your graph, calculate a value for the activation energy, E_a, for this reaction. To gain full marks you must show all of your working.

The Arrhenius equation can be represented as k = A in its exponential form.

 State the effect on k of an increase in; 

i)     The constant, A, (frequency factor) 

[1]

ii)     Activation energy, E_a 

[1]

iii)    Temperature, T

[1]

Using Sections 1 and 2 of the Data Booklet, calculate the activation energy, E_a, of a reaction at 57 ^oC and a rate constant of 1.30 x 10^-4  mol dm^-3 s^-1.

The constant A = 4.55 × 10¹³.

The table below shows how temperature affects the rate of reaction.

Rate constant k/s-1	ln k	Temperature / K
2.0 x 10-5	-10.8	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

Use the results to plot a labelled graph of ln k against .

Using Sections 1 and 2 of the Data Booklet and your graph, calculate a value for the activation energy, E_a, for this reaction.

Nitrogen dioxide and ozone react according to the following equation. 

            2NO₂ (g) + O₃(g) → N₂O₅ (g) + O₂ (g) 

Experimental data shows the reaction is first order with respect to NO₂ and first order with respect to O₃. 

State the rate expression for the reaction.

At 30°C, the initial rate of reaction is 3.46 × 10⁻³ mol dm⁻³ s⁻¹ when the initial concentration of NO₂ is 0.50 mol dm⁻³ and the initial concentration of O₃ is 0.21 mol dm⁻³.

Calculate a value for the rate constant k at this temperature and state its units.

Using Sections 1 and 2 of the Data Booklet and your answer from part (b), calculate a value for the activation energy of this reaction at 30 °C.

For this reaction ln A = 15.8 mol⁻¹ dm³.

The relationship between the rate constant and temperature is given by the Arrhenius equation, k = A 

State how temperature affects activation energy.

A common relationship exists between temperature and rate. 

What temperature change is associated with a doubling of rate? 

An Arrhenius plot of ln k against  for the reaction between A (g) and B (g) at different temperatures is shown in Figure 1 below.

The equation of the line of best fit was found to be: 

            ln k = -6154 - 8.2 

Calculate the activation energy, E_a, for the reaction between A (g) and B (g).

Define the Arrhenius constant, A.

Using the Arrhenius plot, calculate an approximate value for the constant, A.

The graph of ln k against for a general reaction is shown.

Sketch the expected line for a different reaction with a higher activation energy.

A graph of ln k against  for another general reaction is shown.

Sketch the expected line for the same reaction with an added catalyst.

Rate constant data for the reaction of hydrogen and iodine at two different temperatures is shown in the table below. 

H₂ (g) + I₂ (g) → 2HI (g) 

Table 1

Using Sections 1 and 2 of the Data Booklet, calculate the activation energy, in kJ mol^-1, for the reaction.

Using the data from experiment 1 and Sections 1 and 2 in the Data Booklet, calculate a value for the constant, A.

Table 2

A group of students planned how to investigate the effect of changing the concentration of H₂SO₄ on the initial rate of reaction with magnesium: 

Mg (s) + H₂SO₄ (aq) MgSO₄ (aq) + H₂ (g) 

They decided to measure how long the reaction took to complete when similar masses of magnesium were added to acid. 

Two methods were suggested:

Method 1 - Use small pieces of magnesium ribbon, an excess of acid and record the time taken for the magnesium ribbon to disappear

Method 2 - Use large strips of magnesium ribbon, an excess of magnesium and record the time taken for bubbles to stop forming 

Deduce, giving a reason, which of method 1 and method 2 would be the least affected if the masses of magnesium ribbon used varied slightly between each experiment.

Neither method in part a) actually allows the initial rate to be calculated. Outline a method that would allow the calculation of initial rate.

The reaction is to be conducted across a few weeks.

State a factor that has a significant effect on reaction rate, which could vary between experiments across the weeks and therefore needs to be controlled.

One group collected the following data using 1.50 mol dm^-3 acid:

Trial	Time/ s ( 0.01 s)
1	91.56
2	98.33
3	72.08
4	89.41

When investigating the reaction between sulfuric acid and calcium carbonate, it was observed that a small increase of temperature of around 10 ^oC caused a doubling in the rate of the reaction.

Sketch and label Maxwell-Boltzmann curve for the two temperatures T and T+10, and use this diagram to help to explain this effect of temperature on rate.

Identify and explain another factor that affects the number of particles present in a solution with sufficient energy to react.

Some groups investigating the effect of temperature on rate stirred their reactions, some did not.

Explain the effect of stirring upon the rate of the reaction.

0.5 g of magnesium reacts with 50 cm³ of 0.01 moldm^-3 nitric acid. Magnesium is in excess.

A graph monitoring the volume of hydrogen gas produced is shown below:

Compare the expected rate and progress of the reaction if 25 cm³ of 0.2 mol dm^-3 nitric acid was used instead of 50 cm³ of 0.1 mol dm^-3 nitric acid.

Suggest one change to the reaction that could be made to produce more hydrogen gas in total and explain your choice.

Suggest why it is often better to study a slower reaction instead of a faster one.

The following energy profile diagram shows the pathways for both a catalysed and uncatalysed reversible reaction:

Identify the letter(s) representing the activation energy for the catalysed reverse reaction.

State and explain the effect that this catalyst will have on the equilibrium yield.

Vehicles with combustion engines usually have catalytic convertors added to catalyse the oxidation of carbon monoxide into carbon dioxide and to catalyse the reduction of nitrogen oxides to nitrogen. These catalysts are usually rhodium or platinum.

Leaded fuels were phased out as they were found to poison these catalysts, binding irreversibly to the metal surface.

Explain the problems for drivers of the catalysts being poisoned.

Suggest a situation in which using a catalyst would not be appropriate.

The conversion of hydrogen and iodine into hydrogen iodide proceeds via a three step reaction mechanism:

1. I₂ (g)   2I (g)                   fast
2. H₂ (g) + I (g)  H₂I (g)      fast
3. H₂I (g) + I (g) → 2HI (g)    slow

Write the rate equation for this reaction and show how the mechanism is consistent with the stoichiometric equation.

An investigation into the rate of reaction between hydrogen and iodine was carried out at 298 K and the data obtained is shown below.

Determine the rate equation for the reaction and justify your answer.

Calculate the rate constant using Expt 2 data, including its units.

Using section 12 of the Data booklet, determine whether the forward reaction is favoured by an increase in temperature.

The reaction between iodide ions and persulfate ions is a 'clock' reaction and often used to study reaction kinetics.

2I^- (aq) + S₂O₈^2- (aq) → I₂ (aq) + 2SO₄^2- (aq)

Deduce the redox changes taking place in the reaction.

A persulfate-iodide clock reaction was studied and the following rate data obtained.

Deduce the order with respect to persulfate ions and iodide ions.

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

Four mechanisms are proposed for the persulfate-iodide reaction. Deduce which mechanism(s) is/are consistent with the rate equation in part c) and justify your answer.

Mechanism 1:

1. I^- (aq) + I^- (aq) → I₂^2- (aq)                                         slow
2.  I₂^2- (aq) + S₂O₈^2- (aq) → I₂ (aq) + 2SO₄^2- (aq)    fast

Mechanism 2:

1. I^- (aq) + S₂O₈^2- (aq) → S₂O₈I^3- (aq)                     slow
2.  S₂O₈I^3- (aq) + I^- (aq) → I₂ (aq) + 2SO₄^2- (aq)    fast

Mechanism 3:

1. I^- (aq) + S₂O₈^2- (aq)  → S₂O₈I^3- (aq)                    fast
2.  S₂O₈I^3- (aq) + I^- (aq) → I₂ (aq) + 2SO₄^2- (aq)    slow

Mechanism 4:

1.  2I^- (aq) + S₂O₈^2- (aq) → I₂ (aq) + 2SO₄^2- (aq)    slow

The reaction between nitrogen monoxide and hydrogen produces nitrogen and water:

2NO (g) + 2H₂ (g) →  N₂ (g) + 2H₂O (g)

Rate data for this reaction is shown below.

What is the molecularity of the reaction?

Draw a sketch graphs of:

Suggest a possible mechanism for the reaction.

Suggest a Lewis structure for N₂O₂ and draw the shape of the molecule.