How Fast? The Rate of Chemical Change (DP IB Chemistry: HL): Exam Questions

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

i) Label the x and y axes of the graph.

[2]

ii) Sketch a distribution for this same sample of gas, at a higher temperature, and label it as T₂.

[2]

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. 

i) Explain why most collisions between particles in the gas phase do not result in a reaction taking place.

[1]

ii) State and explain one way that the rate of reaction could be increased, other than by increasing the temperature.

[2]

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

A student investigates the reaction between solid A and aqueous solution B:

A (s) + B (aq) → C (g)

In the first experiment, B was the limiting reagent. The volume of gas C was collected over time, as shown by the solid line in the graph below.

Define the term rate of reaction.

Explain what is indicated by the horizontal section of the graph, labelled R.

On the graph, sketch the curve that would be obtained if the experiment were repeated using double the concentration of solution B, with all other conditions kept the same.

Explain why the gradient of the original curve decreases over time.

Explain, using collision theory, why a small increase in temperature has a large effect on the rate of reaction.

The rate of the slow decomposition of aqueous hydrogen peroxide can be investigated by measuring the volume of oxygen gas produced over time. A catalyst, such as manganese(IV) oxide, is often used.

Write the balanced chemical equation for the decomposition of hydrogen peroxide.

Draw a labelled diagram of the assembled apparatus suitable for collecting and measuring the volume of oxygen produced at regular time intervals. 

Explain how the initial rate of reaction could be determined from the experimental results

The graph shown below represents the decomposition of hydrogen peroxide.

Figure 1

Explain why the rate of reaction decreases as the reaction proceeds.

A proposed two-step mechanism for the acid-catalysed decomposition is shown below:

Step 1: H₂O₂ (aq) + H⁺ (aq) → H₃O₂⁺ (aq)

Step 2: H₃O₂⁺ (aq) + H₂O₂ (aq) → 2H₂O (l) + O₂ (g) + H⁺ (aq)

From the mechanism, identify the catalyst and the intermediate, giving a reason for each choice.

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

i) Sketch a graph to show what happens to A and B during the progress of the reaction. 

[1]

ii) On your graph, label the point at which an equilibrium is first established the letter E. 

[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. 

i) Sketch a Maxwell-Boltzmann distribution on the axes below in Figure 2 to show the distribution of molecular energies at a constant temperature with and without a catalyst.

Use E_a to label the activation energy without a catalyst and E_c to label the activation energy with a catalyst.

[3]

Figure 2

ii) Explain what your distribution shows.

[3]

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

i) The temperature of the original reaction is increased, but no other changes are made.

[2] 

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

[2] 

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

[2]

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.

On the axes below, 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.

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.

2H₂O₂ (aq)  O₂ (g) + 2H₂O (l) 

The results she obtained are shown in the below.

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

i) On the same graph, sketch the shape obtained if the student had carried out the same reaction at 60 ^oC.

[1]

ii) Explain the shape of the graph at 60 ^oC.

[2]

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

i) Explain why the volume of oxygen given off can be used as a measure of the concentration of hydrogen peroxide. 

[1]

ii) Suggest one limitation of using the apparatus used.

[1]

iii) Suggest an alternative method of measuring the rate of reaction.

[1]

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.

The reaction between nitrogen dioxide and carbon monoxide is:

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

A graph of the concentration of NO₂ versus time for this reaction is shown.

 Deduce the order of reaction with respect to NO₂.

The experimentally determined rate expression is: 

            Rate = k [NO₂]² 

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

A student proposes that the reaction occurs in a single elementary step:

NO₂ + CO → NO + CO₂

Justify whether this proposed one-step mechanism is consistent with the experimental rate expression.

Another student proposes a two-step mechanism:

Step 1:             NO₂ + NO₂ → NO + NO₃    

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

Explain which of these steps must be the rate-determining step to be consistent with the experimental rate expression.

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.

i) Explain why the rate expression for the oxidation of nitrogen(II) oxide is not rate = k [N₂O₂] [O₂].

[2]

ii) Deduce the rate expression for the oxidation of nitrogen(II) oxide.

[1]

The reaction between iodide ions and persulfate ions in solution is kinetically slow.

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

Explain, in terms of electrostatic forces, why this reaction has a high activation energy.

The reaction can be catalysed by iron(II) ions via the following two-step mechanism:

Step 1: 2Fe²⁺ (aq) + S₂O₈^2- (aq) → 2Fe³⁺ (aq) + 2SO₄^2- (aq)   (slow)

Step 2: 2Fe³⁺ (aq) + 2I^- (aq) → 2Fe²⁺ (aq) + I₂ (aq) (fast)

On the axes below, sketch a labelled potential energy profile for this catalyzed, two-step reaction. The overall reaction is exothermic.

Deduce the rate expression for the catalyzed reaction that is consistent with the proposed mechanism.

A student is investigating the kinetics of the decomposition of hydrogen peroxide, a reaction known to be first-order.

2H₂O₂ (aq) → 2H₂O (l) + O₂ (g)

In a single experiment at 290 K, the student determines the rate constant to be k = 6.62 x 10^-3 s^-1. 

The Arrhenius constant, A, for this reaction is 3.18 × 10¹¹ s^-1.

Using sections 1 and 2 of the data booklet, calculate a preliminary value for the activation energy, E_a. Give your answer to three significant figures.

To determine a more accurate value for the activation energy, the student measures the rate constant at five different temperatures. The data is shown in the table below.

Complete the table by calculating the values of ln k and  needed for an Arrhenius plot.

Plot a graph of ln k against  on the grid provided. Draw a line of best fit.

Using section 2 of the data booklet and your graph, determine a more accurate value for the activation energy, E_a, for this reaction.

The Arrhenius equation, k = A, relates the rate constant of a reaction to temperature and the activation energy.

State the effect on the value of the rate constant, k, of an increase in:

i)     The constant, A, (frequency factor) 

[1]

ii)     Activation energy, E_a 

[1]

iii)    Temperature, T

[1]

A student investigates the kinetics of a first-order reaction. In a preliminary experiment at 57 ^oC, the student determines the rate constant to be k = 1.30 x 10^-4 s^-1. 

The Arrhenius constant, A, for this reaction is 4.55 × 10¹³ s^-1.

Using sections 1 and 2 of the data booklet, calculate a value for the activation energy, E_a. Give your answer to three significant figures.

To determine a more accurate value for the activation energy, the student measures the rate constant at four different temperatures. The student's completed table is shown below.

Plot a graph of ln k against  on the grid provided. Draw a line of best fit.

Using section 2 of the data booklet and your graph, determine a more accurate value for the activation energy, E_a, for this reaction.

The reaction between nitrogen dioxide and ozone is first order with respect to both reactants. The overall equation is:

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

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 [NO₂] is 0.50 mol dm⁻³ and [O₃] is 0.21 mol dm⁻³.

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

For this reaction, the value of ln A is 15.8.

Using your answer from part (b) and sections 1 and 2 of the data booklet, calculate the activation energy, E_a, for this reaction in kJ mol^-1.

State the effect of increasing temperature on the activation energy, E_a.

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.

A student investigates the kinetics of the reaction between hydrogen and iodine gas:

H₂ (g) + I₂ (g) → 2HI (g)

A general Arrhenius plot for a reaction with a known activation energy is shown by the solid line.

On the same axes, sketch a line to represent a reaction that has a higher activation energy but the same Arrhenius constant.

On a separate set of axes, a line for another general reaction is shown.

On these axes, sketch the line that would represent the same reaction in the presence of a catalyst.

The student obtains the following experimental data for the hydrogen-iodine reaction.

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.

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: 

i) Comment on the use of uncertainty when calculating the mean.

[2]

ii) Calculate the mean time for the set of results.

[2]

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.

Why do some collisions at high temperatures still not result in the formation of the product?

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:

i) Calculate the mean rate of reaction over the first 15 seconds of the reaction

[1]

ii) Calculate the actual rate of reaction at 15 seconds

[3]

iii) Explain the difference in values for rate

[1]

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 rate expression for the reaction.

Calculate the rate constant, k, and state its units.

Four mechanisms are proposed for the persulfate-iodide reaction.

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

Deduce which mechanism(s) is/are consistent with the rate equation you determined. Justify your answer.

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.

Determine the overall order of the reaction.

Draw a sketch graphs of:

i) Rate against concentration of NO.

[1]

ii) Rate against concentration of H₂

[1]

Suggest a possible mechanism for the reaction.

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

The rate of reaction between manganate(VII) ions and oxalate ions, C₂O₄^2-, can be investigated by measuring how the concentration of manganate(VII) varies with time.

2MnO₄^- (aq) + 16H⁺ (aq) + 5C₂O₄^2-  →  2Mn²⁺(aq) + 8H₂O(l) + 10CO₂(g) 

The rate is first order with respect to oxalate ions and the general rate equation for the reaction is:

rate = k [MnO₄^-]^p[C₂O₄^2-]^q[H⁺]^r

i) Suggest how the change in manganate(VII) concentration can be measured.

[1]

ii) A student investigated how the concentration of manganate(VII) affected the rate of reaction and produced the following results. The oxalate ions and acid were in excess.

Determine the rate of reaction.

[2]

The student used an acid concentration of 1.0 mol dm^-3. She then varied it, keeping the other concentrations constant. She measured the rate of reaction and found the following results:

Identify the relationship between the relative rate of reaction and H⁺, and hence determine the order of reaction with respect to H⁺ ions.

The student varied the concentration of [MnO₄^-] and plotted the rate against time at three different concentrations:

i) Deduce, with a reason, the order of reaction with respect to MnO₄-.

[2]

ii) Write the rate expression for the reaction.

[1]

A reaction proceeds by a three step mechanism. The energy profile for the reaction is shown below:

Explain the difference between points A, C, E and B, D on the profile.

Deduce which step is the rate determining step of the reaction, giving a reason.

A series of experiments were carried out to investigate how the rate of the reaction of bromate and bromide in acidic conditions varies with temperature.

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

Complete the table above.

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

ln k = ln A +

In this experiment, the rate constant, k, is directly proportional to . Therefore, 

ln = ln A +

Use your answers from part (a) to plot a graph of ln against x 10^-3 on the graph below.

Use section 2 of the data booklet along with your graph and information from part (b) 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.

Three experiments were carried out at a temperature, T₁,  to investigate the rate of the reaction between compounds F and G. The results are shown in the table below:

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

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.

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

k =

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

Use section 2 of the data booklet and your answer to part (b) to calculate a value for the Arrhenius constant, A, for this reaction. 

Give your answer to the appropriate number of significant figures.

The temperature of the reaction is increased to twice the original temperature, T₁. The value of k increases to 0.28 mol^-1 dm³ s^-1 at this new temperature.  

Using sections 1 and 2 of the data booklet and your answer to part (b), determine the original temperature, T₁.

The kinetics of a first-order reaction are being investigated.

It is observed that the rate of reaction doubles when the temperature is increased from from 25.0 °C to 35 °C.

Using section 1 and 2 of the data booklet, calculate the activation energy, E_a, in kJ mol⁻¹ for the reaction.

State and explain the effect that introducing a catalyst would have on the rate constant, k, at a constant temperature

For the uncatalysed reaction, the rate constant at 25.0 °C (298 K) is found to be 7.75 × 10³ s^-1.

The temperature is now reduced to a new temperature, T₂, at which the rate constant is 6.20 × 10³ s^-1.

Using the activation energy calculated in part (a), determine the new temperature, T₂, in °C