Simple Rate Equations, Orders of Reaction & Rate Constants (CIE A Level Chemistry)

The initial rate of the reaction of chlorine dioxide, ClO₂, and fluorine, F₂, is measured in a series of experiments at a constant temperature.

2 ClO₂ + F₂ → 2ClO₂F

The results obtained are shown in Table 1.1.

Table 1.1

The rate equation is rate = k[ClO₂][F₂].

 [1]

k = ............................. units ............................. [2]

initial rate = ...................................... mol dm^–3 s^–1 [1]

[ClO₂] = ............................................ mol dm^–3 [1]

 [1]

[1]

Describe the effect of temperature change on the rate of a reaction and the rate constant.

This question is about the reactions of different unknown compounds.

Two compounds, X and Y, were reacted together. 

The initial rate of reaction was measured when compound X and compound Y were reacted together. The temperature was kept constant and the results of the experiments are shown in Table 2.1.

Three separate experiments were carried out at 400K with different starting concentrations of A and B. The results are shown in Table 2.2.

The overall rate equation for a reaction is rate = k[P]²[Q]

Chemists measured the rate of a chemical reaction in a series of experiments between compounds C and D at a fixed temperature as shown in Table 2.3.

Dedude the order of reaction with respect to

• C ..................................................
• D ..................................................

and write the overall rate equation for this reaction.

The initial rate of reaction for iodine and propanone in acid solution is measured in a series of experiments at constant temperature.

CH₃COCH₃ + I₂  CH₃COCH₂I + HI

The rate equation was determined experimentally to be as shown.

rate = k [CH₃COCH₃][H⁺]

• CH₃COCH₃ ..................................................
• I₂ ..................................................
• H⁺ ..................................................

The rate of this reaction is 5.40 × 10^–3 mol dm^–3 s^–1 when

• the concentration of CH₃COCH₃ is 1.50 × 10^–2 mol dm^–3
• the concentration of I₂ is 1.25 × 10^–2 mol dm^–3
• the concentration of H⁺ is 7.75 × 10^–1 mol dm^–3.

Fig. 3.1 is produced from the results, which shows how the concentration of I₂ changes during the reaction.

Describe how Fig 3.1 could be used to determine the initial rate of the reaction.

On Fig 3.2, sketch a graph to show how the initial rate changes with different initial concentrations of H⁺ in this reaction.

The equation for the decomposition of hydrogen peroxide without a catalyst is shown.

2H₂O₂ (aq) → 2H₂O (l) + O₂ (g)

With this information, a student suggests that the rate equation for this reaction is as follows.

Explain if the student is correct. 

A student carries out separate experiments using different initial concentrations of H₂O₂. The initial rate of each reaction is measured.

The table shows the results that are obtained.

Another student monitors the concentration of H₂O₂ over time. The graph obtained is shown.

Using appropriate calculations, describe how the student could use this graph to prove the order of reaction with respect to H₂O₂. 

Under certain conditions, the decomposition of hydrogen peroxide is found to be first order with respect to hydrogen peroxide, with a rate constant, k, of 2.0 × 10^–6 s^–1.

This question is about nitrogen oxides.

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)

The rate equation for the reaction between nitrogen monoxide (NO) and oxygen (O₂) under certain conditions is given.

The result of an experiment in which NO reacted with O₂ is shown in the table. 

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

Give the units of k.

Nitrogen dioxide reacts with carbon monoxide at 100 ℃ to form nitrogen monoxide and carbon dioxide.

The rate of this reaction was measured at different initial concentrations of the two reagents.

The rate equation was determined to be

The table shows an incomplete set of results.

Nitrogen monoxide, NO (g), reacts with hydrogen, H₂ (g), under certain conditions.

The rate equation for this reaction is given.

One proposed mechanism for this reaction occurs in two steps.

1. 2NO + H₂ → N₂ + H₂O₂ 
2. H₂O₂ + H₂ → 2H₂O

Explain which of the steps is the rate-determining step.

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 in Fig. 1.1.

FIg. 1.1

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

Their results are shown below.

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

Rate equation ...........................................................

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.

Calculate the initial rate of the reaction mixture 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.

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

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.

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)

[2]

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)]

[2]

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.

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

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

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 3.1.

Table 3.1

Temperature (T ) / K	/ K-1	Time (t ) / s	/ s-1	ln
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.

The relationship between the rate constant, k, and the activation energy, E_a, and temperature, T is given by the following equation.

ln k = ln A + 

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

Use your answers from part (a) to plot a graph of ln against  x 10^-3 on the graph in Fig. 3.1.

Fig. 3.1

Use your graph in Fig. 3.1 and information from part (c) to calculate a value for the activation energy, in kJ mol^–1, for this reaction. Show your working. 

The value of the gas constant, R = 8.31 J K^–1 mol^–1