Activation Energy (DP IB Chemistry: HL)

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) 

ii)     Activation energy, E_a 

iii)    Temperature, T

Using Sections 1 and 2 of the Data Booklet, calculate the activation energy, E_a, of a reaction at 57℃ 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 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.

(If you did not get an answer for (a), you may assume that rate = k [F]² [G]². This is not the correct answer)

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

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.

(If you did not get an answer for (b), you may assume that k has a value of 4.97. This is not the correct answer)

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.

(If you did not get an answer for (b), you may assume that k = 16700 mol^-1 dm³ s^-1 This is not the correct answer)

The rate constant for a reaction doubles when the temperature is increased from 25.0 °C to 35 °C.

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

The rate constant is 6.2 x 10³ s^-1 when the temperature is reduced by a factor of a fifth from the original starting temperature, 25 °C.

Calculate the rate constant, in min^-1, using sections 1 and 2 of the data booklet.

A different reaction route is used which reduces the activation energy of the reaction. 

Explain how the rate constant calculated in part(b) would differ.