Investigating the Rate of the Reaction between Bromide and Bromate Ions in Acid Solution

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Investigating the Rate of the Reaction between Bromide and Bromate Ions in Acid Solution

        In this investigation, I aim to fully investigate the factors affecting the rate of the reaction between bromide ions and bromate ions in acid solution. The equation of this reaction is given below:

                5Br(aq) + BrO3(aq) + 6H+(aq) → 3Br2 (aq) + 3H2O(l)        (Equation 1.0.1)

I will attempt to find the rate equation for the reaction, in the form:

                        (Equation 1.0.2)

where k is the rate constant and x, y, and z are the orders of reaction with respect to Br-, BrO3- and H+ respectively. I will also attempt to find a suitable catalyst for the reaction, as well as the activation enthalpy for the reaction with and without a catalyst.

        The reaction is a redox reaction: the bromide is oxidised to bromine and the bromate is reduced to bromine. This can be shown by the oxidation states of bromide, bromate and bromine:

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

Oxidation State:        -1        +5        -2        +1        0        +1        -2

        I shall be using solutions of Potassium Bromide (KBr) and Potassium Bromate (KBrO3) as sources of bromide and bromate ions for the reaction, and Sulphuric Acid (H2SO4) as a source of H+ ions. A solution methyl orange shall be used as an indicator, which will change colour from pink (in acid solution) to colourless when Bromide ions are produced. In order to be able to measure the amount of time it takes for the indicator to change colour, a small amount of Phenol (C6H5OH) is added to the solution. Phenol reacts instantly with any Bromine produced, returning bromide ions:

                3Br2 (aq) + C6H5OH(aq) → C6H2Br3OH(aq) + 3H+(aq) + 3Br(aq)        (Equation 1.0.3)

As soon as all the Phenol has reacted with the Bromine produced, the excess Bromine causes the methyl orange to change colour. The time it takes for this to happen is proportional to the initial rate of the reaction between Bromide and Bromate ions.

1)        Background Chemistry for the Investigation

1.1 – Rates of Reaction

        The rate of a chemical reaction is a measure of how a property changes in a reaction over time. For example, the rate could be measured as the change in concentration of a substance over time. In this case, the units of the rate would be mol dm-3 s-1.

 There are several factors which can affect the rate of a reaction:

  • The temperature at which a reaction takes place
  • The concentration of a reacting solution
  • The surface area of a reacting solid
  • The pressure of a reacting gas
  • The effect of radiation on reactants
  • The use of a catalyst

1.2 – Measuring the Rate of Reaction

        The way in which the rate of a reaction is measured depends very much on the reaction being studied. For example, if the reaction produces a gas, the volume of gas produced can be measured. If the reaction is a neutralisation reaction or involves the production of an acid or alkali, the change in pH can be measured. Colorimetry can be used to measure the intensity of a coloured substance.

1.3 – Collision Theory of Reactions

        All substances are made up of moving particles. For a reaction to occur, the particles must collide with sufficient energy to react. The amount of energy they require is known as the Activation Energy (Ea). This can explain many of the factors which affect rate of reaction. Increasing the concentration or the pressure of a reactant means that there are more reacting particles in the same volume of solution, so collisions are more likely, meaning that more collisions happen in a given amount of time. Reactions involving solids happen on the surface of the solid, so increasing the surface area of a solid causes more area to be available for collisions to take place, leading to an increase in the rate of the reaction. In certain substances, radiation causes particles to move up vibrational energy levels, meaning that they have more energy, so are more likely to have the activation energy required for the reaction to take place.1

 

1.4 – Order of Reaction and the Rate Equation

        The order of a reaction describes the relationship between the concentration of a reactant and the rate of the reaction. It is only possible to know the order of a reaction by performing experiments with different concentrations of reactions and looking at the relationship between concentration and rate.

  • If the concentration of a reactant has no affect on the rate of reaction, the reaction is said to be zero-order with respect to that reactant.
  • If the concentration of a reactant is directly proportional to the change in the rate of reactant, the reaction is said to be first order with respect to that reactant.
  • If the square of the concentration of a reactant is directly proportional to the change in the rate of reactant, the reaction is said to be second order with respect to that reactant.

In general, if;

                        (Equation 1.5.1)

where [reactant] is the concentration of a reactant, then the reaction is nth order with respect to that reactant.

Graphs can be drawn of the rate against the concentration to find the order of the reaction: 

Figure 1.5.1: A zero order reaction        Figure 1.5.2: A first order reaction

Figure 1.5.3: A second order reaction        Figure 1.5.4: A second order reaction – if rate is plotted against           concentration squared, then the relationship is proportional

Consider the reaction;

                A + B → C + D        (Equation 1.5.2)

If the reaction is found to be xth order with respect to A and yth order with respect to y, then:

                        (Equation 1.5.3)

The rate equation can be derived from this:

                        (Equation 1.5.4)

where k is the rate constant for the reaction. The overall order of the reaction is the sum of the orders of reaction of the separate reactants, so reaction is (x+y)th order overall.

        Similarly to the orders of reaction, the value of the rate constant can only be found by experiment. If the orders of reaction with respect to the reactants (in this case A and B) are found, then, using the values for the concentration of the reactants and the initial rate of reaction, the value of k is given by:

                        (Equation 1.5.5)

The units of k depend upon the orders of reaction with respect to the reactants: rate is measured in mol dm-3 s-1 and concentration is measured in mol dm-3; the units of k are found using Equation t and these units.

1.5 – Rate Determining Step

        The majority of chemical reactions do not take place in a single step. The separate steps which form the reaction are known as the reaction mechanism. The reaction mechanism can only be hypothesised from results of experiments – there is no way to “prove” that it is how the reaction takes place. Therefore a mechanism can never be certain. The different steps of the reaction mechanism all take place at different rates and are affected by the concentration in different ways. In many reactions, one of the steps is a lot slower than the others: this is known as the rate determining step.

        If a reaction is zero order with respect to one of the reactants, this implies that the concentration of this reactant has no affect on the rate of reaction. When considering the reaction mechanism, this means that the step involving this reactant happens very fast regardless of the concentration, so this step is not the rate determining step. However, if the reaction is first order with respect to another reactant, then this reactant is involved in the rate determining step of the reaction.

        The rate equation for a reaction can suggest a possible rate determining step. This involves the molecularity of an elementary reaction step. If a reaction step is unimolecular, then it involves one molecule changing (by, for example, dissociation) and forming products. Unimolecular reactions suggest that the reaction is first order. Similarly, a bimolecular reaction involves two atoms, molecules, ions or radicals reacting together to form products. These reactions suggest a rate equation of the form, where A and B are the reactants, rate = [A][B]. Termolecular (involving three reactants) and higher molecularity reactions are unlikely, since these require three or more reacting particles to collide at the same instant. Hence, a rate equation can suggest the molecularity and the mechanism of a rate determining step, but this can only be theorised.

1.6 – The Effect of Temperature on Rate of Reaction

        The temperature of a substance is a measure of the kinetic energy of a substance – something feels warmer if the particles are moving faster. Therefore, collision theory would suggest that temperature affects the rate of a reaction since particles move faster, and hence collide more often, leading to an increase in the rate of reaction. However, this can be shown to be incorrect as the only factor in temperature increasing the rate of reaction.        

        A general approximation for the effect of temperature on the rate of a reaction is that, if the temperature increases by 10K, then the rate of reaction doubles. Temperature is proportional to kinetic energy, and kinetic energy is given by , where m is the mass of a particle, and v is the particle’s speed. Therefore temperature is proportional to the speed squared. Suppose a particle has a speed v1 at a temperature of 300K and a speed v2 at a temperature of 310K. Therefore:

                        (Equation 1.4.1)

This means that the ratio of the speeds is given by:

                        (Equation 1.4.2)

Since the ratio of the speeds is not 2:1, the rate of reaction has not doubled, suggesting that temperature affects the rate of reaction in a different way.

        In fact, the temperature causes an increase in the rate of a reaction by increasing the number of particles with sufficient energy to react. The energy of particles is distributed with a Maxwell-Boltzmann distribution. The number of particles with energy greater than or equal to the activation energy is proportional to the area under the curve from the activation energy (Ea) to infinity (see fig. 1.4.1). At higher temperatures, more particles have a higher speed, and hence a higher kinetic energy. Therefore, the number of particles with energy greater than or equal to the activation energy is higher at higher temperatures (see fig. 1.4.2). As there are more particles with sufficient energy to react, there is a greater chance that a collision will cause a reaction, so there is an increase in the rate of the reaction.1

        Note that the approximate rule that an increase in temperature leads to a doubling in rate of reaction is only valid for reactions for which the activation energy is around 50 kJ mol-1 and with a temperature rise from 300K to 310K.

1.7 – The Effect of Catalysts on the Rate of Reaction

        A catalyst is a substance which changes the rate of a reaction without being used up itself. In general, a catalyst provides an alternative route for the reaction with a lower activation energy, hence increasing the rate of reaction. There are two types of catalyst: heterogeneous catalysts and homogeneous catalysts.

        A heterogeneous catalyst is a catalyst which is in a different physical state to the reactants; for example, a solid catalyst in a solution. These catalysts work by forming temporary weak bonds between the catalyst surface and the reactants – the reactant is adsorbed onto the catalyst surface (see fig. 1.7.1). This causes bonds in the reactant to weaken and break. New bonds can then form between the reactants on the surface of the catalyst; when these bonds have formed, the temporary bonds break and the products diffuse away from the catalyst surface. Examples of heterogeneous catalysis include the Haber process, which uses an iron catalyst to produce ammonia, and catalytic converters in cars, which use a platinum catalyst to convert nitrogen oxides to nitrogen and oxygen.

        A homogeneous catalyst is a catalyst which is in the same physical state as the reactants, which is usually a liquid or a solution. The catalysts that I will test in the reaction between bromide and bromate ions will be homogeneous, in this case solutions of transition metal ions. Homogeneous catalysts work by forming an intermediate compound with one or more of the reactants, which then breaks down to form the products and reform the catalyst – so none of the catalyst is used up in the reaction. The step to form the intermediate has a lower activation energy than the uncatalysed reaction (see fig. 1.7.2), so the reaction can happen faster. An example of heterogeneous catalysis is the destruction of ozone in the atmosphere, which is catalysed by chlorine radicals.1

        Transition metals and transition metal ions are often particularly good as both heterogeneous and homogeneous catalysts. This is due to the incomplete 3d and 4s sub-shells in these ions, as well as their ability to have variable oxidation states. In heterogeneous catalysts, the empty electron orbitals in the 3d and 4s sub-shells allow for weak bonds to be formed on the surface of the metal. When transition metal ions act as homogeneous catalysts, the ion forms an intermediate with one or more of the reactants. The transition metal will often be in a different oxidation state in the intermediate, before changing back to the original oxidation state when the intermediate breaks down. This makes transition metal ions particularly good in redox reactions (such as the reaction between bromine and bromate ions in acid solution), as they can readily move from one oxidation state to another.

1.8 – The Arrhenius Equation

        The Arrhenius Equation gives an expression for the value of the rate constant k, as shown in Equation 1.8.1:

                        (Equation 1.8.1)

where A is the pre-exponential factor (constant), e is the exponential constant (), Ea is the activation energy for the reaction, R is the molar gas constant (), and T is the temperature at which the reaction takes place (in Kelvin). Taking logarithms of both sides of Equation 1.8.1 gives:

                        (Equation 1.8.2)

Simplifying Equation 1.8.2 using the laws of logarithms gives:

                        (Equation 1.8.3)

From Equation 1.8.3, it is clear that if a graph was drawn of  against , the relationship would be a straight line. If the rate equation of the reaction is found, the value of k for different values of T can be found if the rate of reaction is found at different temperatures. Hence, the activation energy of the reaction can be found using:

                        (Equation 1.8.4)

where m is the gradient of the line of the graph of  against .

2)        Method

        In order to investigate the rate of the reaction between bromide and bromate ions in acid solution, I will need to carry out the reaction several times under different conditions. To find the rate equation for the reaction, I will need to find the order of the reaction with respect to Br ions, BrO3 ions and H+ ions. To do this, I will:

  • Measure the time taken for the methyl orange to change colour with five different concentrations of bromide solution
  • Measure the time taken for the methyl orange to change colour with five different concentrations of bromate solution
  • Measure the time taken for the methyl orange to change colour with five different concentrations of acid solution
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        I can plot a graph of 1/time taken against concentration of solution to find the order of the reaction with respect to each of the reactants (see above – page 8). I will then choose set concentrations of each reactant and measure the time taken for the methyl orange to change colour with different temperatures. This, with the Arrhenius Equation, can be used to find the activation enthalpy of the reaction (see above – page 12).

        I will then repeat the reaction using the same set concentrations, but adding ten drops of a transition metal ion solution, which could work ...

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