Kinetics

Collision theory states that for a chemical reaction to take place, particles must collide in the correct orientation and with sufficient energy.

Activation energy, is the energy barrier that must be overcome for the reaction to proceed. It is typically measured as the energy difference between the reactants and the transition state.

This means that for a successful collision to occur, the reactant particles must collide with energy equal to or above the activation energy.

If reactant particles collide with sufficient energy (equal to at least the activation energy, ) and in the correct orientation they will react, leading to an effective collision.

If reactant particles collide with insufficient energy, they bounce off of each other and it will be an ineffective collision.

If reactant particles collide in the incorrect orientation, they will bounce off each other resulting in an ineffective collision.

If the concentration of solutions is increased there are more particles per unit volume.

This will increase the frequency of collisions, and therefore the frequency of effective collisions will also increase.

In the diagram above, the concentrations of the reactant particles have increased. This would increase the frequency of effective collisions , and therefore increase the rate of reaction.

If the pressure of gaseous reactants is increased it has a similar effect to increasing the concentration.

Although the number of particles remains the same, the volume is decreased, and therefore the gaseous particles are more tightly packed. There are more gaseous particles per unit volume.

Increasing the number of particles per unit volume will increase the frequency of effective collisions, leading to an increase in the rate of reaction between the gaseous reactants.

Increasing temperature causes an exponential increase in reaction rate due to the increase in both the frequency of collisions and the proportion of collisions which are successful.

If the temperature of a chemical reaction is increased, the reacting particles gain more kinetic energy and therefore move faster.

This will increase the frequency of collisions and the energy of the collisions, leading to a greater proportion of collisions exceeding the activation energy.

Breaking a solid into smaller pieces increases the surface area, leading to a higher rate of reaction.

If the surface area of a solid reactant is increased, more particles are exposed to react with other reactants.

This will increase the frequency of collisions and therefore the frequency of effective collisions

Catalysts increase the rate of a chemical reaction but are not used up by the overall reaction.

Catalysts increase the rate of a chemical reaction by providing an alternative reaction pathway with a lower activation energy.

This can be shown on enthalpy profiles.

Although catalysts increase the rate of a chemical reaction they do not impact the total frequency of collisions. However, they do increase the proportion of successful collisions and therefore the frequency of successful collisions.

The Maxwell-Boltzmann distribution curve is a graphical representation showing the distribution of energies of molecules at a particular temperature.

The Maxwell-Boltzmann distribution curve plots the number of molecules on the axis and energy of the molecules on the axis.

The area under the curve in the Boltzmann distribution is equal to the number of molecules in the substance.

Upon changing conditions, the total area under the curve does not change.

The peak of the curve represents the most probable energy, ; the mode.

The curve is asymptotic (does not reach the axis), as molecules have no maximum kinetic energy, and starts at the origin , as molecules must have a non-zero energy.

The curve becomes useful in explaining reaction kinetics, as only molecules with energy equal to or greater than the activation energy will result in effective collisions. This is the area under the curve to the right of the line.

Increasing the temperature shifts the Maxwell-Boltzmann distribution curve to the right and down.

The total area under the curve remains unchanged, meaning a shift to the right must be accompanied by a lower peak height.

For decreasing temperature, the curve shifts to the left and the peak height increases.

The Maxwell-Boltzmann distribution shows how a small increase in temperature, from to , results in a larger proportion of molecules having sufficient energy to overcome the activation energy barrier and react.

Since more molecules are able to collide with sufficient energy to, the frequency of successful collisions increases, leading to a faster reaction rate at higher temperatures.

The use of a catalyst has no effect on the energy distribution or the shape of the Maxwell-Boltzmann distribution curve.

Catalysts lower activation energy so the position of the activation energy is shifted to the left.

This means that a greater proportion of molecules have an energy exceeding the activation energy and are able to react; a greater number of collisions per unit time are effective, and there is a faster rate of reaction.

When the concentration of a reactant has no impact on the rate of the reaction it is called zero order.

regardless of the concentration of . There is a zero gradient.

This can be seen on a rate–concentration graph as a horizontal line.

When the rate of reaction depends on the concentration raised to the power of one it is called first order.

This can be seen on a rate–concentration graph as a directly proportional relationship; when the concentration of is doubled the rate will also double.

When the rate of reaction depends on the concentration of a reactant raised to the power of two it is called second order.

This can be seen on a rate–concentration graph as an increasing gradient; when the concentration of is doubled the rate will quadruple.

Zero order concentration–time graphs, obtained through continuous monitoring, are linear with a constant negative slope.

For a zero-order reaction, the gradient of the concentration–time graph is constant and gives the rate constant, .

The unit for in a zero order reaction is .

First order concentration–time graphs are curved and initially show a rapid decrease in concentration, which slows down over time.

For a first-order reaction, the gradient of the concentration–time graph changes over time.

The rate at a particular time, , is given by the slope of the tangent to the curve at that point.

• Draw a tangent to the curve at the specific time, .

• Determine the slope of this tangent using:

First order reactants have a constant half-life.

The half-life, , refers to the time it takes for the concentration of a reactant to reduce by half during a reaction.

In the example below the concentration of bromine halves every .

It takes for the concentration to change from to and a further for the concentration to change from to .

Therefore, the half-life, , for the first order reactant, bromine, is .

Reactions can be monitored by measuring the mass change over time.

Procedure:

• Weigh the reaction vessel empty.
• Add the reactants and record the initial mass.
• At specific time intervals, reweigh and record changes.

Mass loss indicates consumption of solid or liquid reactants and formation of a gaseous product.

Mass gain implies consumption of a gaseous reactant and incorporation in a solid or liquid product.

In the reaction of solid magnesium with aqueous hydrochloric acid, hydrogen gas is produced, leading to a decrease in the mass of the reaction vessel.

Changes of gas volume during a reaction reflect consumption of gaseous reactants, or formation of gaseous products.

Use a gas syringe or displacement method to measure gas volume changes.

Record initial volume and measure at specific time intervals.

Hydrochloric acid reacts with magnesium to produce hydrogen gas, leading to an increase in gas volume as the reaction proceeds. Gas collection can be used to monitor the reaction rate.

Time is a crucial parameter for monitoring reaction rates.

Use a stopwatch or digital timer to record the time taken to reach specific reaction milestones. Accurate timing ensures precise determination of reaction rates.

The time taken for the milestone to be reached is inversely proportional to the reaction rate. This means that longer times indicate slower rates.

The milestone used will depend on the reaction but could include a colour change, onset of gas evolution, or a predefined temperature change.

In the reaction between sodium thiosulfate and hydrochloric acid, a precipitate of sulfur is formed, causing the solution to become cloudy. The reaction milestone is the point at which a covered cross is obscured.

The iodine clock reaction is an initial rates experiment that measures the time required for a set amount of iodine to form.

A specific amount of sodium thiosulfate is included in the reaction mixture and this reacts with the iodine as it is formed.

When enough iodine has been produced to consume the sodium thiosulfate the excess iodine reacts with starch in the reaction mixture a colour change to blue–black is observed.

The rate in each instance is calculated by considering the concentration of iodine produced at the point of the colour change and dividing this by the time taken.

There is a ratio of . The concentration of iodine produced will be half the initial concentration of sodium thiosulfate in the reaction mixture.

Colorimetry can be used in continuous monitoring when a reactant or product has a distinct colour.

To monitor the rate of reaction using colorimetry a calibration curve is required.

Procedure to generate a calibration curve:

1. Prepare standard solutions of known concentrations of the coloured species.
2. Measure their absorbance using a colorimeter.
3. Plot absorbance vs. concentration to create a calibration curve.

Use the calibration curve to convert absorbance readings from the reaction you are monitoring to concentrations.

Results can then be analysed using a concentration–time graph.

The graph below illustrates how to draw a tangent and extract the relevant data from a concentration–time graph in order to calculate reaction rate.

The x-axis for time is often in minutes. When calculating the it is important to convert the time to seconds.

The gradient will commonly have the units of .

This method can also be used if there is a change of mass, change in volume etc. If this is the case, the units for the gradient will be different.

The rate equation can be determined from experimental data using the initial rate method.

To analyse this data, find a pair of reactions where only one concentration changes to find the order with respect to that reagent.

is a first order reactant: between trial 1 and 2, only changes. is doubled and the initial rate also doubles.

is a zero order reactant: between trial 1 and 3 only changes. is doubled and the initial rate remains constant.

is a second order reactant: between trial 1 and 4 only changes. is doubled and the initial rate quadruples (increases by a factor of

Therefore the rate equation for this reaction would be:

The rate constant, , is only valid for a given temperature. The value of increases exponentially with increasing temperature.

Higher temperatures increase the kinetic energy of particles and shift the Maxwell-Boltzmann distribution to the right. The proportion of particles with kinetic energy activation energy is increased.

At higher temperatures there is increasing frequency of successful collisions; more collisions overcome the activation energy within a set time. This represents a higher rate of reaction.

If the rate of reaction increases, whilst the concentration of reactants remains constant, the value to must increase.

The Arrhenius equation can be manipulated to form a linear equation by taking the natural logarithm of both sides:

This can be plotted on a graph.

When is plotted against and , the gradient is and the y-intercept is .

These values can be extracted from the graph.