16.1 - The Rate Expression
Rate = k[A]m[B]n
where: k is a constant, and m, n show the orders of the reaction with respect to each reactant.
It is an experimentally determined equation in that the information (n,m,k etc) can only be found through experimentation and not through theoretical considerations. The rate equation shows the relationship between the speed of a reaction and the concentrations of the individual reactants. Once the orders are found then they provide information regarding the mechanism of the specific reaction.
The overall order of reaction is the total of m+n above.
k is the rate constant. This gives a measure of how fast the reaction proceeds. External factors such as temperature, pressure, particle size and catalysts affect the value of the rate constant.
If a graph of reaction concentration against time is plotted a curve is obtained as the reactant is used up in the course of the reaction. The rate of any reaction is at its greatest at the beginning (time=0). As the reactants are used up the rate decreases.
If a graph of rate against time is plotted then the shape obtained will depend on the overall order of the reaction.
If a curve is obtained then further mathematical treatment of the results is necessary.
as: Rate = k[A]m[B]n
if [B] is kept constant, then: log Rate = log k' + m log[A]
And a plot of log Rate against log [A] will give a straight line of gradient m (the graph has the form y = mx + c)
keeping [A] constant and treating the results of rate when [B] varies will allow a similar determination of the order with respect to B. Once the two orders are ascertained then the rate constant k can be found.
The half life is the time taken for the concentration of reactants to reach half of its original value. For most reactions the half life changes as the reaction procedes but this is not the case for first order reactions where the half life is constant. (short half life= fast rate)
Using the half life to find the rate constant
The rate constant can be found from a concentration/time graph by taking a point, finding its concentration, then finding a point on the graph which corresponds to half this concentration. The half life is the time between these two points. The half life is also equal to ln2/k where k is the rate constant (equation given in data book).
Solving the rate equation by inspection
If a series of experimental results are obtained for rate at different reactant concentrations the change in rate can be ascertained for those reactions when the concentration of one of the reactants is kept constant while the other reactant concentration is changed.
In experiments 1,2 and 3 the concentration of A changes while the concentration of B is kept constant. This means that the rate equation can be written as:
Rate = k'[A]m
For these three experiments. If we inspect the rate of experiments 1,2 and 3 we see that as the concentration of A is doubled so the rate doubles. In other words the order of reaction must be 1 so that whatever happens to the concentration must also happen in equal amounts to the rate.
Similar inspection of experiments 1 and 4 ( or 2 and 5) show that while A is kept constant there is no effect on the rate when the concentration of B is changed. The order with respect to B must be 0.
The orders can now be substituted into the rate equation:
Rate = k[A]1[B]0
To obtain a value for the rate constant we simple substitute the values for one of the experiments above using the newly determined orders. (choose the experiment with the simplest numbers - in this case experiment 1)
Values from experiment 1
6 x 103 = k x [0.1]1 x [0.1]0
k = 6 x 103 / 0.1
k = 6 x 104
The mechanism of a reaction is a series of reactions between the particles of a reaction that eventually lead to the final products. A reaction may have many steps in the mechanism.
k = Ae(-Ea/RT) (data book)
Determination of the activation energy from practical results
If rates experiments are carried out at different temperatures the results can be plotted on a graph to obtain a value for the activation energy for a specific reaction.
A plot of natural log of k against (1/T) will give a straight line of gradient - Ea/R
Enthalpy level diagrams
These show a curve representing the path between the reactants and products in terms of energy. Energy is shown on the y-axis. The reactants and products are of different chemical energies and the curve goes between the two levels (the reactants and products) having an energy maximum between them (with the distance between the highest point and the reactants being equal to the activation energy of the forward reaction).
An energy graph showing an exothermic reaction
Reactions only occur when the reacting particles have energy greater than the activation energy and are able to get over the activation energy barrier.
Catalysts provide an alternative mechanism with lower activation energy. This means that a greater number of collisions will be successful and the reaction procedes at a faster rate
Homogeneous catalysts -- catalysts in the same state (phase -- ie solid, liquid or gas) as the reactants. Hetrogeneous catalysts -- catalysts in a different phase (usually a solid) from the reactants.
Homogeneous catalysts operate by reacting with the reactants and eventually producing a reaction pathway of lower activation energy (and also being regenerated at the end of this process). Hetrogeneous catalysts provide a reactive site on which an activated complex forms, weakening the bonds and increasing the rate of collisions thus increasing the rate of reaction.
Examples of catalysed processes
It acts like a bottleneck in that it prevents the other processes from reaching the end of the reaction and in this way determines the overall rate. It is similar to the idea of a car journey that has to pass through an area of roadworks. The car will be slowed right down by the roadworks and this is therefore the crucial factor in determining the overall time of the journey. return