3.4.1 Kinetics - Simple rate equations
Students should:
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16.1 - The Rate Expression
The rate expression or equation shows the general relationship between the rate of a reaction and the concentrations of the constituent reactants:
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. The orders are the powers to which the individual concentrations must be raised in the rate equation. The orders are usually integers with a value of 0, 1 or 2.
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 sum of the individual orders, i.e. (m+n) in the example above.
k is the rate constant. This gives a measure of how fast the reaction proceeds.
Other factors such as temperature, pressure, particle size and catalysts affect the value of the rate constant.
Graphing results
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.
- 0th order graph:- straight flat line
- 1st order graph:- straight line
- All other orders: curve
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.
Half Life
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.
