The rate equation
The expression rate of reaction means the rate of change of concentration of one named substance taking part in a reaction.
xA + yB --> products
We could study the rate of reaction by measuring [A] (square brackets mean concentration in mol dm-3) The rate change of [A] is given by the symbol rA. However, it may be more convenient to measure how [B] changes with time, rB. In any reaction rA will be found to follow a mathematical expression of the form:
rA= k [A]a [B]b [C]c
This expression is called the rate equation.
Sometimes the concentrations of substances which do not appear in the balanced equation appear in the rate equation (C). The rate equation can only be deduced experimentally and cannot be predicted from the balanced equation.
rA= mol dm-3 s-1
[A]= mol dm-3
The indicies are known as the orders of the reaction. The sum of these indicies is known as the overal order of the reaction.
k=rate constant. It is often used to compare rates of reaction at different temperatures or to compare the rates of different reactions which have similar rate equations. You are often asked to work out the units of k!
Measuring rates of reaction
- Titrimetric- sampling and quenching if necessary
- Collecting any gas evolved
- Measuring the electrical resistance
- Measuring the optical rotation
- Measuring the refractive index
- Measuring the mass.
However, there are certain problems involved in measuring reaction rates
- Usually all reactant concentrations vary at the same time and so it is difficult to discover the effect of one particular reactant.- This can often be overcome by making all the concentrations, apart from the one being investigated, very large compared to the one being investigated so that any change in their concentration is not significant.
- Often there is no easy way of directly finding the rate of reaction at any particular time. In practice we often measure the reactant concentration at various times, plot a graph of reactant concentration against time and it is then possible to deduce the order of reaction from the gradient of the line or curve.
- Some reactions are so slow or so fast that special techniques may be needed to study them.
- Plot a graph of concentation of reactant A (y-axis) against time (x-axis)-- If a straight line is obtained the reaction is zero order with respect to reactant A. If a curve is obtained you need to calculate the half life, i.e. time taken for the concentration to drop by a half. You must work out the half like for 3 different concentrations. If the half life is the same each time then the reaction is first order with respect to reactant A. If the half life increases with time then the reaction is second order with respect to A.
- Plot a graph of concentation (x-axis) against rate (y-axis)--If there is a straigh horizontal line the reaction much be zero order with respect to A. IF the line is a diagonal straight line then rate varies directly with concentration and the reaction is first order. If an upward curve is produced then the reaction must be second order with respect to A.
- From a table of values of how the inital rate varies with the conc of reactants--If the concentration of reactant A is doubled and the initial rate does not alter then the reaction is zero order with respect to A. If the concentation of reactant A is doubled and the initial rate also doubles then the reaction is first order is respect to A. If the concentration of reactant A is doubled and the ratequadruples then the reaction is second order with respect to A.
Reactions occur in more than one step. These steps do not have to take place at the same rate and overall the reation will go at the rate of the slowest slep and this is known as the rate determinig step.
The rate equation describes the rate determining step.If a reaction is second order overal then any proposed mechanism must include just two entities reaction in the slowest step. If the reaction is first order overall then there can only be one entity decomposig in the rate determining step.
Effect of temperature and catalyst on rates
Temp- The collision theory states that not only must a collision take place between two particles before the can react but also that the particles must possess sufficient energy and the correct geometry. The minimum amount of energy is known as the activation energy.
The collsion theory can be represents mathematically in the Arrhenius equation.
K= A e-EA/RT
- k -rate constant
- A- Collision number
- EA- Activation energy
- R- gas constant
- T- absolute temperature (K)
It can be rewritten in the more convenient way which is a straight line on a graph if y is equal to ln k and x is equal to 1/T.
The gradient of the straight line obtained when you plot ln k against 1/T will be equal to -EA/R and hence from such a graph the activation energy can be calculated.
Effect of catalysts on rates
A catalysts increases the rate of a chemical reaction without itself becoming permanently involved in the reaction. It does become temporarily involved and works by providing a new pathway in which the activation energy is lovwer, thus ensuring that more particles have enough energy to react.
Heterogenous catalysis is when the catalyst is in a different state to the reactants, e.g. reacting gas molecules are absorbed onto the surface of a metal.
Homogenous catalysis is when the catalyst and reactants are all in the same state, e.g. all dissolved in the same solvent. The catalyst usually combines with one reacting species producing a relatively stable intermediate and a pathway of lower activation energy. The intermediate then decomposes releasing the catalyst again at a later stage.