5.1.1 (d,e,f,g) Rate graphs and orders
Syllabus
(d,e,f,g) Rate graphs and orders
(d) from a concentration–time graph:
(i) deduction of the order (0 or 1) with respect to a reactant from the shape of the graph
(ii) calculation of reaction rates from the measurement of gradients
{Concentration–time graphs can be plotted from continuous measurements taken during the course of a reaction (continuous monitoring).}
(e) from a concentration–time graph of a first order reaction, measurement of constant half-life, t1/2
{Learners should be aware of the constancy of half-life for a first order reaction.}
(f) for a first order reaction, determination of the rate constant, k, from the constant half-life, t1/2, by using the relationship: k = ln 2/t1/2
{Learners will not be required to derive this equation from the exponential relationship between concentration and time, [A] = [A0]e–kt.}
(g) from a rate–concentration graph:
(i) deduction of the order (0, 1 or 2) with respect to a reactant from the shape of the graph
(ii) determination of rate constant for a first order reaction from the gradient
{Rate–concentration data can be obtained from initial rate investigations of separate experiments using different concentrations of one reactant}
{Clock reactions are an approximation of this method where the time measured is such that the reaction has not proceeded too far}
What does this mean?
Order of reaction from Concentration-Time graphs
And you may well be asked to calculate the order of a reaction with respect to a reactant from a graph.
Both First and Second order give us curved Concentration-Time graphs so it pays to be careful.
The easiest method is to check the half-life.
Simply halve the initial concentration and read off the time taken.
In this case 400 seconds.
It's a good idea to check if the concentration halves in the next 400s.
In this case it does so we can say that the reaction is First Order with respect to this reactant because the half-life is constant.
First order reactions can use the equation k = ln (2/half-life) to calculate the rate constant
In this case the concentration halves in 50 seconds the first time.
But the half life is 100 seconds that next time.
And 200 seconds the next time.
This reaction is second order.
The syllabus doesn't mention these so we may assume a curved graph is first order - but it would still be a good idea to check.
This graph plots data from a first and second order reactant on the same axes, showing the difference in the shapes.
When the reaction is zero order with respect to a reactant then that reactant has no effect on the rate.
So its graph is not curved at all, but is straight.
Notice that the concentration of this reaction still declines even though it is not involved in the rate equation.
Clearly this tells you that this substance is being used up in the reaction but since it doesn't affect the rate it suggests that the reaction is not straight forward.
Most likely it proceeds in two (or more) steps (see below).
Rate of Reaction from Concentration-Time graphs
As at GCSE, rate of reaction at any time can be determined by drawing tangents to the curve.
The rate of reaction is then found by calculating the gradient of that tangent.
Gradient = Difference in y / Difference in x
Rate-Concentration Graphs
Don't confuse these with Concentration-Time graphs as the shapes are very different and so the conclusions you can safely make from the shapes are also different.
This rate of reaction is completely unaffected by increasing the concentration of this reactant.
So it must be Zero Order with respect to this reactant.
This graph shows that rate of reaction and concentration of this reactant are proportional to each other.
In other words, doubling the concentration of this reactant doubles the rate of the reaction.
This is the definition of a First Order reaction.
This graph shows that increasing the concentration of this reactant has a disproportionate effect on the rate of the reaction.
In other words, doubling the concentration more than doubles the rate.
If we looked more closely at the numbers we could show that doubling the concentration causes the rate of reaction to quadruple.
This is the definition of a Second Order reaction.
A Level questions won't involve Third Order graphs to all curved Rate-Concentration Graph are assumed to be Second Order.
First Order Rate Constants
Since the shape of First Order Rate-Concentration graphs is straight it has a constant gradient.
Finding the gradient of this line gives us the Rate Constant, k.
We can only do this for First Order graphs, however.
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