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, t_1/2

{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, t_1/2, by using the relationship: k = ln 2/t_1/2

{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

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.