5.1.1 (a,b) Orders, rate equations and rate constants

Syllabus

(a) explanation and use of the terms: rate of reaction, order, overall order, rate constant,half-life, rate-determining step.

What does this mean?

Most people will be familiar with Rates of Reaction from GCSE studies.

Everything you learned is relevant but we now need to extend the knowledge.

To do so will involve using technical terms correctly so it is important that we understand those terms accurately.

Rate of Reaction

This hasn't changed since GCSE.

The rate of a reaction is either:

the speed at which a reactant is destroyed
the speed at which a product is formed

Either way it will be calculated by: Rate of reaction = [Change of concentration of reactant/product] /Time

Consequently, the units of Rate of Reaction will always be mol dm^-3s^-1

Order of Reaction and Overall Order

No one will have mentioned this at GCSE so you may well think that doubling the concentration of a reactant would always double the rate.

Sometimes that is true. Often it is not.

The Order of the reaction may well be different with respect to each reactant.

Imagine a reaction such as A+ B + C --> D

If you found experimentally that doubling the concentration of A had no effect on the rate of the reaction you might reasonably say that the reaction was Zero Order with respect to A.

If you then found experimentally that doubling the concentration of B doubled the rate of the reaction in the way you might expect you would say that the reaction was First Order with respect to B.

If you then found experimentally that doubling the concentration of C quadrupled the rate of the reaction you would say that the reaction was Second Order with respect to C.

Rate orders never go higher than this.

We can now write a Rate Equation: Rate of Reaction = k [A]⁰[B]¹[C]² where [A] = concentration of A , k = Rate Constant

Of course, any number raised to the power zero = 1 (you knew that from GCSE Maths!) so we wouldn't usually include [A]⁰.

And, any number raised to the power 1 is unchanged (you knew that from GCSE Maths too!) so we would usually write [B] rather than [B]¹

So a more usual Rate Equation would be: Rate of Reaction = k [B][C]²

The Overall Order of the reaction would be Third Order since 3 is the number get from adding the orders of each reactant.

The rate constant is simply a number that allows the equation to work.

It is unchanged by changes to concentration but will increase at higher temperatures etc.

A typical question may give you data about the initial rate of a reaction with different initial concentrations of the reactions.

For example:

Comparing Expt 1 and Expt 2 the only change in initial conditions was a doubling of the concentration [A].

This doubled the rate.

This means that the reaction is first order with respect to A.

Comparing Expt 2 and Expt 4 the only change in conditions was a doubling of the concentration [C].

This doubled the rate.

This means that the reaction is also first order with respect to C.

Comparing Expt 1 and Expt 3 the only change in conditions was a trebling of the concentration [B].

This trebled the rate.

This means that the reaction is also first order with respect to B.

So, Rate of Reaction = k[A][B][C] and the reaction has an overall order of 3.

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Half-life

Similarly to the radioactivity topic in GCSE Physics, the Half-life of a reaction is the time it takes for the concentration of a reactant to halve.

Half-lives in Physics are always constant. That's not true of Half-life of reactions

And you may well be asked to calculate it from a graph.

Both First and Second order give us curved Concentration - Time graphs so it pays to be careful.

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.

See 5.1.1 (d,e,f,g) Rate graphs and orders for details of what we can learn from Half-Lives.

Rate -Determining step.

Simple reactions happen when two reactants collide such as Sodium reacting with acid.

H⁺ + Na --> Na+ + ¹/₂H₂

But more complex reactions often happen in more than one step.

A + 2B --> C suggests three reactant molecules must collide with enough energy and the right orientation for a reaction to happen.

This is unlikely but not impossible.

It is far more likely that the reaction happens in two steps such as:

Step One: B + B --> AB

Step Two: AB + A --> C - which overall is still A + 2B --> C

It's likely that one of these two steps has a much higher activation energy than the other.

This step will proceed slowly while the other will proceed almost instantly by contrast.

It is this slow step that controls the overall speed of the reaction - it is the Rate-Determining Step.

And the rate -determining step is therefore reflected in the rate equation, while the other step is not.

Of which, more later.

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