orders of reaction and rate equations
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ORDERS OF REACTION AND RATE EQUATIONS
Changing the concentration of substances taking part in a reaction usually changes therate of the reaction. A rate equation shows this effect mathematically. Orders of reaction
are a part of the rate equation. This page introduces and explains the various terms you
will need to know about.
Rate equations
Measuring a rate of reaction
There are several simple ways of measuring a reaction rate. For example, if a gas wasbeing given off during a reaction, you could take some measurements and work out the
volume being given off per second at any particular time during the reaction.
A rate of 2 cm3 s-1 is obviously twice as fast as one of 1 cm3 s-1.
Note: Read cm3 s-1 as "cubic centimeters per second".
However, for this more formal and mathematical look at rates of reaction, the rate is
usually measured by looking at how fast the concentration of one of the reactantsis
falling at any one time.
For example, suppose you had a reaction between two substances A and B. Assume
that at least one of them is in a form where it is sensible to measure its concentration -
for example, in solution or as a gas.
For this reaction you could measure the rate of the reaction by finding out how fast theconcentration of, say, A was falling per second.
You might, for example, find that at the beginning of the reaction, its concentration was
falling at a rate of 0.0040 mol dm -3 s-1.
Note: Read mol dm-3 s-1 as "moles per cubic decimetre (or litre) per second".
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This means that every second the concentration of A was falling by 0.0040 moles per
cubic decimeter. This rate will decrease during the reaction as A gets used up.
Summary
For the purposes of rate equations and orders of reaction, the rate of a reaction is
measured in terms of how fast the concentration of one of the reactants is falling. Its
units are mole dm-3 s-1.
Orders of reaction
I'm not going to define what order of reaction means straight away - I'm going to sneak
up on it!
Orders of reaction are always found by doing experiments. You can't deduce anything
about the order of a reaction just by looking at the equation for the reaction.
So let's suppose that you have done some experiments to find out what happens to the
rate of a reaction as the concentration of one of the reactants, A, changes. Some of the
simple things that you might find are:
One possibility: The rate of reaction is proportional to the concentration ofA
That means that if you double the concentration of A, the rate doubles as well. If you
increase the concentration of A by a factor of 4, the rate goes up 4 times as well.
You can express these using symbols as:
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Writing a formula in square brackets is a standard way of showing a concentration
measured in moles per cubic decimeter (liter).
You can also write this by getting rid of the proportionality sign and introducing a
constant, k.
Another possibility: The rate of reaction is proportional to the square of the
concentration ofA
This means that if you doubled the concentration of A, the rate would go up 4 times (22).
If you tripled the concentration of A, the rate would increase 9 times (32). In symbol
terms:
Generalizing this
By doing experiments involving a reaction between A and B, you would find that the
rate of the reaction was related to the concentrations of A and B in this way:
This is called the rate equationfor the reaction.
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The concentrations of A and B have to be raised to some power to show how they
affect the rate of the reaction. These powers are called the orders of reactionwith
respect to A and B.
For UK A' level purposes, the orders of reaction you are likely to meet will be 0, 1 or 2.But other values are possible including fractional ones like 1.53, for example.
If the order of reaction with respect to A is 0 (zero), this means that the concentration of
A doesn't affect the rate of reaction. Mathematically, any number raised to the power of
zero (x0) is equal to 1. That means that that particular term disappears from the rate
equation.
The overall order of the reactionis found by adding up the individual orders. For
example, if the reaction is first order with respect to both A and B (a = 1 and b = 1), theoverall order is 2. We call this an overall second order reaction.
Some examples
Each of these examples involves a reaction between A and B, and each rate equation
comes from doing some experiments to find out how the concentrations of A and B
affect the rate of reaction.
Example 1:
In this case, the order of reaction with respect to both A and B is 1. The overall order of
reaction is 2 - found by adding up the individual orders.
Note: Where the order is 1 with respect to one of the reactants, the "1" isn't written into the equation. [A]
means [A]1.
Example 2:
This reaction is zero order with respect to A because the concentration of A doesn't
affect the rate of the reaction. The order with respect to B is 2 - it's a second order
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reaction with respect to B. The reaction is also second order overall (because 0 + 2 =
2).
Example 3:
This reaction is first order with respect to A and zero order with respect to B, because
the concentration of B doesn't affect the rate of the reaction. The reaction is first order
overall (because 1 + 0 = 1).
What if you have some other number of reactants?
It doesn't matter how many reactants there are. The concentration of each reactant will
occur in the rate equation, raised to some power. Those powers are the individual
orders of reaction. The overall order of the reaction is found by adding them all up.
The rate constant
Surprisingly, the rate constant isn't actually a true constant! It varies, for example, if you
change the temperature of the reaction, add a catalyst, or change the catalyst.
The rate constant is constant for a given reaction only if all you are changing is the
concentration of the reactants. You will find more about the effect of temperature and
catalysts on the rate constant on another page.
Calculations involving orders of reaction
You will almost certainly have to be able to calculate orders of reaction and rate
constants from given data or from your own experiments.
There are all sorts of ways of doing these sums, and it is important that you practice the
methods that your syllabus wants. Check your syllabus and past exam papers to see
what sort of examples you need to be able to work out.
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Many text books make these sums look really difficult. In fact for A' level purposes, the
calculations are usually fairly trivial. You will find them explained in detail in my
chemistry calculations book.