# Reversible reactions

Consider the following reaction:

In this topic we are not concerned with the reacting chemical or the products of the reaction but with the type of arrow used in chemical equations; → or ⇌ . What does the use of the → in the above equation tell us?

This arrow tells us that the reaction goes to completion. This means that all of the reactants are turned into products. Most of the equations you have seen in science will probably have used this type of arrow; however very few reactions occur where all the reactants are turned into products. Neutralisation and combustion are two examples of reactions that you will have met that go to completion; however most reactions are reversible.

## Reversible reactions

Most chemical equations are written with a different arrow (⇌); this arrow is used to show that the reaction is reversible:
This equation might look very similar to the one above except for the arrow; which is obviously different. However this reaction is very different from the one mentioned above. You can think of it as two separate reactions that are happening at the same time

The important fact is that these two reactions are happening at the same time. The equation below basically shows two reactions in one!

##### A + B ⇌ C + D
As the reactants A and B react and turn into the products C and D; the products C and D are reacting and turning back into the reactants A and B. That is the reaction is reversible. Both these reactions happen at the same time.

We can use the symbols Rf and Rb to represent the rates of the forward and reverse reactions. It is a common error to assume that these two rates are equal but this is rarely the case. It is important to realise that during a reversible reaction you will end up with a mixture of A, B, C and D once the reaction gets going. The proportions of A, B, C and D will depend to a large extend on the rate of the forward and reverse reactions.

The simple diagram below may help to give you a mental picture of what is happening during a reversible reaction. Here the large glass troughs are filled with water; the water in each trough represents the reactants and products in a reaction. The amount of water in each beaker will give an indication of the speed or rate of reaction for the forward and reverse reactions. What you have to imagine is pouring the contents of the two beakers backwards and forwards at the SAME TIME into the two troughs.

What do you think will happen to the amount of reactants and products in each of the troughs in the image below if you use the two beakers to tip the “water” backwards and forwards between the two troughs at the same time?

Well in the first example below since each beaker is the same size it will hold the same volume of water or we can say the beakers will hold the same amounts of reactants and products, since this is what the water represents. This means that the amount of reactants and products will NOT change with time, even if you spent all day tipping water backwards and forwards between the two troughs. The amounts of reactants and products will not change.

What we can say here is the rate at which the reactants are turning into products is the same as the rate at which the products are turning back into reactants; or the rate of the forward reaction is the same as the rate of the back reaction.

### Some simple examples to consider:

Example 1. In this example below the rate of the forward and reverse reactions are the same; this is represented by the fact both the beakers are the same size and contain the same volume of water. This means that given enough time the amounts of reactants and products in each trough will be the same.

Example 2. In the example below the rate of the back reaction; that is the rate at which the products turn back into reactants is faster than the rate of the forward reaction. So there will always be more reactants than products.

Example 3. In this final example below the rate of the forward reaction is faster than the rate of the back reaction. There will be more products than reactants.

### Dynamic equilibrium

The water in the troughs above represents the amount of reactants and products in a chemical reaction. Imagine tipping water from the reactants trough into the products trough and from the products trough back into the reactants trough at the SAME TIME.

To start with the reactants beaker will be almost full; since the reaction has not started and there will be lots of reactants available. The products beaker tipping into the reactants trough will be empty to begin with since there are no products yet. But as the reaction proceeds; or as you keep tipping from one trough to another AT THE SAME TIME the amount of water in each beaker will EVENTUALLY be the same. At this point the volume of the reactants and products in each trough will NOT CHANGE even though you are still tipping water in and out of the troughs.

At this point the reaction is at equilibrium; that is the rate of the forward and reverse reactions are the same or we can say that at equilibrium the amount of reactants and products is not changing. It is important to realise that at equilibrium the reaction has not stopped; it is still continuing it is just that the rate of the forward and reverse reactions are the same. In our image below this means that the volume of water being poured from the reactants trough into the products trough is the same as the volume of water being poured from the products trough into the reactants trough. In a real life practical experiment what would you observe? Well since the amount of reactants and products is not changing it would appear that the reaction has stopped but as you know this is not the case.

At equilibrium the amount of water transferring between the troughs is the same, that is the rate of the forward and reverse reactions are the same. The amounts of reactants and products is not changing despite the fact that water is being tipped continually between them.

If this was a chemical reaction it would appear to have stopped since the amount of reactants and products is not changing. However the reaction has NOT stopped; it has achieved dynamic equilibrium. It is called dynamic equilibrium because dynamic implies movement and the reaction is still going on despite the fact that the amount of reactants and products is not changing and equilibrium implies a balance point has been reached.

At equilibrium:
• The amounts of reactants and products stay the same despite the fact that the forward and reverse reactions are still going on.
• The rate of the forward and reverse reactions are the same.
• The amounts of reactants and products are not necessarily equal, they are just constant.
• It is only possible to achieve equilibrium in closed systems; that is systems (reactions) in which no reactants or products can escape or leave or any new substances are added.

These changes at equilibrium are summarised in the graph shown below. Here the green line represents the amount of reactant and the red line the amount product. To begin with there is 100% reactant present and 0% of the product since the reaction has not started. However both lines for the reactants and products level out at a constant amount, this is the point at which the forward and reverse reactions are proceeding at the same rate. The reaction has achieved dynamic equilibrium and the amount of reactants and products does not change despite the fact that both the forward and reverse reactions are still proceeding.

### Examples of reversible reactions

Copper sulfate is a colourless (white) ionic crystalline solid. However if you have a bottle of copper sulfate in the lab it will be blue and not white (colourless). The reason for this is that the colourless anhydrous copper sulfate absorbs water from the air and this turns it blue. The dry or anhydrous copper sulfate has the formula CuS04; it is an ionic compounds with a giant ionic lattice structure. The water it absorbs from the air fits into this lattice structure and is held weakly in place. The wet or hydrated copper sulfate has the formula: CuS04.5H2O (the .5H2O just means that it has 5 moles of water are associated with it crystal structure). This water can be easily evaporated from the lattice by heating. This is shown below; once it has evaporated it loses its blue colour and turns white or colourless to form anhydrous copper sulfate. Addition of water again forms the hydrated blue form of copper sulfate. This is outlined in the image below:

We can show this reversible reaction in an equation as:

### The thermal decomposition of ammonium chloride

Ammonium chloride is a colourless solid which will decompose when heated to form a mixture of two gases; ammonia and hydrogen chloride gas. This reaction is reversible and when cooled the mixture of the basic ammonia and the acidic hydrogen chloride gases will reform solid crystals of ammonia chloride. This reaction can be shown as:

##### NH4(s) ⇌ NH3(g) + HCl(g)
The diagram opposite shows the reaction. On heating the solid crystals of ammonium chloride decompose to form the basic gas ammonia and the acidic gas hydrogen chloride. These two gases quickly rise up the boiling tube and if they meet a cool surface they will immediate react and reform crystals of ammonium chloride. During the experiment shown if the boiling tube is gently heated from below then the middle and top of the boiling tube will remain sufficiently cool for crystals of ammonium chloride to reform on the sides of the boiling tube. Once the two gases leave the boiling tube they will also cool down enough for a cloud of white solid ammonium chloride to form.

### Dynamic equilibrium

The examples above all show reversible reactions, however none of these reactions will ever achieve dynamic equilibrium. The reason for this is simple - equilibrium can only be achieved in closed systems. That is a system where there is no transfer or movement of matter (solids, liquids or gases) in or out of the system. As a simple example consider two conical flasks filled with a little water. One flask is left open to the surrounding while the other represents a closed system, simply by placing a rubber bung in the flask.

If left evaporation of water will start in both flasks. In the open flask given enough time the water (which represents the reacting chemicals or the system) will simply evaporate and enter the surroundings- the atmosphere. However in the closed flask the water molecules will also begin to evaporate and leave the liquid phase to enter the gas phase in the conical flask. The amount of water molecules in the gas phase will increased with time and eventually some will start to re-enter the liquid phase. When the rate of evaporation and the rate of condensation are the same then the amounts of water vapour and liquid water will remain constant despite the fact that evaporation and condensation are still going on. The key point is that a balance has been achieved, the rates of condensation and evaporation are equal - we say they are in equilibrium or balance. The word dynamic implies movement and since the two processes of evaporation and condensation are in balance but still continuing we say dynamic equilibrium has been reached,

What would happen if we set up three conical flasks, each fitted with a stopper to ensure a closed system and with:

• Flask 1 - here 100g of water vapour or steam was placed in the conical flask.
• Flask 2 - here 100g of water was placed in the conical flask.
• Flask 3 - here 50g of water and 50 g of steam was placed in the conical flask.
The three flasks were then placed in a warm room for 1 week. What do you think you could say about the contents of the flasks after 1 week?

After 1 week the contents of the flasks would be the same, each flask would contain the same amount of water vapour and liquid water. This simple experiment demonstrates an important point regarding equilibrium; that is it can be approached from either 100% reactants or products or some mixture of the two. Equilibrium is a low energy point in a reacting system and the reaction will always end up at this low energy point at any given temperature no matter from where you start.

## Key Points

• Reversible reactions are chemical reactions that can be reversed. In a reversible reaction the products can react with each other and reform the reactants.
• Dynamic equilibrium is the point in a reversible reaction where the rate at which the reactants form products is exactly matched by the rate at which products reform reactants.
• It is only possible to achieve dynamic equilibrium in reactions which are closed. This means no reactants or products are allowed to escape or leave the reacting system e.g. no gases are allowed to escape otherwise equilibrium will never be achieved.
• Equilibrium can be approached from 100% reactants, 100% products or a mixture of reactants and products. The end amounts of each reactant and product will be the same at any given temperature or pressure.