Use this tutorial to explore how the chance behaviour of particles and energy determines the direction and reversibility of chemical reactions

Perhaps the most fundamental question in chemistry is ‘why do particular chemical reactions occur?’ More specifically, we want to know why one reaction occurs, while the reverse one does not.

This tutorial encourages students to think about how the random behaviour of particles and quanta of energy gives rise to predictable reactions, taking place in a particular direction. Students explore and develop their understanding of key ideas, including:

- Reversible reactions, or how the direction of some chemical reactions can change
- The importance of chance and the role of statistics in making randomness predictable
- The concept of entropy, and how particles adopt the most probable arrangements by chance alone

The tutorial also features two videos demonstrating the irreversible reaction between magnesium and dilute hydrochloric acid.

**Note**

The interactive ‘simulations’ for this tutorial are currently unavailable. However, you may find it helpful to read any accompanying instructions, observations and conclusions relating to the simulations below.

## The direction of chemical reactions

If we place a piece of magnesium in dilute hydrochloric acid, hydrogen gas is evolved and magnesium chloride solution is produced. However, no amount of bubbling hydrogen into magnesium chloride solution will get back the magnesium and the hydrochloric acid.

More formally, the following reaction occurs:

Mg_{(s)} + 2HCl_{(aq)}→ H_{2}_{(g)} + MgCl_{2(aq)}

But the reverse reaction, below, does not:

H_{2(g)} + MgCl_{2(aq)}→ Mg_{(s)} + 2HCl_{(aq)}

There seems to be some direction associated with this (and other) reactions – we can say that this reaction is irreversible. What governs the ‘direction’ of this, and other chemical reactions, and can we predict it or even change it?

### Video demonstrations

#### Magnesium and hydrochloric acid

#### Hydrogen and magnesium chloride

## Reversible reactions

Some reactions obviously are reversible and we can push them in one direction or the other by changing the conditions such as temperature.

For example, at room temperature (around 298 K), calcium oxide will react with carbon dioxide (in the air, for example) to form calcium carbonate:

CaO_{(s)} + CO_{2}→ CaCO_{3(s)}

(Note: calcium oxide is used in absorption tubes to protect other chemicals from CO2 in the air.)

However, above about 1200 K the opposite reaction occurs, as calcium carbonate decomposes to form calcium oxide and gives off carbon dioxide. This is what happens in lime kilns where limestone (calcium carbonate) is heated to form lime (calcium oxide).

CaCO_{3}_{(s)}→ CaO_{(s)} + CO_{2(g)}

For this reason, it might make more sense to write:

CaCO_{3}_{(s)}⇌ CaO_{(s)} + CO_{2}_{(g)}

Notice that this reversal of the reaction has nothing whatsoever to do with the fact that increasing temperature makes reactions go faster. Here temperature has changed the direction of the reaction, not just its speed.

## The answer is chance!

A little thought will lead us to a surprising answer to our original question, ‘why do particular chemical reactions occur?’. It is that the outcome of chemical reactions is governed by chance alone.

This has to be the case because chemicals cannot ‘know’ what the outcome of a reaction should be – calcium, carbon and oxygen atoms cannot ‘know’ that at a certain temperature they are ‘supposed’ to arrange themselves as CaCO_{3}, while at some other temperature they ‘should’ be arranged as CaO and CO_{2}. Atoms, molecules and ions arrange themselves in the way that is most probable by chance alone.

Initially this may seem unlikely – the outcomes of chemical reactions are totally predictable, how can they be driven by chance alone? Magnesium always reacts with hydrochloric acid to produce hydrogen gas and magnesium chloride in entirely predictable quantities. It does not seem to be down to chance in any way.

However, statistics tell us that events governed by chance are predictable if there are enough of them. We cannot predict the outcome of a single throw of a die but if we throw it very many times, we can predict with great confidence that there will be an equal number of occurrences of each number.

Very large numbers is the key and, of course, in chemical systems we are always dealing with vast numbers. Typically, in a school experiment, we might be dealing with quantities containing up to a mole of atoms or molecules, and a mole is 6 x 10^{23} particles – an unimaginably large number. Industrially, reactions use many times more than this.

### Mixing marbles demonstration

You might like to illustrate the inevitability of mixing by shaking similar numbers of marbles of two different colours (eg a dozen of each) in a large measuring cylinder (preferably a plastic one to avoid the risk of breakage).

Start with all the marbles of one colour at the top. Does it ever occur that, after shaking, all the marbles of one colour end up at the top?

### Entropy and disorder simulation

#### Introduction and instructions

We can use a computer simulation to investigate chance behaviour. Initially we will use a simple system which is not even a chemical reaction:

- Up to 200 objects can be placed in either of two boxes as a starting position.
- These then move entirely at random from one box to the other.
- You can use the two sliders to vary the total number of objects and the number in each box at the start. (As a tip, it probably makes sense to start with all the objects in one box or the other initially).
- The histograms below each box show a running total of the number of objects in each box.
- You can step through the simulation one move at a time or let the simulation run for as long as you like – the ‘run’ option will be better once you have got the idea of what is happening.

This is a little like molecules of gas in gas jars separated by a cover slip. One contains a gas, and the other a vacuum. What happens when the partition is removed and why?

#### Observations

- The objects end up evenly distributed between the two boxes whatever the starting position. This totally predictable result is produced entirely at random.
- In fact, the distribution is not entirely even – there are small statistical variations. You can see the histograms wavering slightly, but these variations become less significant as the number of objects increases.
- If this trend continues and we apply it to realistic numbers of molecules for an everyday amount of substance (say 1 mole, or 6 x 10
^{23}particles), the less significant are the statistical variations and we get an entirely predictable outcome from an entirely random process. - This is an important lesson that we will be able to apply to real chemical systems later.

#### Conclusion

The outcome of the simulation is, of course, consistent with what happens in real life. If we remove the cover slip between a gas jar full of gas and an empty one, we know with absolute certainty that a gas will spread evenly between two jars.

The important point to realise is that this happens by chance alone and not because the molecules of gas ‘know’ where they should be.

It is also worth emphasising that although the numbers of molecules in each jar remain constant, they are not the same molecules: there is continued movement of molecules back and forth but the rate of movement from left to right is exactly the same as that from right to left. We call this situation a ‘dynamic equilibrium’.

**Note**

In the case of real molecules in a gas jar, the molecules are not ‘sucked’ into the vacuum in the empty jar. They move at random, and if they happen to be travelling in the direction of the empty jar, they will arrive there. Once there, collision with the sides of the jar or other particles may send them back again.

### Arranging objects simulation

#### Introduction

This simulation allows you to look at the probability of different arrangements of objects between two boxes with different numbers of particles.

We saw in the ‘Entropy and disorder’ simulation that objects moving at random will arrange themselves equally between two boxes. This simulation looks a little more closely at why this should be. Like ‘Entropy and disorder’, it does not try to closely model a real chemical situation.

#### Instructions

It is important to distinguish between a particular state that we might be able to observe and the way(s) that it is made up. This simulation lets you investigate the number of ways that make up a particular state and see how this varies with the number of objects.

Try this example: set the number of objects to 2 using the left hand slider. Now, using the right hand slider, determine the most likely distribution of objects. The higher the number the more probable the state.

#### Observations

When there are two boxes (1 and 2) and two objects (A and B), there is only one way to distribute both objects in the same box:

- A and B in box 1
- A and B in box 2

However, there are two ways of distributing one object in a box:

- Object A in box 1 and object B in box 2
- Object B in box 1 and object A in box 2

If all the objects are identical, we cannot distinguish between them and they all lead to the same state. However, some states are more probable than other because there are more arrangements that lead to them.

50 : 50 arrangements (and those close to this) are much more likely than ones where one box has few objects and the other many. This probability increases enormously as the total number of objects increases and would become virtually certain for an everyday number of particles such as a mole (6 x 10^{23}).

For just two particles, A and B, the table below shows the possible arrangements. This leads to three possible observable ‘states’ of the system – we cannot distinguish between the two 1/1 arrangements because the particles are identical.

Box 1 | Box 2 | State | Number of arrangements leading to this state |
---|---|---|---|

A and B | none | 2/0 | 1 |

A only | B only | 1/1 | 2 |

B only | A only | 1/1 | 2 |

none | B and A | 0/2 | 1 |

A 1/1 mixing is obtainable in two ways – there are two arrangements that lead to this state. It is twice as likely as either of the ‘unmixed’ states which each have only one arrangement. There is a total of four arrangements.

The table below shows the possible arrangements for three particles – A, B and C – leading to four observable states.

Box 1 | Box 2 | State | Number of arrangements leading to this state |
---|---|---|---|

A, B, C | none | 3/0 | 1 |

A, B | C only | 2/1 | 3 |

B, C | A only | 2/1 | 3 |

C, A | B only | 2/1 | 3 |

A only | B, C | 1/2 | 3 |

B only | C, A | 1/2 | 3 |

C only | A, B | 1/2 | 3 |

none | A, B, C | 0/3 | 1 |

**Extension**

Students might be asked to do a similar table for four particles in two boxes – there is a total of 16 (24) arrangements and five observable states.

In general, there are *xy* arrangements where *x* = number of boxes and *y* = number of particles.

With six particles, there is still only one way of having all the particles in box A but 20 ways of arranging three in box A and three in box B.

#### Conclusion

Notice how states with more mixing are more probable than those with less because there are more arrangements that lead to them. We say that these mixed arrangements are more disordered or random than the ‘unmixed’ ones.

If we extend the argument to 100 particles, an arrangement of one particle in the left hand box and 99 on the right is very unlikely while arrangements of 50 : 50 and others close to it such as 49 : 50 are very likely. This is because there are many more ways of these distributions happening.

The reason that particles spread evenly between the two boxes is that there are more arrangements of particles between the boxes that correspond to mixing than ones that correspond to separation. We say that the ‘all-in-one-box’ arrangements are more ordered (less random) than the ones that are evenly spaced out.

### Additional information

This resource was originally published by the Royal Society of Chemistry in 2015 as part of the Quantum Casino website, with support from Reckitt Benckiser.

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