Coding the reactivity series

A list that holds a rule

In the chapter, you learned the reactivity series: potassium at the top, gold at the bottom. A series is just a list in order. And the rule of displacement can be said in one line:

A metal displaces another from a solution of its salt if it is earlier in the list.

A program is good at a rule like this. It does not get tired, and it does not forget a pair. With a list of eleven metals, there are $11 \times 10 = 110$ pairs to check. By hand, that is a long job. For the program, it is a fraction of a second.

The list and the rule

The place of a metal in the list is its index: $0$ for potassium, $1$ for sodium, and so on. A smaller index is a more reactive metal. So the rule is that series.index(metal) < series.index(other). If this is true, the metal displaces the other. If it is false, there is no reaction.

The rule is a model. A model is a simple idea that we use to predict. We ask: does it agree with what we see?

Test the model

A model is useful when it agrees with what we see. We know three results.

• Zinc in copper sulphate solution: a reaction (the blue colour fades, and brown copper forms).
• Copper in zinc sulphate solution: no reaction.
• Iron in magnesium sulphate solution: no reaction.

If the program says the same for all three, the model works. If it says something different for even one, then the model, or the list, has a mistake.

How to build it, step by step

1. Put the metals in a list, from the most reactive to the least.
2. Write a function that takes two metals and returns True if the first is earlier than the second.
3. Make a list of pairs to test, and print the result of each.
4. Compare the printout with the known results.

You should find that doubling the list from $10$ to $20$ metals almost quadruples the number of tests.

Where the model stops

• Potassium, sodium and calcium react with the water of the solution before they can displace any metal. The simple model does not know this.
• It says if a reaction happens. It does not say how fast.
• It lists only the metals in the series that we give it. A metal that is not in the list gives an error.

Every model has limits. A good scientist says what they are.

Practise with new numbers

Try it in Python

This program tests some pairs with the rule.

Common mistakes

• Reversing the comparison. The smaller index is the more reactive metal, so the test is <.
• Forgetting that index starts at 0. Potassium is at index $0$.
• Asking about a metal that is not in the list. series.index("Li") gives an error until you add it.
• Believing the model too much. It does not know about the water of the solution.

Remember these

• The series is a list in order, and the rule is: earlier in the list displaces later.
• A model is tested against known results, and it has limits (potassium, sodium and calcium react with water first).
• A smaller index means a more reactive metal.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. In the list series of the lesson, what is the index of iron?

2. By the model, does lead displace copper from copper sulphate solution?

3. Why does the model not apply to sodium in copper sulphate solution?

4. How many tests does a program need for a list of $9$ metals, if the order matters?