A molar mass calculator

Why write a program for a sum?

The molar mass of water is a quick sum. The molar mass of copper sulphate crystals, $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$, takes longer, and a chemist does such sums all day. A program does them in a moment, for any formula, and never forgets an atom.

In this lesson you build a molar mass calculator in three steps:

1. Keep the atomic masses in a dictionary.
2. Read a formula such as C6H12O6 into symbols and counts.
3. Open brackets, as in Ca(OH)2.

Step 1: a dictionary of atomic masses

A dictionary links a key to a value. Here each key is an element symbol, and each value is its atomic mass in grams per mole, from the NCERT table.

The line with sum reads like the rule itself: for each element and its count, multiply the atomic mass by the count, and add them all up. glucose.items() gives the pairs ("C", 6), ("H", 12) and ("O", 6).

The f before the string makes it an f-string. {M:.2f} prints M with two decimal places.

Step 2: reading a formula

Typing {"C": 6, "H": 12, "O": 6} each time is slow. It is easier to type C6H12O6 and let the program read it. Look at the pattern of a formula:

• an element symbol is one capital letter, sometimes followed by one small letter: C, Ca, Cl;
• a number may follow it; no number means one atom.

A regular expression describes exactly this pattern. Python's module re finds every match:

It prints [('Na', ''), ('H', ''), ('C', ''), ('O', '3')]. Read the pattern piece by piece:

• [A-Z] is one capital letter, and [a-z]? is at most one small letter;
• \d* is any number of digits, possibly none;
• the brackets in the pattern make two groups, so each match is a pair.

An empty count means one atom, so we write int(n or 1). When the count is "", the or gives 1.

Step 3: brackets

Slaked lime is Ca(OH)2. The 2 belongs to the whole bracket: two oxygen and two hydrogen atoms. The program finds each bracket with its number, counts the atoms inside, multiplies them, and writes them back without the bracket. Ca(OH)2 becomes CaO2H2, which Step 2 can read.

Percent composition

Once you have the counts, the mass percent of each element is its mass in one mole divided by the molar mass, times $100$. For slaked lime the program prints about $54.1\%$ calcium, $43.2\%$ oxygen and $2.7\%$ hydrogen. The percentages always add up to $100$, which is a good test of your code.

Practise with new numbers

Try it in Python

The whole calculator: the dictionary, the reader with brackets, the molar mass and a percent composition table.

Common mistakes

• A symbol missing from the dictionary. molar_mass("KCl") stops with KeyError: 'K'. Add every element you need to atomic.
• Reading an empty count as a number. int("") stops with ValueError: invalid literal for int() with base 10: ''. Write int(n or 1).
• Capital letters matter. Co is cobalt, but CO is carbon and oxygen. The reader is right to treat them differently, so type formulas with care.
• Forgetting the bracket's number. In Ca(OH)2 the 2 multiplies both the oxygen and the hydrogen.
• Testing only one formula. Test water, a formula with a two-letter symbol, and one with brackets.

Remember these

• Molar mass $=$ the sum of atomic mass times count, for every element: sum(atomic[el] * n for el, n in counts.items()).
• re.findall(r"([A-Z][a-z]?)(\d*)", formula) gives pairs of a symbol and its count; an empty count means one.
• Open brackets first, multiplying the atoms inside by the number after the bracket.
• Mass percent $= \dfrac{\text{atomic mass} \times \text{count}}{M} \times 100$, and the percentages add up to $100$.

Check yourself

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

1. What does re.findall(r"([A-Z][a-z]?)(\d*)", "MgCl2") return?

2. Why does the program write int(n or 1) and not int(n)?

3. How many hydrogen atoms are in one unit of Al(OH)3?

4. Your function gives percentages for a compound that add up to $87\%$. What does that tell you?

5. Why is a dictionary a good choice for the atomic masses?