Counting by Weighing

Counting by weighing is one of the most efficient ways of counting large numbers of objects. Suppose that you have a job packing 1,000 nuts and 1,000 bolts in big bags, and you get paid for each bag you fill. So what’s the most efficient and quickest way of counting out nuts and bolts? Weigh out a hundred, or even ten, of each and then figure out how much a thousand of each will weigh. Fill up the bag with nuts until it weighs the amount you figured for 1,000 nuts. After you have the correct amount of nuts, use the same process to fill the bag with bolts.

In chemistry, you count very large numbers of particles, such as atoms and molecules. To count them efficiently and quickly, you use the count-by-weighing method, which means you need to know how much individual atoms and molecules weigh. Here’s where you find the weights:

✓ Atoms: Get the weights of the individual atoms on the periodic table — just find the atomic mass number.

✓ Compounds: Simply add together the weights of the individual atoms in the compound to figure the molecular weight or formula weight. (Note: Molecular weights refer to covalently bonded compounds, and formula weights refer to both ionic and covalent compounds.)

Here’s a simple example that shows how to calculate the molecular weight of a compound: Water, H₂O, is composed of two hydrogen atoms and one oxygen atom. By looking on the periodic table, you find that one hydrogen atom weights 1.0079 amu and one oxygen atom weighs 15.999 amu . To calculate the molecular weight of water, simply add together the atomic weights of two hydrogen atoms and one oxygen atom:

Two hydrogen atoms: 2 × 1.0079 amu = 2.016 amu

One oxygen atom: 1 × 15.999 amu = 15.999 amu

Weight of the water molecule: 2.016 amu + 15.999 amu = 18.015 amu

Now try a little harder one. Calculate the formula weight of aluminum sulfate, Al₂(SO₄)₃. In this salt, you have two aluminum atoms, three sulfur atoms, and twelve oxygen atoms.

After you find the individual weights of the atoms on the periodic table, you can calculate the formula weight like this:

[2 aluminum atoms + 3 sulfur atoms + 12 oxygen atoms] = weight of Al₂(SO₄)₃

[(2 × 26.982 amu) + (3 × 32.066 amu) + (12 × 15.999 amu)] = 342.15 amu