The first chemical reaction that takes place when making the yttrium-barium-copper oxide superconductors is:

In order to obtain the correct ratio of the starting ingredients, it is necessary to have the correct molecular ratios.  Since all of the atoms and molecules have different weights, the weight ratios of the atoms and molecules must be known before the correct weight ratios of the chemical powders can be calculated.

The molecular weight of a compound is the weight of a compound, in grams, that countains 6.02 x 10²³ molecules.  The molecular weight of a compound is easily calculated by adding up its constituent atomic weights.  For example, the chemical formula for yttrium oxide is Y₂O₃, meaning that each molecule of yttrium oxide has two atoms of yttrium and three atoms of oxygen.  The atomic weight of yttrium is 88.9059.  (In other words, 88.9509 grams of yttrium contains 6.02 x 10²³ atoms.) The atomic weight of oxygen is 15.9994.  (Since oxygen atoms are much lighter than yttrium, only 15.9994 grams of oxygen contains 6.02 x 10²³ oxygen atoms.)

For Y₂:    2 x 88.9059 = 177.8818

For O₃:   3 x 15.9994 = 47.9982

Molecular Weight of Y₂O₃ = 225.88

Therefore 225.88 grams of yttrium oxide contains 6.02 x 10²³ molecules.

Since the atomic weight of barium is 137.33 and the atomic weight of carbon is 12.011, the molecular weight of barium carbonate can be calculated in a similar fashion to be 197.35.

Since the atomic weight of copper is 63.546, the molecular weight of cupric oxide is 63.546 + 15.9994 = 79.5454.

Therefore the proper ratios for the desired chemical reaction are:

• 0.5 x 225.88 = 112.94 grams of Y₂O₃
• 2 x 197.35   =   394.7 grams of BaCO₃
• 3 x 79.5454 = 238.6362 grams of CuO

Since these weights are the correct ratios, they can all be multiplied or divided by any number to obtain more convenient quantities in the proper ratios.  By dividing by 10 (and doing some rounding off), we obtain these weights:

• 11.29 grams of yttrium oxide
• 39.47 grams of barium carbonate
• 23.86 grams of cupric oxide

The result of mixing and heating the chemicals of this combination of weights will be 6.02 x 10²² molecules of the YBa₂Cu₃O_6.5 starting compound.  When this compound is later heated under flowing oxygen, it will take on additional oxygen into its crystal structure and become YBa₂Cu₃O₇, which is a superconductor when cooled below its critical temperature.

Return to the Instructions for Making Superconductors.