The periodic table and stoichiometry: how to go from atoms to grams

How the periodic table organizes elements

Elements are arranged by increasing atomic number, which counts the protons in the nucleus. Rows are called periods and correspond to the highest principal energy level occupied; columns are groups, and elements in the same group have similar valence behavior. The block label names the subshell being filled: s, p, d or f.

The main grid is 18 columns wide. The 15 lanthanides and 15 actinides are f-block elements and are usually shown as two extra rows below the table, with placeholders in group 3 so the main shape stays readable. Their position still records the period: lanthanides belong to period 6 and actinides to period 7.

Atomic number, mass number and atomic weight

The atomic number is exact: it is the number of protons and defines the element. The mass number of a particular atom counts protons plus neutrons, so it is a whole number and differs between isotopes. Chlorine, for example, is mostly chlorine-35 with some chlorine-37, which is why its atomic weight is the non-integer 35.45.

The standard atomic weight in the periodic table is a weighted average over the naturally occurring isotopes. Its unit is the unified atomic mass unit, and one mole of atoms has a mass in grams equal to that number, which is why the same value is written as g/mol. Ionic or isotopic samples can differ from the average; the table's value describes the natural mixture.

Moles: the bridge from particles to grams

One mole contains 6.02214076 × 10²³ entities, the Avogadro constant. Because the periodic table's atomic weight is also the molar mass in g/mol, dividing a mass by that value gives moles: n = m / M. Four grams of hydrogen gas, H2, has a molar mass of 2.016 g/mol, so it is 4 / 2.016 = 1.984 mol of H2.

The same conversion works for compounds once the formula's molar mass is known: add the atomic weights of every atom in the formula unit. The molar mass and mole calculators on this site perform both steps and show the arithmetic, which is worth checking the first few times.

Stoichiometric ratios from a balanced equation

A balanced equation gives the mole ratio of the reaction. For 2H2 + O2 → 2H2O the coefficients 2, 1 and 2 mean that two moles of hydrogen react with one mole of oxygen to form two moles of water. Any amount of one species scales every other species by the ratio of coefficients.

With 4 g of hydrogen, the moles of H2 are 1.984. The ratio of water to hydrogen is 2:2, so water also forms 1.984 mol; its molar mass is 18.015 g/mol, giving 1.984 × 18.015 = 35.74 g. Oxygen is consumed in a 1:2 ratio, so 1.984 / 2 = 0.992 mol, which is 0.992 × 31.998 = 31.74 g. The masses balance: 4.00 g + 31.74 g = 35.74 g.

Percent composition and the limits of ideal stoichiometry

Percent composition is the same molar mass arithmetic read the other way: each element's contribution divided by the total, times 100. Water is 2.016 / 18.015 = 11.19% hydrogen and 88.81% oxygen by mass, and a 50 g sample therefore contains about 5.60 g of hydrogen.

Stoichiometry as calculated here is ideal: it assumes the reaction goes to completion along the balanced ratio and that no side reactions, losses or impurities intervene. It does not decide which reactant runs out first. To find the limiting reagent, convert each reactant to moles, divide by its coefficient and compare the quotients; the smallest one limits the reaction. Real yields are lower than the theoretical mass, which is why percent yield compares the two.

• Balance the equation before using any ratio.
• Convert everything to moles, then apply coefficients, then convert back to grams.
• Check that reactant and product masses match as a guard against arithmetic slips.
• Compare reactant quotients to find the limiting reagent; the tool does not do this for you.