History: Mendeleev and Modern Periodic Law

The modern periodic law states that the properties of the elements are a periodic function of their atomic numbers, and it grew out of Dmitri Mendeleev’s periodic table of 1869, which arranged the known elements by atomic mass and left gaps for undiscovered ones. In brief: Mendeleev predicted the properties of eka-silicon, which was discovered in 1886 as germanium, and the later work of Henry Moseley in 1913 replaced atomic mass with atomic number as the basis of the table.

The periodic table is one of the most important achievements of chemistry. It was not invented by one person in one moment, but built by several scientists who noticed patterns among the elements. This article describes the early attempts to classify elements, explains Mendeleev’s method and his successful predictions, shows why Moseley’s work was needed, compares the old and new periodic laws in a table, works through a prediction example and gives some common misunderstandings.

What came before Mendeleev?

By 1860, about 60 elements were known, and chemists had begun to see relationships among them. In 1829, Johann Döbereiner noticed “triads”, groups of three similar elements in which the atomic mass of the middle element was about the average of the other two, for example lithium, sodium and potassium. In 1865, John Newlands arranged the elements by atomic mass and observed that every eighth element had similar properties, which he called the “law of octaves”, though his idea was ridiculed since it failed beyond calcium. In 1864 and 1870, Lothar Meyer published tables based on atomic volume, which showed periodic changes in physical properties.

How did Mendeleev build his table?

In 1869, the Russian chemist Dmitri Mendeleev wrote the elements on cards and arranged them in order of increasing atomic mass, grouping elements with similar chemical properties in the same column. He published his table when he was writing a chemistry textbook. His key decisions were bold:

• He left gaps for elements that he believed had not yet been discovered, instead of forcing elements into the wrong place.
• He reversed the order of some elements when their properties required it, such as tellurium (atomic mass 127.6) and iodine (126.9), placing iodine after tellurium because it behaves like the other halogens.
• He corrected some atomic masses that he thought were wrong, for example for beryllium and uranium.

Which predictions did Mendeleev make?

Mendeleev predicted the existence and properties of several elements, which he named using the prefix eka, from Sanskrit for “one”, for the element below a known one. His predictions were later checked with remarkable success.

He also predicted eka-aluminum, discovered in 1875 as gallium by Paul-Émile Lecoq de Boisbaudran, and eka-boron, discovered in 1879 as scandium by Lars Fredrik Nilson. The discovery of gallium was especially striking: Mendeleev suggested that the measured density of the new element was wrong, and when the density was measured with a purer sample, it matched his prediction of about 5.9 g/cm³.

Worked example: predicting properties of a missing element

Mendeleev’s method of estimating the properties of a missing element was to average the values of its neighbors in the table. In the group of silicon, tin lies below the gap that germanium would fill (Mendeleev’s eka-silicon), with silicon above it.

1. Atomic mass. Silicon has an atomic mass of 28.09 and tin has 118.7. The average of the neighbors above and below the gap, silicon and tin, is (28.09 + 118.7) ÷ 2 = 73.4, which is close to the real value of germanium, 72.6. Mendeleev refined this by also using the horizontal neighbors, gallium’s predicted mass of 68 and arsenic’s 75, which average to (68 + 75) ÷ 2 = 71.5, giving a prediction of about 72.
2. Density. Silicon has a density of 2.33 g/cm³ and tin 7.31 g/cm³. The average is (2.33 + 7.31) ÷ 2 = 4.82 g/cm³, and Mendeleev’s estimate of 5.5 g/cm³ from all neighbors is within about 3% of the measured 5.35.
3. Formula of the oxide. The elements in this group form oxides with the formula XO₂ (CO₂, SiO₂, SnO₂), so eka-silicon should form EsO₂, which agrees with germanium dioxide.
4. Percentage error. For the atomic mass, |72 − 72.6| ÷ 72.6 × 100% = 0.8%. For the density, |5.5 − 5.35| ÷ 5.35 × 100% = 2.8%.

Why was the table changed to atomic number?

Ordering by atomic mass worked in most places, but a few pairs were in the wrong order: argon (39.95) and potassium (39.10), cobalt (58.93) and nickel (58.69), tellurium and iodine. Mendeleev put them in the order that fit their properties and suspected that the masses were wrong. In 1913, Henry Moseley studied the X-rays emitted by many elements and found that the square root of the frequency varies in a straight line with a whole number, which equals the nuclear charge, the atomic number. When elements are arranged by atomic number, all the reversals disappear. Moseley also showed, among other gaps, that elements with atomic numbers 43, 61 and 75 were still missing, which were later found as technetium, promethium and rhenium, so the number of undiscovered elements could be counted for the first time.

What is the modern periodic law?

Today the periodic law is explained by quantum mechanics: elements in the same group have similar outer-shell electron configurations, and these repeat in a regular way as the atomic number increases.

Timeline of the periodic table

Which mistakes are common?

Mistake 1: Saying that Mendeleev discovered the periodic law alone

Others, especially Lothar Meyer, found similar patterns. Mendeleev’s advantage was his boldness in predicting new elements and in correcting data.

Mistake 2: Believing that the modern table is ordered by atomic mass

It is ordered by atomic number. Mass order would put some pairs the wrong way round.

Mistake 3: Thinking that Mendeleev knew about the noble gases

They were discovered in the 1890s, and they fitted into a new group without disturbing his scheme, which was a strong confirmation.

Mistake 4: Treating the periodic table as finished

The table is complete up to element 118, but chemists still study the properties of the heaviest elements and attempt to make new ones.