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Most students meet germanium as the element that proved Mendeleev right. But someone had to find it, and he did so because his numbers refused to add up. This post tells the story of Clemens Winkler, works through the kind of mass-balance calculation that exposes a hidden element, and ends with habits you can use in your own chemistry.
For Mendeleev's side, including how close his predictions were, see our post on Mendeleev and the periodic table. Here the focus is Winkler's analysis.
Who was Clemens Winkler?
Britannica records that Clemens Alexander Winkler was born in Freiberg, Germany, on 26 December 1838 and died in Dresden on 8 October 1904. Before becoming an academic he spent 12 years managing a cobalt glassworks. In 1873 he joined the Freiberg School of Mining, in a silver-mining district. That combination of factory chemistry and a mining school's analytical tradition is exactly what the germanium problem needed.
How was germanium found?
The Royal Society of Chemistry's germanium page tells the sequence:
In September 1885 a miner at the Himmelsfürst silver mine near Freiberg found an unusual ore.
It went to Albin Weisbach at the nearby Mining Academy, who confirmed it was a new mineral and asked his colleague Winkler to analyse it.
Winkler found 75% silver, 18% sulfur, and 7% he could not explain.
By February 1886 he realised the missing part was a new element. As its properties emerged, it became clear it was the element below silicon that Mendeleev had predicted.
The mineral is now called argyrodite, Ag₈GeS₆. Winkler named the element after Germania, the Latin name for Germany.
He announced it in 1886 in a paper titled Germanium, Ge, ein neues, nichtmetallisches Element ("Germanium, Ge, a new non-metallic element"). The RSC now classifies germanium as a metalloid and describes Winkler recognising it as "metal-like". He followed up with papers titled Mittheilungen über das Germanium ("Communications on germanium") in 1886 and 1887.
Worked example: what the missing 7% tells you
Start with the modern formula Ag₈GeS₆ and standard atomic weights from CIAAW: Ag 107.87, Ge 72.63, S 32.06.
Mass of one formula unit: 8 × 107.87 + 72.63 + 6 × 32.06 = 862.96 + 72.63 + 192.36 = 1,127.95.
Percent silver: 862.96 ÷ 1,127.95 = 76.5%.
Percent sulfur: 192.36 ÷ 1,127.95 = 17.1%.
Percent germanium: 72.63 ÷ 1,127.95 = 6.4%.
Compare Winkler's 75%, 18% and 7%. His analysis of a brand-new mineral was close.
Now run it backwards, as a reasoning exercise rather than a record of Winkler's own method. Take 100 g of the mineral with the modern percentages.
Moles of silver: 76.5 ÷ 107.87 = 0.709 mol.
Moles of sulfur: 17.05 ÷ 32.06 = 0.532 mol. The ratio 0.709 ÷ 0.532 = 1.33 = 8 ÷ 6, which fits Ag₈S₆.
If the formula has one unknown atom per eight silver atoms, moles of X = 0.709 ÷ 8 = 0.0887 mol.
Molar mass of X = 6.44 g ÷ 0.0887 mol = 72.6 g/mol.
That lands in the gap between gallium (69.7) and arsenic (74.9), right where eka-silicon belongs. The catch is step 3: the answer depends on the formula you assume. Chemists needed other evidence, such as the element's compounds and properties, to fix it.
Common slips:
Ignoring a shortfall. Percentages from a complete analysis must total 100%.
Rounding too early. Keep three or four figures until the last step, or a 0.2% error can move you to the wrong element.
Forgetting that the formula is an assumption. Change it and the molar mass changes too.
How did germanium match Mendeleev's prediction?
The RSC notes Mendeleev expected an atomic weight of about 71 and a density of about 5.5 g/cm³. Germanium's standard atomic weight is 72.630. NCERT's Class 11 Chemistry unit on classification of elements describes the gaps Mendeleev left under aluminium and silicon, and tabulates his predictions for eka-aluminium and eka-silicon beside the measured values for gallium and germanium.
What can a student take from Winkler's way of working?
Check that your sums close. Mass balance is one of the strongest checks in chemistry, from a mineral analysis to a stoichiometry problem.
Keep good company. A miner noticed the ore, a mineralogist recognised it as new, and an analyst found the element. Each step needed someone paying attention.
Be ready to revise. Winkler first called germanium non-metallic. Further work refined that picture, and that is normal.
If periodic trends still feel like a list to memorise, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can see why germanium sits where it does.
Next step: repeat the backwards calculation assuming the formula Ag₈X₂S₆ and see which element that would point to.
