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The NCERT Class 12 chapter on solutions gives you π = CRT in two lines. Behind those lines is a botanist who spent years making a membrane that would not leak or burst. This post covers who Wilhelm Pfeffer was, how he built the first working osmometer, what his numbers showed, and how to check them against the formula yourself.
Who was Wilhelm Pfeffer?
The Neue Deutsche Biographie entry on Pfeffer records that he was born on 9 March 1845 in Grebenstein near Kassel and died in Leipzig on 31 January 1920. He trained first as a pharmacist, took a doctorate in chemistry at Göttingen in 1865, and then turned to botany, working with Julius Sachs at Würzburg. He became a professor at Bonn in 1873, Basel in 1877 and Tübingen from 1878 to 1887, then spent three decades in Leipzig. The entry also lists his membership of the Royal Society in 1897, and *Nature* marked his death with an obituary as a Foreign Member.
His book on osmosis, *Osmotische Untersuchungen*, was published in Leipzig in 1877. You can read a scanned copy of the 1877 edition online.
Why was the membrane the hard part?
To measure osmotic pressure you need a membrane that lets water through, stops sugar, and survives the pressure. Van 't Hoff listed exactly those three conditions in his 1901 Nobel lecture, crediting Pfeffer as the first to meet them, in 1877.
Pfeffer's book describes the trick. A precipitate of copper ferrocyanide makes a good semipermeable film, but on its own it bulges and bursts. So he took porous clay cells of the kind used in electric batteries, soaked them with copper sulphate solution, then filled them with potassium ferrocyanide solution. Where the two met inside the clay wall, a thin reddish-brown membrane formed, supported by the clay. He connected each cell to a mercury manometer and read the pressure as a height of mercury.
The current NCERT chapter on solutions describes semipermeable membranes such as parchment and cellophane and defines osmotic pressure as the extra pressure needed to stop solvent flowing into the solution. Pfeffer's clay cell was a way of building one that could hold a large pressure.
What did Pfeffer measure?
In Table 9 of his book, measured between 13.5 and 16.1 °C, cane sugar solutions gave these mercury heights:
1% sugar: 53.5 cm
2%: 101.6 cm
4%: 208.2 cm
6%: 307.5 cm
His own ratio columns show pressure divided by concentration staying between 0.95 and 1 of the 1% value. Doubling the sugar roughly doubled the pressure. In Table 12 he measured 1% solutions at different temperatures and the pressure rose, for example from 51.0 cm at 14.2 °C to 54.4 cm at 32.0 °C.
Pfeffer could not find the law behind these numbers. Van 't Hoff says Pfeffer even asked the physicist Clausius, who could not either, and that the results "remained in a specialized botanical paper". The NDB entry says van 't Hoff built his theory of solutions on Pfeffer's results. Our post on van 't Hoff and the tetrahedral carbon atom covers his other big idea.
Worked example: does π = CRT predict Pfeffer's number?
Take a 1% sugar solution: about 1 g of sucrose in 100 g of solution. For a dilute solution, treat that as about 10 g per litre.
Moles of sucrose (M = 342.3 g mol⁻¹): 10 ÷ 342.3 = 0.0292 mol, so C ≈ 0.0292 mol L⁻¹.
Temperature: take 15 °C, the middle of his range, so T = 288 K.
π = CRT = 0.0292 × 0.0821 × 288 = 0.690 atm.
Convert Pfeffer's reading: 53.5 cm ÷ 76 cm per atm = 0.704 atm.
The prediction is within about 2% of his measurement. Van 't Hoff's Nobel lecture gives the same headline: a 1% sugar solution exerts about 2/3 atm.
Now check the temperature result. From 14.2 °C to 32.0 °C, the kelvin temperature rises by a factor of 305.2 ÷ 287.4 = 1.062. Pfeffer's pressure rose by 54.4 ÷ 51.0 = 1.067. Again, close to the formula.
Common mistakes to avoid:
Using mass percent as molarity. Convert grams to moles and the solution volume to litres first.
Using Celsius. T must be in kelvin.
Mismatched units. With R = 0.0821 L atm K⁻¹ mol⁻¹ you get atm; with 0.083 L bar K⁻¹ mol⁻¹, as NCERT uses, you get bar.
Forgetting ions. Salt solutions give larger pressures; the van 't Hoff factor in our post on colligative properties handles that.
For more problems like this, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student learn from Pfeffer?
Fix the instrument first. Pfeffer's real breakthrough was a membrane that worked. Many failed experiments are equipment problems.
Record the conditions. He noted the temperature of every run, which is what let others test the temperature law later.
Cross subjects. A pharmacist turned botanist produced data that physical chemists needed.
Try it now: use π = CRT to predict the mercury height for Pfeffer's 4% solution, then compare your answer with his 208.2 cm.
