This slide depicts data that was included in Wöhler's letter to Berzelius, and which was also included in his paper. For purpose of comparison, this slide also lists each element's percent by mass as it is accepted nowadays, as well as Professor McBride's recalculation of each element's percent by mass based on the atomic weights Berzelius found experimentally.
Wöhler decided to find out if ammonium cyanate really was urea, as the tests he had done seemed to indicate. He used values found through Dr. Prout's earlier elemental analysis of urea. Rather than conducting experimental analysis, Wöhler calculated the percent by mass of each element (N, C, H, O) in ammonium cyanate based on the atomic weights Berzelius found by experiment. He compared his numbers (based on theory) to Dr. Prout's numbers (based on experiment) and found that they agreed with a discrepancy of less than 2%. This discrepancy was small enough for Wöhler to be satisfied with the result, since it was in full agreement with the accuracy expected at that time. However, there were actually many errors and misconceptions involved in the agreement between these numbers.
There are several things to learn from the data on this page:
(1) Experiment vs. Theory: Dr. Prout's values (based on experiment… maybe) are closer to the modern accepted values than Wöhler's calculated values (based on the molecular formula of ammonium cyanate). This teaches us that experiment is often better than theory and that we should not dry-lab the way Lavoisier did. Because of this demonstration of experiment being better than theory, Dr. Prout is recognized for his experimental skill. In fact, his values don't even add up to 100%, as they ought to. This seems to be because of his honesty.
(2) Wöhler's errors: Wöhler used the known formula of ammonium cyanate and the atomic masses found by Berzelius to calculate the percent composition of each atom in the compound. Yet, strangely, his numbers do not add up to 100% either. In fact, they are even farther off from 100% than Prout's values (99.80% vs. 99.875%). Why is this? Comparing Wöhler's numbers to those recalculated by Professor McBride, we can see that Wöhler truncated rather than rounding off his numbers - this is equivalent to always rounding down and would account for his percentage being lower than 100%. However, this doesn't account for all the error in his final percentage. He also made a dislectic error by writing the tenths- and hundredths-digits backwards in his percentage for oxygen!
(3) Dr. Prout's error: Dr. Prout added up the percentages incorrectly, and Wöhler didn't even notice.
(4) Dr. Prout, dry-labber: Compare Dr. Prout's values to the modern values, and notice that his percent mass for nitrogen was accurate to four significant digits. He did not just get lucky. Unbeknownst to Wöhler, Dr. Prout dry-labbed by making a approximate analysis by volume of gas to figure out what the small, whole-number ratios of atoms should be, and then using his own theory to come up with percent mass values. His theory about atomic weight took hydrogen to be the base, assuming that every element was made up by different numbers of hydrogen atoms. This is actually not very far from the truth. Nonetheless, Dr. Prout presented theoretical values as experimental ones - bad science! So much for the paragon of accuracy and honesty…
(5) Experiment vs. Theory, round two: Now that we realize that Dr. Prout's numbers were not entirely experimental after all, we can make an interesting observation - Dr. Prout's theory worked better than Berzelius's experiments on the atomic weights of different elements!
(See the following web page for more detail: https://webspace.yale.edu/chem125/125/history99/4RadicalsTypes/UreaPaper1828.html)
It seemed at the time that Ammonium Cyanate was indeed Urea.
How does ammonium cyanate become urea? The process is as follows:
(1) The lone pair on the nitrogen atom in the cyanate ion :N-=C=O (high HOMO) attacks the N-H antibonding σ* orbital in the ammonium ion +NH4 (low LUMO), creating the products isocyanic acid (H-N=C=O) and ammonia (:NH3).
(2) The lone pair on the nitrogen of the product ammonia (:NH3) is a high HOMO because there is no overlap. But where is the low LUMO? We recall from last quarter that the antibonding π* orbital of C=O is a low LUMO because of poor overlap and the high nuclear charge of oxygen. However, the antibonding π* orbital of C=N is also a low LUMO for the same reasons. The high HOMO (unshared pair in :NH3) can therefore attack the π* orbital of either the C=O bond or the N=C bond. If it attacks the C=O bond, it creates product (Structure 1):
And if it attacks the N=C bond, it creates the product (Structure 2):
The two resulting structures, depicted above, are in "resonance" with one another.
(3) The molecular orbitals within each of these structures mix together.
(a) In Structure 2, one of the unshared pairs on N- (high HOMO) attacks the σ* orbital of one of the N-H bonds in -+NH3 (low LUMO), creating a structure with C as the central atom surrounded by -NH2, -NH2, and =O.
(b) In Structure 1, one of the unshared pairs on O- (high HOMO) attacks the σ* orbital of one of the N-H bonds in -+NH3 (low LUMO), creating a structure with C as the central atom surrounded by =NH, -NH2, and -OH.
However, in either (a) or (b) these molecular orbitals have poor overlap, so such an interaction would likely be intermolecular rather than intramolecular.
Ultimately we get the product structure that is the most stable:
According to reliable lore, which we will learn later, the C=O is very stable and will be formed in preference to =NH, so path (a) will dominate over path (b). Actually, you can also somewhat understand the stability of structure from path (a) based on HOMO/LUMO analysis.
However, ammonium cyanate can exist without turning into the urea structure described in the previous frame. This was first demonstrated by Dunitz and Harris in 1998. They created a crystalline powder of the salt, according to the procedure of Wöhler and Liebig. It was not possible to grow a nice crystal, because ammonium cyanate in a non-urea form converts so easily to urea, but using modern techniques they were able to solve the structure using x-ray diffraction from the powder.
Notice that in the crystal structure depicted on this slide, the lone pair on the nitrogen atom in the cyanate ion (:N-=C=O) points toward the oxygen of another cyanate ion rather than toward the hydrogen of an ammonium ion (+NH4). There is therefore only poor overlap between the high HOMO on :N-=C=O and the low LUMO on +NH4, and the ions cannot react as described in (1) of the previous frame. Perhaps for this reason this crystal structure does not tend to form urea as easily as it might.
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