Stoichiometry
You may think that this is easy and simple stuff. But wait, did anyone halt to ponder on –
- Where did the Avogadro’s number come from?
- Why do we treat it as a constant?
- How was such a big number calculated?
- Why is there an equivalence of the number of atoms or molecules present in the gram atomic mass of every element?
Avogadro’s number is just the ratio of 1 gram to mass of one proton/neutron. Put it not simply, it is the ratio of 12 grams to mass of 1 Carbon 12 atom (which has a total of 12 protons and neutrons).
Table of Contents
Calculating the mass of the proton or neutron
Coulometry
The earliest accurate method to measure the mass of a proton or neutron was based on coulometry.
Here’s how Coulometry works.
X-ray Crystal Density (XRCD) Method
A modern method to determine the mass of a proton or neutron is the use of X-ray crystallography. With time as the platinum-iridium prototypes are deteriorating by 50 micrograms every year, there’s an urge to shift from the physical standard of the kilogram to a sort of more fundamental and environmentally non-vulnerable standard. This is when physicists moved to define the kilogram with the number of atoms of a specific entity.
Accurate measurement of atoms > More precise measurement of the Avogadro’s constant
Professor Stephen Curry perfectly visualizes how X-ray crystallography works:
Usually, the XRCD method can be used with any element but pure crystals of Si-28 have been specifically produced for this purpose because these crystals do not have any voids or dislocations.
Their unit cells within the lattice consist of 8 Si atoms each (as has been observed by the interferometers). Also, being free from dislocations, there are no structural uncertainties in the Si-28 lattice. The basic uncertainty can just be eliminated by making more and more precise interferometers (however, in coulometry, Planck’s constant is the source of the uncertainty whose elimination is much slower than in the XRCD method).
Experiment & Calculation:
The detailed experiment with calculations is here.
Are constants really constant?
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and has a constant value in time. ~ Wikipedia
Uncertainty leading to Inconsistency
| Constant | Symbol | Relative standard uncertainty |
| Proton-electron mass ratio | mp/me | 9.5×10–11 |
| Molar mass constant | Mu | 0 (defined) |
| Rydberg constant | R∞ | 5.9×10–12 |
| Planck constant | h | 1.2×10–8 |
| Speed of light | c | 0 (defined) |
| Fine-structure constant | α | 2.3×10–10 |
| Avogadro constant | NA | 1.2×10–8 |
An uncertainty is an interval or limit under which a measurement may vary. Uncertainties are present in every system due to two basic immovable limiting factors: Systematic and Random errors. We may avoid systematic errors but random errors are so subtle, thus unavoidable.
Our limited dimensional reach
Another constraint we’re tied to is that our observations are just limited to the 3-D universe we see. With increasing studies indicating the existence of other dimensions than just the visible three, it may be possible that whatever physical constants that have been measured so far also exist partially in other dimensions too. But our limit up to the 3-D space is keeping us from accuracy. (Reference: Scientific American)
The uncertainties and our dimensional limits affect only the measurements of various constants up to precision. The entity-value of various constant quantities is the same over time and we might approach closer to that value in the future with more precise measurements and a wider dimensional access.
If uncertainty is universal then, what is the basis of determining constants?
How do we know that we’re reaching an uncertainty?
Taking the case of Avogadro constant calculation: It depends on how frequently you get a particular measurement and if these measurements deflect then, within what range. So, the most frequently obtained measure is assumed as the true value and the range of deflection contributes to the uncertainty.
You may see that even the true value of a physical measurement is assumed by taking the average. This is because we may never go beyond what we can analyze consciously.
If information is an innate property of the universe and logically inseparable from consciousness, a universe without the capacity for conscious beings cannot exist. ~ Fine-tuned Universe
How close are we to pure consistency?
Practically speaking, we’re never close enough unless we have access to every single dimension that exists so far. And who knows if there’re more we have not even clues of!
