Avogadro's Number - Value, Measurement of electron mass and Coulometry

Avogadro’s number is defined as the various number of component particles such as atoms, molecules, and ions of different charges that are present in the particular amount of material provided by one mole. We can see this as a proportionality aspect which helps relate the mass of the sample to the molar mass of any material. Avogadro’s number can be showed in SI units as 6.022*10²³ mol-1.

In terms of German works, Avogadro’s number can be termed as Loschmidt Constant. This was further defined into several molecules in 12 g of isotope carbon - 12. Apart from that, some more amount of weight can also be added to increase their molecular weight. This number can be dimensionless. They also found out to be having the value of Avogadro constant. This constant can be used as a measurement of the reciprocating number of materials.

This constant was first discovered by a scientist named Amedeo Avogadro in the year 1811. He concluded that the gas volume is proportional to the number of gas molecules irrespective of the gas’s nature.

Measurement of Coulometry

Initially, an accurate technique to measure the constant value of Avogadro was found on coulometry. It is a standard that is derived to calculate F (Faraday constant), which is the electric charge followed by a single mole of electrons. To get the Avogadro constant, this can be separated by elementary charge, e.

There involved a first experiment based on dissolving the silver metal away from the anode contained in the electrolysis cell. This had to be performed while having constant electric current I, for a specific amount of time t. This whole setup was invented by Davis and Bower. Given below is the value for Faraday constant,

From the above equation,

F = Faraday constant (which is the electric charge)

I = electric current

t = time

m = mass of lost silver

Ar = silver’s atomic weight

To compensate for the total amount of the lost silver that was lost during some mechanical reasons present in the anode, the NIST scientists came up with an idea. It illustrates an analysis based on the isotope of the silver that helped to formulate its atomic weight. F90=96485.39 13 C/mol. This is considered the conventional Faraday constant. This helps resemble a value for the Avogadro constant, which is 6.022*10²³ mol-1. It can be seen that both of the values comprise a relative regular uncertainty value of 1.3*10-6.

Measurement of electron mass

CODATA is a Committee of Data for Science and Technology published a various set of constant physical values for international use. It can regulate the constant from molar mass to the rest mass of the electron. We can express this as,

From the above equation, Ar (e) is regarded as the relative atomic mass of the electron which is derived directly as a calculated quantity. In the SI, Mu can be considered as the constant of molar mass. With the help of other measured constants, the rest mass of electrons can be measured as given below,

International Avogadro coordination

One of the main reasons this Avogadro project was assigned is to make maximum efforts to define the kilograms in terms of a physical constant that can be used universally. It can also help balance the Planck constant measurements with the help of Kibble balances. As of now, the most recent definitions of the SI (International System) units made a statement that the Avogadro constant is the secondary calculation of Planck’s constant.

This defined calculation uses silicon balls which are all highly polished along with the weight of one kilogram. They can help reduce the complexity of measurement of size as well as the density to decrease the effects of coating oxide on its outer surface. The first type of measurements used certain silicon balls that contain natural isotopic composition. They also contained a relative uncertainty of 3.1*10-7.

It seemed the above discussed first outcomes were not so consistent. This is because they have mismatched values with Planck’s constant which results in the false attainment of Kibble balance calculation. But currently, the source that caused inconsistent values is found to be known.

The balls of silicon are said to have a diameter of a repeatable value of around 0.3 nm. On the other hand, the uncertainty in the quantity is valued to be 3 μg.