# GCSE Science/Chemistry Calculations

You need to know how to do quite a few chemistry calculations e.g. how to calculate a mole.

MOLES

Moles are really quite simple to figure out. All you need is periodic table which you will be given in your exam so don't worry! The Mole is simply the name given to a certain number: 602 300 000 000 000 000 000 000 or 6.023 x 10 to the power of 23. When you get precisely that number of atoms of carbon-12 it weighs exactly 12g. So if you get that number of any element or compound and it will weigh exactly the same number of grams as the relative atomic mass, Ar OR Mr

Some Notes on Avogadro's Number, 6.023 x 1023

Chemists use Avogadro's number every day. It is a very valuable number for a chemist to know how to use, and use properly. Where did Avogadro's number come from? Did Avogadro himself do all the calculations? Was it just arbitrarily made up? How can it be measured? Some possible answers follow.

Amadeo Avogadro (1776-1856) was the author of Avogadro's Hypothesis in 1811, which, together with Gay-Lussac's Law of Combining Volumes, was used by Stanislao Cannizzaro to elegantly remove all doubt about the establishment of the atomic weight scale at the Karlsruhe Conference of 1860.

The name "Avogadro's Number" is surely just an honorary name attached to the calculated value of the number of atoms, molecules, etc. in a gram molecular weight of any chemical substance. Of course if we used some other mass unit for the mole such as "pound mole", the "number" would be different. The first person to have calculated the number of molecules in any mass of substance seems to have been Josef Loschmidt, (1821-1895), an Austrian high school teacher, who in 1865, using the new Kinetic Molecular Theory (KMT) calculated the number of molecules in one cubic centimeter of gaseous substance under oridnary conditions of temperature of pressure, to be somewhere around 2.6 x 1019 molecules. This has always been known as the "Loschmidt Number."

I have been searched for some time to determine the first time the term "Avogadro Number" was used. My best estimate is that it was first used in a 1909 paper by Jean Baptiste Jean Perrin (1870-1942) entitled "Brownian Movement and Molecular Reality." This paper was translated into English from the French in "Annales De Chimie et de Physique" by Fredric Soddy and is available. Perrin, was the 1926 Nobel Laureate in Physics for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium. Perrin should be very well known to Dr. Northrup, of our chemistry department here at TTU who does calculation in molecular dynamics using methods developed by Perrin. In his paper Perrin says "The invariable number N is a universal constant, which may be appropriately designated "Avogadro's Constant."

In a simple minded way, here is how it might have come about:

```   First chemists discovered the combining ratios of the elements by mass. Those are the atomic weights. e.g. Na and Cl combine on a 1:1 ratio BY ATOM; BY MASS they combine on a 23 gram to 35.5 gram ratio. This has to mean that an atom of Na weighs less than an atom of Cl.
The Atomic Weight scale was worked out by observations like these.
Next chemists decided to take the Atomic Weight of an element and define that many grams of it to be ONE MOLE.  That meant that 1 gram of H is a mole of H; 12 grams of C is a mole of C 23 grams of Na is a mole of Na, etc.
Finally they measured how many atoms are in ONE MOLE. It comes out to be the number 6.023x1023 atoms Therefore 1 mole of substance = 6.023x1023 particles. This is called Avogadro's Number.
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