# Yotto

1,000,000, 000,000, 000,000, 000,000 units = 1024 units = 1 yotta-unit.
Definition: one yotto of a substance contains 1024 of molecules of that substance
NR = 1024.

Number of yottoes
Let us consider an amount of gas. The gas contains N molecules.
N stands for the number of molecules in the gas. N is a huge number.
Agreement: if N = n × NR, then there is n yotto of gas.
The molecules each have mass m. Then the mass of the gas is mgas = m × N = m × n × 1024

In this way 5·7 yotto of oxygen contains 5·7 1024 molecules of oxygen.
3·8 yotto of sugar contains 3·8 1024 molecules.
0·033 yotto of H2SO4 in diluted solution contains 2 × 0·033 yotto of H+ and 1 × 0·033 yotto of SO42-

The yotto is a didactical and useful replacement of the mole.
1 mole = 0·602214 yotto.

If you want to see the consequences for some chemical calculations
else skip next section.

Comparison with hydrogen
The lightest molecules are those of hydrogen gas. Each hydrogen molecule has a mass equal to 3·32 10-24 gram.
So then one yotto hydrogen has a mass which equals 3·32 gram.
It seems handy to compare the mass of all kinds of substances with the lightest molecules, so those of hydrogen.

In the next explanations we use sugar as an example all the time.
The mass of a sugar molecule is 171 times the mass of a hydrogen molecule.
Then the mass of a yotto of sugar then is 171 × 3·32 gram = 568 gram.

However there are two snags somewhere.
Pitfall 1: a hydrogen molecule consists of two hydrogen atoms. Seldom these atoms are single.
Pitfall 2: unfortunately hydrogen atoms do not all have the same mass. It concerns two different isotopes.
Because carbon exists practically only as one isotope, scientists choose carbon as their unit.
(We can ignore the very rare C-14-isotope.)
That is why we take a look at carbon.

Compare with carbon
Carbon has practically only one isotope. That makes comparing the mass of molecules a lot easier.
The mass of a carbon atom is (about) 12 times the mass of a hydrogen atom.
That explains the number 12 in the next definition.

Relative molecule mass
By definion the relative molecule mass of sugar equals
the absolute mass of a sugar molecule times 12 and divide by the abolute mass of a carbon atom.
The relative molecule mass is abbreviated to Mrel.

The Mrel of all kind of substances you find in chemical tables.Mrel(sugar) = 342.

The chemical mass unit
The mass of a 1024 of carbon atoms is very well measurable.
That is why has been defined:

the chemical mass unit equals the mass of a yotto of carbon atoms divided by 12 exactly.
The chemical mass unit is 1·66054 gram.
This universal constant belongs in a list with scientific constants.
In short: Mchem = 1·66054 gram.
Thus 1·66054 gram is exactly one 1024 times the the atomic mass unit.

The yotto mass of sugar
The yotto mass of sugar = the mass of a yotto of sugar =
= the relative molecule mass of sugar times the chemical mass unit.
In short: M(sugar) = Mrel(sugar) × Mchem

M(sugar) = 342 × 1·66 g = 568 gram.

The mass of sugar
The relative molecule mass of sugar = Mrel(sugar) = 171,
so the mass of one yotto sugar is 342 × 1·66 gram = 284 gram.
If we have 4·00 yotto of sugar, then the mass is: 4·00 × 284 gram = 1·14 kg.
If the number of yotto is generally n , then we can use the next formula: m(sugar) = M(sugar) × n
Of course also the mass equals density times volume.