Measuring Atoms -- By their masses and numbers

1. Definitions

Masses (amu, gram)

Atomic Mass Unit (amu) : One atomic mass unit, or 1 amu, is exactly 1/12 the mass of a carbon-12 atom.

Average Atomic Masses: Average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an an element.


Numbers

Mole : A mole is the amount of a substance that contains as many particles as there are atoms in exactly 12 g of carbon-12. This number is NA = 6.022x10^23 (Avagadro's Number).


Relating numbers to masses

Molar Mass (g/mol): Molar mass is the mass of one mole of a pure substance.


2. Relationships

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No. of atoms - Mass(amu) - Mass(mass of 1 C-12 atom) - Mass (g) - No. of atoms (mole)

-----------------------------------------------------------------------------------------------------------------

1C ------------------ 12 ------------------ 1 --------------------------------- 12/Na -------------------- 1/N

1H ------------------ 1 ------------------ 1/12 -------------------------------- 1/Na ---------------------1/Na

1X ------------------ X ------------------ X/12 -------------------------------- X/Na -------------------- 1/Na

NaC ----------------- Na12----------------- Na ---------------------------------- 12 ---------------------- 1

NaH ----------------- Na ----------------- Na/12 -------------------------------- 1 ----------------------- 1

NaX ----------------- NaX----------------- NaX/12 ------------------------------- X ----------------------- 1

===================================================================================================

3. Comments

How are the content of the table obtained?

-- This table contains 5 columns and 6 rows.

-- Columns 1 and 5 are the "Number of atoms" with column 1 in terms of "atoms" and column 5 in terms of "mole of atoms". Columns 2, 3 and 4 are masses with column 2 in terms of "amu", column 3 in terms of "mass of C-12", and column in terms of "grams".

-- Rows 1, 2 and 3 are for 1 atom of C-12, H, and X (general element with amu of X. Rows 4, 5, and 6 are for Na=6.22x10^23 (1 mole) of atoms for C-12, H and element X.

-- Row 1 column 1, 2 and 3 are obtained based on the definition of amu: each amu has a mass of 1/12 of that of an atom of C-12. Therefore, each C-12 has 12 amu.

-- Row 2 column 1, 2 and 3 are also obtained based on the fact that 1 H atom has a mass of 1/12 of that of C-12. Therefore, it has amu of 1.

-- Row 3 column 1, 2 and 3 are obtained based on the fact that 1 X atom has a mass of X(1/12) of that of C-12. Therefore, it has amu of X. The amu number X for element X is recorded in the Periodic Table and it is in fact the average amu of all isotopes of element X based on the abundance of the each isotope.

-- Columns 1, 2 and 3 of Row 4, 5 and 6 are obtained for Na=6.22x10^23 atoms (1 mole) for C-12, H, and X by multiplying row 1, 2 and 3 by Na. Column 5 of row 4, 5, and 6 are obtained based on the fact that Na is just 1 mole.

-- Column 4 of row 4 is obtained from the definition of mole: A mole is the amount of a substance that contains as many particles as there are atoms in exactly 12 g of carbon-12. This number is NA = 6.022x10^22 (Avagadro's Number).

-- Column 4 of rwo 5 and 6 are obtained based on the fact that the mass ratio betwen H and C-12 is 1/12
and the mass ratio between X and C-12 is X/12 for the same number of atoms. A term is given for Column4 of row 4, 5 and 6: molar mass. As it can be seen, it has the exact same numerical value as the average amu for each element which can be found from Periodic Table.

-- Row 1, 2 and 3 of column4 is obtained from rows 4, 5 and 6 of column 4 by dividing each of them by Na.

-- Column 5 of row 1, 2 and 3 are obtained by the fact that 1 atom of any element is just 1/Na of mole of that element.

-- In summary, all of the relationships can be derived from definition of amu and mole. The amu of a general element can be found from the Periodic Table. Another fact to remember is that 1 mole is nothing but 6.22x10^23 (Avagadro's number).

4. Observations

Convertion factors are obtained by looking at entries marked as 1.

4.1 gram <--> amu (absolute mass <--> relative mass)

-- Column 2, 3 and 4 reveals the relationship among different units of mass (amu and gram). That is,
1 amu = 1/Na gram
1 gram = Na amu
It does not matter what element it is. This relationship relates one mass unit (amu) to another mass unit (gram)

This relationship is not oftern used since ... .


4.2 gram <--> mole (molar mass; absolute mass <--> number)

1 mole of any atom X = X gram
= Na atoms
= Na * X amu

-- Molar mass relates mass (gram) and number (mole). Again, numerically, molar mass of a specific element is the same as the amu of that element which can be found in Periodic Table. The molar mass is often used to convert mass into moles in stoichiometry since the chemical reaction equation establishes the relationship in terms of moles, not mass.

4.3 amu <--> atom (relative mass <--> number)

1 atom of element X = X amu
1 amu = 1/X atom of X
= 1 atom of H

4.4 atom <--> mole (absolute number <--> relative number )

1 mole = Na atoms
1 atom = 1/Na mole

4.5 atom <--> amu

See periodic table