Relative masses of atoms and molecules

 

Relative masses of atoms and molecules

 Since atomic particles are so small, masses of atoms, molecules, etc are given in the Carbon-12 scale. The unit of mass will be 1/12 parts of a Carbon-12 atom (also represented as C-12 or ¹²C). On this scale, the ¹²C isotope is given a mass of exactly 12 units, and the masses of all other isotopes/atoms/molecules are measured on the same scale. The unit f

 Relative isotopic mass

The relative isotopic mass, is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.

Isotopes are atoms of the same element, with different numbers of neutrons. The difference in the number of neutrons produces atoms with different masses but with the same chemical properties. (Electrons and protons are in the same amount in any isotope of the same element). 

Isotopes of Chlorine:

Isotope	Protons	Electrons	Neutrons
Chlorine-35	17	17	18
Chlorine-37	17	17	20

An atom of the ¹H isotope is only 1/12 of the mass of the ¹²C isotope and so is given a relative isotopic mass of 1.
An atom of the ³⁷Cl isotope is 37 times the mass of 1/12 of the mass of ¹²C.

Relative atomic mass – A_r

The relative atomic mass of an element is the weighted average of the masses of its isotopes relative to 1/12 of the mass of a carbon-12 atom.

A weighted average must be calculated since we do not have the same amount of isotopes in an atom.

Example:

In chlorine, there are 75% atoms of chlorine-35 and 25% of chlorine-37. We will calculate the “weighted average”

The total mass (for 100 atoms) would be (75 x 35) + (25 x 37) = 2625 + 925 =

The average mass of these 100 atoms would be 3550 / 100 = 35.5

This is the value we find for the relative atomic mass of chlorine in the periodic table, so

35.5 is the relative atomic mass of chlorine.

Relative molecular mass, M_r 

(BE CAREFUL: The term relative formula mass or Mr will be used for ionic compounds)

The relative molecular mass of a substance is the weighted average of the masses of the molecules relative to 1/12 of the mass of a carbon-12 atom.

Many times we get confused.

• The term Molecular mass M_r will be used only for covalent compounds that actually form molecules as well as the monoatomic molecules formed by the noble gases.
• For ionic compounds we will be use the term Formula Mass but we will represent it with the same symbol: M_r

In other words: Mr will be used for the relative mass of any compound, we will call this symbol “Molecular mass” or “Formula mass” based on the substance nature (covalent or ionic) 

 

Relative formula mass, M_r

The relative formula mass of a substance is the weighted average of the masses of the formula units relative to 1/12 of the mass of a carbon-12 atom.

PLease note: The relative formula mass is given exactly the same symbol, M_r, the same as the relative molecular mass.

We will use Molecular mass for covalent compounds and Formula mass for ionic compounds.

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 Relative masses of atoms and molecules

Exercises

Working out masses: (worked examples)

Relative atomic mass from isotopic masses: 

a) FROM % ABUNDANCE

Isotopes	Mass (AMU)	Abundance (%)
C-12	12.000000	98.90
C-13	13.003355	1.10

To calculate the average atomic mass, each exact isotopic mass is multiplied by its % abundance and divided by 100

 [(12.000000 AMU x 98.90) +(13.003355 AMU x  1.10)] / 100 = 12.011 AMU  

or, we can work with the percentages in decimals, avoiding the division by 100 later: 

[(12.000000 AMU) (0.9890) + (13.003355 AMU) (0.0110)] = 12.011 AMU

b) FROM MASS OF SUBSTANCE

Isotopes	Mass (AMU)	Abundance (g)
C-12	12.000000	39.56
C-13	13.003355	0.44

 To calculate the average atomic mass, each exact isotopic mass is multiplied by its mass of each abundance in grams and then divided by the total mass of all isotopes together (In this case, they add up to 40 g of sample)

 [(12.000000 AMU x 39.56 g) +(13.003355 AMU x  0.44 g )] / 40 g = 12.011 AMU   

Relative isotopic masses from relative atomic mass

Molecular masses from relative atomic masses

Formula masses from relative atomic masses

Relative atomic masses from Molecular masses or Formula masses.

 

Write down the formula, and then add up all the relative atomic masses of the atoms it contains.

Example 1

The relative formula mass of NaCl = 23 + 35.5 = 58.5

Example 2

The relative formula mass of copper(II) sulfate crystals, CuSO₄.5H₂O:

 

M_r of CuSO₄.5H₂O = 63.5 + 32 + (4 x 16) + 5 x [(2 x 1) + 16] = 249.5

 

Note:   The relative atomic mass of copper is often quoted as 64.  I am using 63.5 here because that is the figure that comes from the CIE Periodic Table.

Be careful with things which contain water of crystallisation like the copper(II) sulfate crystals in this example.  Add the water up first and then multiply it by 5 (or whatever other number you need).  If you try to do it as hydrogen and oxygen separately, you stand a good chance of getting it wrong.  Students usually remember to multiply the 2 hydrogens by 5, but forget to multiply the oxygen by 5.  If you add the water up as a whole, that can’t happen.

Defining the relative formula mass

I find it hard to imagine an exam question in which you were asked to define relative formula mass rather then just work it out, but just in case . . .

Either:

1. 1. 1. 1. 1. 1. 1. 1. • The relative formula mass of a substance is the weighted average of the masses of the formula units on a scale on which a carbon-12 atom has a mass of exactly 12 units.

Or:

1. 1. 1. 1. 1. 1. 1. 1. •  

The “formula unit” is just the formula as you have written it.