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THE MOLE. How many particles are there really? 6.02 x 10 23 "Happy Mole Day to You" Chemistry Song. Mass of a given amount of substance (g). Amount of substance (mol). m. n =. M. Molar Mass (g mol -1 ). The Rule. Worked Example.

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The mole


How many particles are there really?

6.02 x 1023

"Happy Mole Day to You" Chemistry Song

The rule

Mass of a given

amount of substance (g)

Amount of substance (mol)


n =


Molar Mass

(g mol -1)

The Rule

Worked example

Worked Example

  • Calculate the mass of 0.35 mol of magnesium nitrate (Mg(NO3)2.

  • What is the formula we use?????

  • How do we work out M



  • m = n x M

  • (Mg(NO3)2 = 24.3 + 2(14.0 + 3 x 16.0)

    = 24.3 + 2 x 62.0

    = 148.3 g mol-1


    m(Mg(NO3)2= n(Mg(NO3)2 x M(Mg(NO3)2

    = 0.35 mol x 148.3 g mol-1

    = 52 g

    Why only two significant figures?

Counting by weighing

Counting by Weighing

  • If we have a known mass of a substance can we possibly know the number of particles present?

  • We can by combining both the equations we have learnt so far.

  • m = n x M and N = n x NA

  • How do we do this??

Worked example1

Worked Example

  • a) Calculate the amount (in mol) of CO2 molecules present in 22 g of carbon dioxide.

  • b) What is the number of molecules present in this mass of CO2.



n =



n(CO2) =


22 g

n(CO2) =

44.0 g mol-1


  • Since

    M(CO2) = 12.0 + 2 x 16.0

    = 44.0 g mol-1

= 0.50 mol

Solution part b

Solution Part b)

b) Since N = n x NA, where N is the number of specified particles:

N(CO2) = n(CO2) x NA

= 0.50 x 6.02 x 1023

= 3.0 x 1023

So, 22 g of carbon dioxide contains 3.0 x 1023 ??

Atoms, ions or molecules?


Percentage composition

Percentage Composition

  • The values for molar masses of elements in compounds can be used to calculate the percentage composition of a compound once its formula is known.

  • This type of calculation is important in chemistry.

  • If for example, a company is producing aluminium from alumina (Al2O3), the management will want to know the mass of aluminium that can be extracted given a quantity of alumina.

The rule1

Mass of element in 1 mole of compound

% by mass

of the element

x 100


Mass of 1 mole of compound

The Rule

  • Percentage Composition

Worked example2

Worked Example

  • Calculate the percentage of aluminium in alumina (Al2O3).

  • Solution:

    Step 1. Find the molar mass of Al2O3

    M(Al2O3) = (2 x 27) + (3 x 16)

    = 102 g mol-1


Mass of Al in 1 mole of Al2O3


x 100


x 100


% of Al in Al2O3


Mass of 1 mole of Al2O3


  • Step 2:

    Find the percentage of aluminium in the alumina.

    Since 1 mol Al2O3 contains 2 mol Al atoms:

    Mass of aluminium in 1 mol (102 g) of Al2O3 = 2 x 27 g

    = 54 g

= 52.9%

The company management, therefore, knows that aluminium

comprises about 53% by mass of any sample of alumina.

Empirical formulas

Empirical formulas

  • The empirical formula of a compound is the formula that gives the simplest whole number ratio, by number of moles, of each element in the compound.

  • You may have wondered how chemists have determined the formulas of compounds such as water, carbon dioxide, nitrogen dioxide and other compounds.

Empirical formulas1

Empirical Formulas

Empirical formulas2

Empirical Formulas

  • Empirical formulas are determined experimentally, usually by determining the mass of each element present in a given mass of compound.

  • To determine the empirical formula of a compound, therefore, an experimentally determined ratio by mass must be converted to a ratio by numbers of atoms.

  • This is done by calculating the amount (in mol) of each element

Empirical formulas the process

Empirical Formulas – the process

Step 1: Measure the mass (m) of each

element in the compound

Step 2: Calculate the amount in mole (n)

of each element in the compound

Step 3: Calculate the simplest whole number ratio of moles

of each element in the compound

Step 4: Determine the empirical formula of the compound

Worked example3

Worked example

  • A compound of carbon and oxygen is found to contain 27.3% carbon and 72.7% oxygen by mass. Calculate the empirical formula of the compound.






= 2.27

= 1

= 4.54

= 2










The empirical formula of this compound is therefore CO2

Molecular formula

Molecular Formula

  • While an empirical formula gives the simplest whole number ratio of each element in a compound, a molecular formula gives the actual number of atoms in one molecule of the compound.

  • Note that the empirical formula for a compound can be the same or different from its molecular formula

Molecular formula1

Molecular Formula

The molecular formula is always a whole number multiple of the

empirical formula. A molecular formula can be obtained from the

empirical formula if the molar mass of a compound is known.

Worked example4

molar mass of compound

78 g mol-1



molar mass of one unit

13 g mol-1

Worked example

  • A compound has the empirical formula CH. The molar mass of this compound is 78 g mol-1. What is the molecular formula of this compound?

  • Solution

    The molecule must contain a whole number of (CH) units.

    The molar mass of a (CH) unit is 13 g mol-1.

    If the compound has a molar mass of 78 g mol-1, then:

    The number of CH units in a molecule

= 6

The molecular formula of the compound is, therefore, 6 x CH

Ie C6H6

End of outcome 1

End of Outcome 1


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