Relationship between moles, mass and formula mass http://www.docbrown.info/page04/4_73calcs07mam.htm
Problems based on moles, mass and molecular mass
(1) mole of Z = g of Z / atomic or formula mass of Z,
(2) or g of Z = mole of Z x atomic or formula mass of Z
(3) or atomic or formula mass of Z = g of Z / mole of Z where Z represents atoms, molecules or formula of the particular element or compound defined in the question and all masses quoted in grams (g).
1. How many moles of nitrogen atoms and hydrogen atoms in 1 mole of ammonia?
2. How many moles of aluminium atoms and oxygen atoms in 1 mole of aluminium oxide?
3. How many moles of potassium ions and bromide ions in 0.25 moles of potassium bromide?
4. How many moles of calcium ions and chloride ions in 2.5 moles of calcium chloride
5. How many moles of lead and oxygen atoms are needed to make 5 moles of lead dioxide?
6. How many moles of aluminium ions and sulphate ions in 2 moles of aluminium sulphate?
7. How many moles of chlorine gas in 6.5g?
A r
(Cl) = 35.5)
8. How many moles of iron in 20g?
(Fe = 56)
9. How many grams of propane C
3
H
8
are there in 0.21 moles of it?
(C = 12, H = 1)
10. 0.25 moles of molecule X was found to have a mass of 28g. Calculate its molecular mass.
11. What mass and moles of magnesium chloride is formed when 5g of magnesium oxide is dissolved in excess hydrochloric acid?
12. What mass and moles of sodium chloride is formed when 21.2g of sodium carbonate is reacted with excess dilute hydrochloric acid?

Using the Avogadro Constant , calculate the number of particles in known quantity of material.
13. How many water molecules are there in 1g of water, H
2
O ?
14. How many atoms of iron (Fe = 56) are there in an iron filing of mass 0.001g ?
15. How many particles of 'Al
2
O
3
' in 51g of aluminium oxide?
Atomic masses: Al =27, O = 16

Answers
Examples:

Example 7.1.1: 1 mole of ammonia, NH
3
, o consists of 1 mole of nitrogen atoms combined with 3 moles of hydrogen atoms.
o Or you could say 2 moles of ammonia is formed from 1 mole of nitrogen molecules
(N
2
) and 3 moles of hydrogen molecules (H
2
).

Example 7.1.2: 1 mole of aluminium oxide, o Al
2
O
3
, consists of 2 moles of aluminium atoms combined with 3 moles of oxygen atoms o ( or 1.5 moles of O
2
molecules).
For calculation purposes learn the following formula for 'Z' and use a triangle if necessary.
(1) mole of Z = g of Z / atomic or formula mass of Z,
(2) or g of Z = mole of Z x atomic or formula mass of Z
(3) or atomic or formula mass of Z = g of Z / mole of Z where Z represents atoms, molecules or formula of the particular element or compound defined in the question and all masses quoted in grams (g).

Example 7.2.1
: How many moles of potassium ions and bromide ions in 0.25 moles of potassium bromide?
o 1 mole of KBr contains 1 mole of potassium ions (K + ) and 1 mole of bromide ions (Br -
).
o So there will be 0.25 moles of each ion .

Example 7.2.2
: How many moles of calcium ions and chloride ions in 2.5 moles of calcium chloride?
o 1 mole of CaCl
2
consists of 1 mole of calcium ions (Ca 2+ ) and 2 moles of chloride ion
(Cl ).
o So there will be 2.5 x 1 = 2.5 moles of calcium ions and 2.5 x 2 = 5 moles chloride ions.

Example 7.2.3
: How many moles of lead and oxygen atoms are needed to make 5 moles of lead dioxide?
o 1 mole of PbO
2
contains 1 mole of lead combined with 2 moles of oxygen atoms (or
1 mole of oxygen molecules O
2
).
o So 1 x 5 = 5 mol of lead atoms and 2 x 5 = 10 mol of oxygen atoms (or 5 mol oxygen molecules) are needed.

Example 7.2.4
: How many moles of aluminium ions and sulphate ions in 2 moles of aluminium sulphate?
o 1 mole of Al
2
(SO
4
)
3
contains 2 moles of aluminium ions (Al 3+ ) and 3 moles of sulphate ion (SO
4
2).
o So there will be 2 x 2 = 4 mol aluminium ions and 2 x 3 = 6 mol of sulphate ion .

Example 7.2.5
: How many moles of chlorine gas in 6.5g?
A r
(Cl) = 35.5) o chlorine consists of Cl
2
molecules, so M r
= 2 x 35.5 = 71 o moles chlorine = mass / M r
= 6.5 / 71 = 0.0944 mol

Example 7.2.6
: How many moles of iron in 20g?
(Fe = 56) o iron consists of Fe atoms, so moles iron = mass/A r
= 20/56 = 0.357 mol Fe

Example 7.2.7
: How many grams of propane C
3
H
8
are there in 0.21 moles of it?
(C = 12,
H = 1)

o M r
of propane = (3 x 12) + (1 x 8) = 44, so g propane = moles x M r
= 0.21 x 44 =
9.24g

Example 7.2.8
: 0.25 moles of molecule X was found to have a mass of 28g. Calculate its molecular mass.
o M r
= mass X / moles of X = 28 / 0.25 = 112

Example 7.2.9
: What mass and moles of magnesium chloride is formed when 5g of magnesium oxide is dissolved in excess hydrochloric acid?
o reaction equation: MgO + 2HCl ==> MgCl
2
+ H
2
O o means 1 mole magnesium oxide forms 1 mole of magnesium chloride (1 : 1 molar ratio) o formula mass MgCl
2
= 24+(2x35.5) = 95, o MgO = 24+16 = 40, 1 mole MgO = 40g, so 5g MgO = 5/40 = 0.125 mol o which means 0.125 mol MgO forms 0.125 mol MgCl
2
, o Mass = moles x formula mass = 0.125 x 95 = 11.9g MgCl
2

Example 7.2.10
: What mass and moles of sodium chloride is formed when 21.2g of sodium carbonate is reacted with excess dilute hydrochloric acid?
o reaction equation: Na
2
CO
3
+ 2HCl ==> 2NaCl + H
2
O + CO
2 o means 1 mole sodium carbonate gives 2 moles of sodium chloride ( 1:2 ratio in equation)
 Formula mass of Na
2
CO
3
= (2x23) + 12 + (3x16) = 106
 Formula mass of NaCl = 23 + 35.5 = 58.5
o moles Na
2
CO
3
= 21.2/106 = 0.2 mole o therefore 2 x 0.2 = 0.4 mol of NaCl formed.
o mass of NaCl formed = moles x formula mass = 0.4 x 58.5 = 23.4g NaCl
Using the Avogadro Constant , you can actually calculate the number of particles in known quantity of material.
16.
Example 7.3.1: How many water molecules are there in 1g of water, H
2
O ?
a.
formula mass of water = (2 x 1) + 16 = 18 b.
every mole of a substance contains 6 x 10 23 particles of 'it' (the Avogadro
Constant).
c.
moles water = 1 / 18 = 0.0556
d.
molecules of water = 0.0556 x 6 x 10 23 = 3.34 x 10 22 e.
Since water has a density of 1g/cm3, it means in every cm 3 or ml there are f.
33 400 000 000 000 000 000 000 individual H
2
O molecules or particles.
17.
Example 7.3.2: How many atoms of iron (Fe = 56) are there in an iron filing of mass
0.001g ?
a.
0.001g of iron = 0.001 / 56 = 0.00001786 mol b.
atoms of iron in the nail = 0.00001786 x 6 x 1023 = 1.07 x 10 19 actual Fe atoms c.
(10.7 million million million atoms!)
18.
Example 7.3.2: (a) How many particles of 'Al
2
O
3
' in 51g of aluminium oxide?
a.
Atomic masses: Al =27, O = 16, f. mass Al
2
O
3
= (2x27) + (3x16) = 102 b.
moles 'Al
2
O
3
' = 51/102 = 0.5 mol c.
Number of 'Al
2
O
3
' particles = 0.5 x 6 x 10 23 = 3 x 10 23 d.
(b) Aluminium oxide is an ionic compound. Calculate the number of individual aluminium ions (Al 3+ ) and oxide ions (O 2) in the same 51g of the substance.
e.
For every Al
2
O
3
there are two Al 3+ and three O 2 ions.
f.
So in 51g of Al
2
O
3
there are ...
g.
0.5 x 2 x 6 x 10 23 = 6 x 10 23 Al 3+ ions , and h.
0.5 x 3 x 6 x 10 23 = 9 x 10 23 O 2 ions .