1. (A) GETTING THE MOST FROM REACTANTSHC
CHEMISTRY HC
CHEMISTRY
(A) GETTING THE MOST FROM REACTANTS
The Mole & Molar Volume
After completing this lesson you should be able to :
Balanced equations show the mole ratio(s) of reactants and products.
The molar volume is the same for all gases at the same temperature and pressure. Calculations involving molar volume.
Determination of quantities of reactants and/or products using balanced equations and moles.
The molar volume (in units of litres mol-1 ) is the same for all gases at the same temperature and pressure. The volume of a gas can be calculated from the number of moles and vice versa.
Determination of quantities of reactants and/or products using balanced equation and:
 gram formula masses (GFM) and mass
 moles
 concentrations and volumes of solutions
 masses of solutes
 molar volumes and volumes for gaseous reactions
The concentration of a solution can be expressed in mol l-1 .
Balanced equations can be used in conjunction with concentrations and volumes of solutions and/or masses of solutes to determine quantities of reactants and/or products.
The volumes of reactant and product gases can be calculated from the number of moles of each reactant and product.

2. The Mole Working in atomic mass units is not practical? Why?
The mole is the gram formula mass expressed in grams
Calculate the mass of
1mole of water H2O
1 mole of methane CH4

3. The Mole Consider the equation below: C + O2 CO2
This equation tells us about the number of moles that are reacting together but tells us nothing about the mass of atoms reacting.
Can you estimate how many atoms will be reacting in this equation?

4. When reactions take place in a test tube or in cells it is not just one atom that is reacting but many millions.
It would be impractical when we wanted to quantify a reaction to write down the actual number of atoms that are reacting.
In chemistry we use a special quantity called the mole.

5. The mole is a convenient way of scaling down the large number of atoms: One mole of atoms contains 6.02x 1023atoms.
This number is Avogadros constant.
1 mole of any element contains the same number of atoms as any other element.
Avogadros constant is given the formula unit L.

6. The term formula unit refers to the type of particle present in a substance.
For monatomic gases and metals the formula unit is an Atom.
1 mole of Argon gas contains L atoms
For covalent substances the formula unit is a molecule.
1 mole of hydrogen (H2) gas contains L molecules
But will contain 2L atoms

7. For ionic compounds the formula unit is the ratio of ions expressed by the ionic formula of the compound.
1mole of NaCl contains L formula units
1 mole of NaCl contains 2L ions as it is made up of both Na+ ions and Cl- ions.

8. Try the Following examples
How many hydrogen atoms are present in 1 mole of ammonia (NH3)
How many ions are present in 0.5 moles of sodium oxide (Na2O)
How many ions are present in 2.25mol of a solution of dilute H2SO4

9. Gram Formula Mass
The gram formula mass of an element or a compound is the atomic mass expressed as grams.
The gram formula mass of carbon is 12g.
The gram formula mass of oxygen is 32g (remember oxygen is diatomic)
The gram formula mass of water is (2x1) + 16 = 18g

10. Calculations
We can calculate the number of moles in a sample of an element or a compound if we know the mass of the sample and the molar mass (atomic mass) by using the formula
No of moles = mass ÷ gram formula mass m n
gfm

11. Try the following examples;-Calculate the number of moles in each of the following.
a) 40g of sodium chloride (NaCl)
b)50g of calcium carbonate (CaCO3)
c) 100g of glucose (C6H12O6)

12. Working with solutions
In chemistry work is often carried out using solutions where concentration is measured as the number of moles of substance dissolved in a litre of water moll-1 n C V
No. of moles
Conc. in moll-1
Vol. in litres

13. Concentration of a solution
In calculating the concentration both the number of moles and the volume of the solvent must be taken into consideration
Normally, the amount of substance, is measured in moles and the volume in litres (1000 cm3)
Note: 1 litre = 1000 cm3 = 1 dm3
The usual unit of concentration is expressed in moll-1 (moles per litre)
Concentration is generally expressed in terms of molarity or molar concentration

14. Molar Volume of Gases
Remember gases do not have either a finite shape or a finite volume.In addition it is difficult to measure the mass of a gas.
For gases it is more appropriate to work with volume.

15. At 0oC and 1 atmosphere pressure
The table below shows that density of a gas increases in proportion to atomic mass.
At 0oC and 1 atmosphere pressure
Gas H2
CH4 N2 O2 Ar
CO2
gfm 2 16 28 32 40 44
Density
0.09
0.71
1.25
1.43
1.78
1.98
Molar Volume
22.2
22.5
22.4
Within limits the molar mass of all gases is the same under given conditions of temperature and pressure.

16. Other Calculations
Another knowledge triangle allows us to make further calculations.
If we know the molar volume of the gas (Vmol) we can use the equation to calculate the volume of a gas or rearrange it to calculate the number of moles of a gas V n
Vmol

17. COPY
Avogadro's number
Avogadro’s constant, symbol NA or L, is the number of ‘elementary particles’ in one mole of any substance.
It has the value of 6.02 x 1023

18. COPY
Things to understand about Avogadro's number
It is a number, just as is "dozen"; you can think of Avogadro's number as the "chemist's dozen".
It is a huge number, far greater in magnitude than we can visualize
6.02 x 1023
602 billion trillion
602,000,000,000,000,000,000,000
An Avogadro's number of standard soft drink cans would cover the surface of the earth to a depth of over 200 miles.
If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

19. Amadeo Avogadro (1766-1856) COPY
Avogadro’s hypothesis states that “equal volumes of different gases, under STP, contain equal numbers of molecules.”
Avogadro's number is one of the fundamental constants of chemistry.
6.02 x 1023
602 billion trillion
602,000,000,000,000,000,000,000 
Avogadro never knew his own number; it was named in his honor by a French scientist in Its value was first estimated by Josef Loschmidt, an Austrian chemistry teacher, in 1895.

20. COPY
Molar Gas Volume
One mole of all gases at the same temperature and pressure will have the same volume.
1 mole of oxygen
1 mole of nitrogen
1 mole of carbon dioxide
Comparing gas volumes
Since the larger ‘balloon’ has twice the volume it must have twice the number of moles of gas within it. It must also have twice as many particles.
5 litres
2.5 litres

21. COPY Mole and gas volume
The molar volume of a gas is its volume per mole, litre mol-1.
It is the same for all gases at the same temperature and pressure.
The value, though, is temperature and pressure dependent.
The molar volume of all gases is approximately
24 litre mol-1 at 20oC and 22.4 litre mol-1 at 0oC.
Volume (l)
Molar Volume (l) x n

22. Why?
COPY
It may seem surprising that the molar volume is the same for all gases, even at the same temperature and pressure. In a gas the molecules have much more kinetic energy and are relatively far apart so the volume of the gas does not depend on the sizes of the particles. In a gas at room temperature and pressure the molecules only occupy about 0.1% of the volume of a gas. The rest is empty space!

23. Calculations involving molar gas volume
COPY
At room temperature and pressure the molar gas volume is 24 litres mol-1.
Worked example 1. Calculate the volume of moles of oxygen.
1 mole  24 litres
 /1 x 24 = litres
Worked example 2. Calculate the number of moles in 72 litres of hydrogen.
1 mole  litres
72/24 x  litres
= 3 moles

24. Calculations involving molar gas volume
COPY
Calculations involving molar gas volume
What is the mass of steam in 180 cm3 of the gas, when the molar volume is 24 litres mol-1?
0.135 g

25. Calculations involving mass and volume
COPY
Calculations involving mass and volume
Worked example 1.The equation below shows the reaction between calcium carbonate and hydrochloric acid.
CaCO3(s) + 2HCl(aq)  CaCl2(aq) CO2(g) H2O(l)
20g of calcium carbonate reacts with excess hydrochloric acid.
Calculate the volume of carbon dioxide gas formed. (Take the molar volume to be 24.0 litre mol-1)
Write the balanced equation
CaCO3(s) + 2HCl(aq)  CaCl2 (aq) CO2(g) H2O(l)
1 mol  mol
Show mole ratio
Change moles into required units
100 g  litres
20 g  /100 x 24.0 litre
4.8 litres
Use proportion

26. Calculations involving density and molar volume
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Calculations involving density and molar volume
The molar volume is the volume occupied by one mole of a gas.
Worked example 1. In an experiment the density of carbon dioxide was measured and found to be 1.85 g l-1.
Calculate the molar volume of carbon dioxide.
1.85 g  1 litre
So 1 mole, g  44/1.85 x 1 = litres
Worked example 2. A gas has a molar volume of 24 litres and a density of 1.25 g l -1.
Calculate the mass of 1 mole of the gas.
1 litre  g
So 1 mole, litre  24/1 x = 30 g

27. COPY 0.015moles 0.96L 22.22 litres 64.1 g Calculations for you to try.
Calculate the number of moles in 0.36 litres of argon (molar gas volume = 24 litres mol-1 ).
Calculate the volume of 0.04 moles of CO2. (molar gas volume = 24 litres mol-1 ).
0.015moles
0.96L
3. Under certain conditions oxygen has a density of 1.44 g l-1. Calculate
the molar volume of oxygen under these conditions.
22.22 litres
4. A gas has a density of 2.74 g l-1 and a molar volume of 23.4 litre mol-1. Calculate the molecular mass of the gas.
64.1 g

28. Gas Volume Calculations
COPY
Gas Volume Calculations
Calculate the volume of nitrogen dioxide gas produced when 100cm3 of nitrogen is sparked in excess oxygen
N2 (g) + 2O2 (g)  2NO2 (g)
1mole moles
1vol vol
100cm3
200cm3
200cm3 of NO2 28

29. Gas Volume Calculations
COPY
Gas Volume Calculations
Combustion of methane
What volume of C02, is produced if 100 cm3 of O2 is used to completely to burn some CH4 gas?
Balanced equation
CH4 (g) + 2O2 (g)  CO2 (g) + 2 H20 (l)
50cm3 of CO2 29

30. Gas Volume Calculations
COPY
Gas Volume Calculations
50 cm3 of C0, is burned with 20cm3 of oxygen.
Which gas is in excess
What is the volume and composition of the resulting gas mixture
CO (g) + ½ O2 (g)  CO2 (g)
Balanced equation
CO in excess
10cm3 CO + 40cm3 CO2 = 50cm3 of gas 30

31. Gas Volume Calculations
COPY
Gas Volume Calculations
Combustion of propane
10 cm3 of propane gas is mixed with 75cm3 of O2 and the mixture exploded.
Calculate the volume and the composition of the resulting gas mixture.
What will be the change in volume when the resulting gas mixture is shaken with dilute sodium hydroxide solution.
Balanced equation
C3H8 (g) + 5O2 (g)  3CO2 (g) + 4H20 (l)
25cm3 of O2 + 30cm3 of CO2 = 55cm3 of gas
Volume will decrease by 30cm3 (CO2) removed 31

32. Equimolar amounts of substances contain equal
numbers of elementary entities
Copper
Water
Sodium chloride
Formula Cu
H2O
Na+Cl-
1mole
63.5g
18g
58.5g
Elementary entities
Atoms
Molecules
Formula units
1 mole contains
6.02x1023 atoms
6.02x1023 molecules
6.02x1023 formula units

33. The Mole and Avogadro’s constant
Worked example 1.
Calculate the number of atoms in 6 g of carbon.
1 mole  x 1023 Carbon atoms
12g  x Carbon atoms
6 g  (6/12 ) x 6.02 x 1023
= 3.01 x 1023 Carbon atoms

34. The Mole and Avogadro’s constant
Worked example 2.
How many molecules are in 6g of water?
1 Mole of water 
Avogadro’s constant of molecules
18 g 
6.02 x molecules
6 g 
(6/18) x 6.02 x 1023
= 2 x 1023 molecules

35. The Mole and Avogadro’s constant
Worked example 3.
Calculate the number of atoms in 4 g of bromine.
1 mole  x 1023 Br2 molecules
160g  (2 x 6.02 x 1023 ) Br atoms
4 g  (4/160 ) x x 1024
= 3.01 x 1022 bromine atoms

36. The Mole and Avogadro’s constant
Worked example 4.
Calculate the number of sodium ions in 71g of sodium sulphate (Na+)2SO42-
1 mole  x 1023 Formula units
142g  (2 x 6.02 x 1023 ) Na+ ions
71 g  (71/142 ) x x 1024
= 6.02 x 1023 sodium ions

37. Calculations for you to try.
How many atoms are there in 0.01 g of carbon?
2. How many oxygen atoms are there in 2.2 g of carbon dioxide?
Calculate the number of sodium ions in 1.00g of sodium carbonate.
4. Calculate the number of molecules in 25.5g of ammonia.
5. A sample of the gas dinitrogen tetroxide, N2O4, contained x 1022 oxygen atoms. What mass of dinitrogen tetroxide was present?

38. How many atoms are there in 0.01 g of carbon?
5.02 x 1020 C atoms

39. 2. How many oxygen atoms are there in 2.2 g of carbon dioxide?
6.02 x O atoms

40. Calculate the number of sodium ions in 1.00g of sodium carbonate.
1.14 x 1021 Na+ ions

41. 4. Calculate the number of molecules in 25.5g of ammonia.
9.03 x 1023 molecules

42. 5. A sample of the gas dinitrogen tetroxide, N2O4, contained 2
5. A sample of the gas dinitrogen tetroxide, N2O4, contained x 1022 oxygen atoms. What mass of dinitrogen tetroxide was present?
0.92 g

43. 1. The mass of 1 mol of sodium is 23 g.
What is the approximate mass of one sodium atom?
A 6 × 1023g
B 6 × 10–23g
C 3.8 × 10–23g
D 3.8 × 10–24g C

44. 2. In which of the following pairs do the gases
contain the same number of oxygen atoms?
A 1 mol of oxygen and 1 mol of carbon monoxide
B 1 mol of oxygen and 0.5 mol of carbon dioxide
C 0.5 mol of oxygen and 1 mol of carbon dioxide
D 1 mol of oxygen and 1 mol of carbon dioxide D

45. 3. The Avogadro Constant is the same as the number of
A molecules in 16 g of oxygen
B electrons in 1 g of hydrogen
C atoms in 24 g of carbon
D ions in 1 litre of sodium chloride solution,concentration 1 mol l–1. B