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Quantitative Aspects of Chemical Change

An equation for a chemical reaction can provide us with a lot of useful information. It tells us what the reactants and the products are in the reaction, and it also tells us the ratio in which the reactants combine to form products. Look at the equation below:

Fe + S FeS Fe + S FeS

In this reaction, every atom of iron (FeFe) will react with a single atom of sulphur (SS) to form one molecule of iron sulphide (FeSFeS). However, what the equation doesn't tell us, is the quantities or the amount of each substance that is involved. You may for example be given a small sample of iron for the reaction. How will you know how many atoms of iron are in this sample? And how many atoms of sulphur will you need for the reaction to use up all the iron you have? Is there a way of knowing what mass of iron sulphide will be produced at the end of the reaction? These are all very important questions, especially when the reaction is an industrial one, where it is important to know the quantities of reactants that are needed, and the quantity of product that will be formed. This chapter will look at how to quantify the changes that take place in chemical reactions.

The Mole

Sometimes it is important to know exactly how many particles (e.g. atoms or molecules) are in a sample of a substance, or what quantity of a substance is needed for a chemical reaction to take place.

The amount of substance is so important in chemistry that it is given it's own name, which is the mole.

Definition 1: Mole

The mole (abbreviation 'n') is the SI (Standard International) unit for 'amount of substance'.

Now that we know what a mole is, we can relate it to something that we know already. This is the relative atomic mass. For example, if we have a sample containing 1g of hydrogen then we have 1 mole of hydrogen, since the relative atomic mass of hydrogen is 1u.

We can build up to the idea of Avogadro's number. For example, if you have 12 eggs then you have a dozen eggs. After this number we get a gross of eggs, which is 144 eggs. Finally if we wanted one mole of eggs this would be 6,022× 10236,022×1023. That is a lot of eggs!

In one mole of any substance, there are 6,022× 10236,022×1023 particles. When we talk about the mole, we should always say what the particles are. The particles can be atoms, molecules, electrons, or almost anything else.

Definition 2: Avogadro's number

The number of particles in a mole, equal to 6,022× 10236,022×1023.

If we were to write out Avogadro's number then it would look like: 602200000000000000000000602200000000000000000000. This is a very large number. If we had this number of cold drink cans, then we could cover the surface of the earth to a depth of over 300km300km! If you could count atoms at a rate of 10 million per second, then it would take you 2 billion years to count the atoms in one mole!

Note: Interesting Fact :

The original hypothesis that was proposed by Amadeo Avogadro was that 'equal volumes of gases, at the same temperature and pressure, contain the same number of molecules'. His ideas were not accepted by the scientific community and it was only four years after his death, that his original hypothesis was accepted and that it became known as 'Avogadro's Law'. In honour of his contribution to science, the number of particles in one mole was named Avogadro's number.

Moles and mass

  1. Complete the following table:
    Table 1
    ElementRelative atomic mass (u)Sample mass (g)Number of moles in the sample
    Hydrogen1.011.01 
    Magnesium24.3124.31 
    Carbon12.0124.02 
    Chlorine35.4570.9 
    Nitrogen 42.08 
    Click here for the solution
  2. How many atoms are there in...
    1. 1 mole of a substance
    2. 2 moles of calcium
    3. 5 moles of phosphorus
    4. 24,31g24,31g of magnesium
    5. 24,02g24,02g of carbon
    Click here for the solution

Molar Mass

Definition 3: Molar mass

Molar mass (M) is the mass of 1 mole of a chemical substance. The unit for molar mass is grams per mole or g·mol-1g·mol-1.

You will remember that when the mass, in grams, of an element is equal to its relative atomic mass, the sample contains one mole of that element. This mass is called the molar mass of that element.

You may sometimes see the molar mass written as MmMm. We will use MM in this book, but you should be aware of the alternate notation.

It is worth remembering the following: On the periodic table, the relative atomic mass that is shown can be interpreted in two ways.

  1. The mass of a single, average atom of that element relative to the mass of an atom of carbon.
  2. The mass of one mole of the element. This second use is the molar mass of the element.
Table 2: The relationship between relative atomic mass, molar mass and the mass of one mole for a number of elements.
Element Relative atomic mass (u) Molar mass (g·mol-1g·mol-1) Mass of one mole of the element (g)
Magnesium 24,31 24,31 24,31
Lithium 6,94 6,94 6,94
Oxygen 16 16 16
Nitrogen 14,01 14,01 14,01
Iron 55,85 55,85 55,85

Exercise 1: Calculating the number of moles from mass

Calculate the number of moles of iron (FeFe) in a 11,7g11,7g sample.

Solution

  1. Step 1. Find the molar mass of iron :

    If we look at the periodic table, we see that the molar mass of iron is 55,85g·mol-155,85g·mol-1. This means that 1 mole of iron will have a mass of 55,85g55,85g.

  2. Step 2. Use the molar mass and sample mass to calculate the number of moles of iron :

    If 1 mole of iron has a mass of 55,85g55,85g, then: the number of moles of iron in 111,7g111,7g must be:

    111 , 7 g 55 , 85 g · mol - 1 = 2 mol 111 , 7 g 55 , 85 g · mol - 1 = 2 mol
    (1)

    There are 2 moles of iron in the sample.

Exercise 2: Calculating mass from moles

You have a sample that contains 5 moles of zinc.

  1. What is the mass of the zinc in the sample?
  2. How many atoms of zinc are in the sample?

Solution

  1. Step 1. Find the molar mass of zinc :

    Molar mass of zinc is 65,38g·mol-165,38g·mol-1, meaning that 1 mole of zinc has a mass of 65,38g65,38g.

  2. Step 2. Calculate the mass of zinc, using moles and molar mass. :

    If 1 mole of zinc has a mass of 65,38g65,38g, then 5 moles of zinc has a mass of: 65,38g×5mol=326,9g65,38g×5mol=326,9g (answer to a)

  3. Step 3. Use the number of moles of zinc and Avogadro's number to calculate the number of zinc atoms in the sample. :
    5 × 6 , 022 × 10 23 = 30 , 115 × 10 23 5 × 6 , 022 × 10 23 = 30 , 115 × 10 23
    (2)

    (answer to b)

Moles and molar mass

  1. Give the molar mass of each of the following elements:
    1. hydrogen
    2. nitrogen
    3. bromine
    Click here for the solution
  2. Calculate the number of moles in each of the following samples:
    1. 21,62g21,62g of boron (BB)
    2. 54,94g54,94g of manganese (MnMn)
    3. 100,3g100,3g of mercury (HgHg)
    4. 50g50g of barium (BaBa)
    5. 40g40g of lead (PbPb)
    Click here for the solution

An equation to calculate moles and mass in chemical reactions

The calculations that have been used so far, can be made much simpler by using the following equation:

n ( number of moles ) = m ( mass of substance in g ) M ( molar mass of substance in g · mol - 1 ) n ( number of moles ) = m ( mass of substance in g ) M ( molar mass of substance in g · mol - 1 )
(3)

Tip:

Remember that when you use the equation n=mMn=mM, the mass is always in grams (gg) and molar mass is in grams per mol (g·mol-1g·mol-1).

The equation can also be used to calculate mass and molar mass, using the following equations:

m = n × M m = n × M
(4)

and

M = m n M = m n
(5)

The following diagram may help to remember the relationship between these three variables. You need to imagine that the horizontal line is like a 'division' sign and that the vertical line is like a 'multiplication' sign. So, for example, if you want to calculate 'M', then the remaining two letters in the triangle are 'm' and 'n' and 'm' is above 'n' with a division sign between them. In your calculation then, 'm' will be the numerator and 'n' will be the denominator.

Figure 1
Figure 1 (CG11C6_001.png)

Exercise 3: Calculating moles from mass

Calculate the number of moles of copper there are in a sample that weighs 127g127g.

Solution

  1. Step 1. Write the equation to calculate the number of moles :
    n = m M n = m M
    (6)
  2. Step 2. Substitute numbers into the equation :
    n = 127 63 , 55 = 2 n = 127 63 , 55 = 2
    (7)

    There are 2 moles of copper in the sample.

Exercise 4: Calculating mass from moles

You are given a 5 mol sample of sodium. What mass of sodium is in the sample?

Solution

  1. Step 1. Write the equation to calculate the sample mass :
    m = n × M m = n × M
    (8)
  2. Step 2. Substitute values into the equation :

    MNa=22,99g·mol-1Na=22,99g·mol-1

    Therefore,

    m = 5 × 22 , 99 = 114 , 95 g m = 5 × 22 , 99 = 114 , 95 g
    (9)

    The sample of sodium has a mass of 114 , 95 g114,95g.

Exercise 5: Calculating atoms from mass

Calculate the number of atoms there are in a sample of aluminium that weighs 80 , 94 g80,94g.

Solution

  1. Step 1. Calculate the number of moles of aluminium in the sample :
    n = m M = 80 , 94 26 , 98 = 3 moles n = m M = 80 , 94 26 , 98 = 3 moles
    (10)
  2. Step 2. Use Avogadro's number to calculate the number of atoms in the sample:

    Number of atoms in 3 mol aluminium =3 ×6,022×1023=3×6,022×1023

    There are 18,069×102318,069×1023 aluminium atoms in a sample of 80,94g80,94g.

Some simple calculations

  1. Calculate the number of moles in each of the following samples:
    1. 5,6g5,6g of calcium
    2. 0,02g0,02g of manganese
    3. 40g40g of aluminium
    Click here for the solution
  2. A lead sinker has a mass of 5g5g.
    1. Calculate the number of moles of lead the sinker contains.
    2. How many lead atoms are in the sinker?
    Click here for the solution
  3. Calculate the mass of each of the following samples:
    1. 2,5mol2,5mol magnesium
    2. 12mol12mol lithium
    3. 4,5× 10254,5× 1025 atoms of silicon
    Click here for the solution

Molecules and compounds

So far, we have only discussed moles, mass and molar mass in relation to elements. But what happens if we are dealing with a molecule or some other chemical compound? Do the same concepts and rules apply? The answer is 'yes'. However, you need to remember that all your calculations will apply to the whole molecule. So, when you calculate the molar mass of a molecule, you will need to add the molar mass of each atom in that compound. Also, the number of moles will also apply to the whole molecule. For example, if you have one mole of nitric acid (HNO3HNO3), it means you have 6,022× 10236,022×1023 molecules of nitric acid in the sample. This also means that there are 6,022× 10236,022×1023 atoms of hydrogen, 6,022× 10236,022×1023 atoms of nitrogen and (3× 6,022× 10233×6,022×1023) atoms of oxygen in the sample.

In a balanced chemical equation, the number that is written in front of the element or compound, shows the mole ratio in which the reactants combine to form a product. If there are no numbers in front of the element symbol, this means the number is '1'.

e.g. N2+3H22NH3N2+3H22NH3

In this reaction, 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.

Exercise 6: Calculating molar mass

Calculate the molar mass of H2SO4H2SO4.

Solution

  1. Step 1. Use the periodic table to find the molar mass for each element in the molecule:

    Hydrogen =1,008 g·mol-1=1,008g·mol-1; Sulphur = =32,07 g·mol-1=32,07g·mol-1; Oxygen =16 g·mol-1=16g·mol-1

  2. Step 2. Add the molar masses of each atom in the molecule :
    M ( H 2 S O 4 ) = ( 2 × 1 , 008 ) + ( 32 , 07 ) + ( 4 × 16 ) = 98 , 09 g · mol - 1 M ( H 2 S O 4 ) = ( 2 × 1 , 008 ) + ( 32 , 07 ) + ( 4 × 16 ) = 98 , 09 g · mol - 1
    (11)

Exercise 7: Calculating moles from mass

Calculate the number of moles there are in 1kg1kg of MgCl2MgCl2.

Solution

  1. Step 1. Write the equation for calculating the number of moles in the sample :
    n = m M n = m M
    (12)
  2. Step 2. Calculate the values that you will need, to substitute into the equation :
    1. Convert mass into grams
      m=1kg×1 000=1 000gm=1kg×1 000=1 000g
      (13)
    2. Calculate the molar mass of MgCl2MgCl2.
      M(MgCl2)=24,31+(2×35,45)=95,21g·mol-1M(MgCl2)=24,31+(2×35,45)=95,21g·mol-1
      (14)
  3. Step 3. Substitute values into the equation :
    n = 1000 95 , 21 = 10 , 5 mol n = 1000 95 , 21 = 10 , 5 mol
    (15)

    There are 10 , 5 moles10,5moles of magnesium chloride in a 1kg1kg sample.

Exercise 8: Calculating the mass of reactants and products

Barium chloride and sulphuric acid react according to the following equation to produce barium sulphate and hydrochloric acid.

BaCl 2 + H 2 SO 4 BaSO 4 + 2 HCl BaCl 2 + H 2 SO 4 BaSO 4 + 2 HCl

If you have 2g2g of BaCl2BaCl2...

  1. What quantity (in g) of H2SO4H2SO4 will you need for the reaction so that all the barium chloride is used up?
  2. What mass of HClHCl is produced during the reaction?

Solution

  1. Step 1. Calculate the number of moles of BaCl2BaCl2 that react. :
    n = m M = 2 208 , 24 = 0 , 0096 mol n = m M = 2 208 , 24 = 0 , 0096 mol
    (16)
  2. Step 2. Determine how many moles of H2SO4H2SO4 are needed for the reaction :

    According to the balanced equation, 1 mole of BaCl2BaCl2 will react with 1 mole of H2SO4H2SO4. Therefore, if 0 , 0096 mol0,0096mol of BaCl2BaCl2 react, then there must be the same number of moles of H2SO4H2SO4 that react because their mole ratio is 1:1.

  3. Step 3. Calculate the mass of H2SO4H2SO4 that is needed. :
    m = n × M = 0 , 0096 × 98 , 086 = 0 , 94 g m = n × M = 0 , 0096 × 98 , 086 = 0 , 94 g
    (17)

    (answer to 1)

  4. Step 4. Determine the number of moles of HClHCl produced. :

    According to the balanced equation, 2 moles of HClHCl are produced for every 1 mole of the two reactants. Therefore the number of moles of HClHCl produced is (2 ×0,00962×0,0096), which equals 0,0096moles0,0096moles.

  5. Step 5. Calculate the mass of HClHCl. :
    m = n × M = 0 , 0192 × 35 , 73 = 0 , 69 g m = n × M = 0 , 0192 × 35 , 73 = 0 , 69 g
    (18)

    (answer to 2)

Group work : Understanding moles, molecules and Avogadro's number

Divide into groups of three and spend about 20 minutes answering the following questions together:

  1. What are the units of the mole? Hint: Check the definition of the mole.
  2. You have a 56g56g sample of iron sulphide (FeSFeS)
    1. How many moles of FeSFeS are there in the sample?
    2. How many molecules of FeSFeS are there in the sample?
    3. What is the difference between a mole and a molecule?
  3. The exact size of Avogadro's number is sometimes difficult to imagine.
    1. Write down Avogadro's number without using scientific notation.
    2. How long would it take to count to Avogadro's number? You can assume that you can count two numbers in each second.

Figure 2
Khan academy video on the mole - 1

More advanced calculations

  1. Calculate the molar mass of the following chemical compounds:
    1. KOHKOH
    2. FeCl3FeCl3
    3. Mg(OH)2Mg(OH)2
    Click here for the solution
  2. How many moles are present in:
    1. 10g10g of Na2Na2SO44
    2. 34g34g of Ca(OH)2Ca(OH)2
    3. 2,45×10232,45×1023 molecules of CH4CH4?
    Click here for the solution
  3. For a sample of 0,2moles0,2moles of potassium bromide (KBrKBr), calculate...
    1. the number of moles of K+K+ ions
    2. the number of moles of Br-Br- ions
    Click here for the solution
  4. You have a sample containing 3moles3moles of calcium chloride.
    1. What is the chemical formula of calcium chloride?
    2. How many calcium atoms are in the sample?
    Click here for the solution
  5. Calculate the mass of:
    1. 3moles3moles of NH4OHNH4OH
    2. 4,2moles4,2moles of Ca(NO3)2Ca(NO3)2
    Click here for the solution
  6. 96,2g96,2g sulphur reacts with an unknown quantity of zinc according to the following equation: Zn+SZnSZn+SZnS
    1. What mass of zinc will you need for the reaction, if all the sulphur is to be used up?
    2. What mass of zinc sulphide will this reaction produce?
    Click here for the solution
  7. Calcium chloride reacts with carbonic acid to produce calcium carbonate and hydrochloric acid according to the following equation: CaCl2+H2CO3CaCO3+2HClCaCl2+H2CO3CaCO3+2HCl If you want to produce 10g10g of calcium carbonate through this chemical reaction, what quantity (in g) of calcium chloride will you need at the start of the reaction?
    Click here for the solution

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