Topic: Calculations

1:15 know the structure of an atom in terms of the positions, relative masses and relative charges of sub-atomic particles

An atom consists of a central nucleus, composed of protons and neutrons.

This is surrounded by electrons, orbiting in shells (energy levels).

Atoms are neutral because the numbers of electrons and protons are equal.

 
 MassCharge
Proton1+1
Neutron10
Electronalmost 0-1

1:16 know what is meant by the terms atomic number, mass number, isotopes and relative atomic mass (Aᵣ)

Atomic number: The number of protons in an atom.

Mass number: The number of protons and neutrons in an atom.

Isotopes: Atoms of the same element (same number of protons) but with a different number of neutrons.

Relative atomic mass (Ar): The average mass of an atom compared to 1/12th the mass of carbon-12.

1:17 be able to calculate the relative atomic mass of an element (Aᵣ) from isotopic abundances

75% of chlorine atoms are the type 35Cl (have a mass number of 35)

25% of chlorine atoms are of the type 37Cl (have a mass number of 37)

In order to calculate the relative atomic mass (Ar) of chlorine, the following steps are used:

  1. Multiply the mass of each isotope by its relative abundance
  2. Add those together
  3. Divide by the sum of the relative abundances (normally 100)

    \[ A_r = \frac{( (35 \times 75) + (37 \times 25) )}{100} \]

    \[ A_r = 35.5 \]

 

Example question:

A sample of bromine contained the two isotopes in the following proportions: bromine-79 = 50.7% and bromine-81 = 49.3%.

Calculate the relative atomic mass (Ar) of bromine.

    \[ A_r = \frac{( (79 \times 50.7) + (81 \times 49.3) )}{100} \]

    \[ A_r = 79.99 \]

 

1:19 understand how to deduce the electronic configurations of the first 20 elements from their positions in the Periodic Table

Electrons are found in a series of shells (or energy levels) around the nucleus of an atom.

Each energy level can only hold a certain number of electrons. Low energy levels are always filled up first.

Rules for working out the arrangement (configuration) of electrons:

Example – chlorine (Cl)

1) Use the periodic table to look up the atomic number. Chlorine’s atomic number (number of protons) is 17.

2) Remember the number of protons = number of electrons. Therefore chlorine has 17 electrons.

3) Arrange the electrons in levels (shells):

  • 1st shell can hold a maximum of 2
  • 2nd can hold a maximum of 8
  • 3rd can also hold 8

Therefore the electron arrangement for chlorine (17 electrons in total) will be written as 2,8,7

4) Check to make sure that the electrons add up to the right number

The electron arrangement can also be draw in a diagram.

Electron arrangement for the first 20 elements:

1:26 calculate relative formula masses (including relative molecular masses) (Mᵣ) from relative atomic masses (Aᵣ)

Relative formula mass (Mr) is mass of a molecule or compound (on a scale compared to carbon-12).

It is calculated by adding up the relative atomic masses (Ar) of all the atoms present in the formula.

Example:

The relative formula mass (Mr) for water (H2O) is 18.

Water                     = H2O

Atoms present      = (2 x H) + (1 x O)

Mr                           = (2 x 1) + (1 x 16) = 18

1:31 understand how the formulae of simple compounds can be obtained experimentally, including metal oxides, water and salts containing water of crystallisation

Finding the formula of a metal oxide experimentally

The formulae of metal oxides can be found experimentally by reacting a metal with oxygen and recording the mass changes.

Example: When magnesium is burned in air, it reacts with oxygen (O2) to form magnesium oxide (MgO).

Method:
• Weigh a crucible and lid
• Place the magnesium ribbon in the crucible, replace the lid, and reweigh
• Calculate the mass of magnesium
   (mass of crucible + lid + Magnesium – mass of crucible + lid)
• Heat the crucible with lid on until the magnesium burns
   (lid prevents magnesium oxide escaping therefore ensuring accurate results)
• Lift the lid from time to time (this allows air to enter)
• Stop heating when there is no sign of further reaction
   (this ensures all Mg has reacted)
• Allow to cool and reweigh
• Repeat the heating , cooling and reweigh until two consecutive masses are the same
   (this ensures all Mg has reacted and therefore the results will be accurate)
• Calculate the mass of magnesium oxide formed (mass of crucible + lid + Magnesium oxide – mass of crucible + lid)

 

Finding the formula of a salt containing water of crystallisation

When some substances crystallise from solution, water becomes chemically bound up with the salt.  This is called water of crystallisation and the salt is said to be hydrated. For example, hydrated copper sulfate has the formula  CuSO4.5H2O  which formula indicates that for every CuSO4 in a crystal there are five water (H2O) molecules.

When you heat a salt that contains water of crystallisation, the water is driven off leaving the anhydrous (without water) salt behind. If the hydrated copper sulfate (CuSO4.5H2O) are strongly heated in a crucible then they will break down and the water lost, leaving behind anhydrous copper sulfate (CuSO4). The method followed is similar to that for metal oxides, as shown above. The difference of mass before and after heating is the mass of the water lost. These mass numbers can be used to obtain the formula of the salt.

1:32 know what is meant by the terms empirical formula and molecular formula

The empirical formula shows the simplest whole-number ratio between atoms/ions in a compound.

The molecular formula shows the actual number of atoms of each type of element in a molecule.

   For example, for ethane:

        Molecular formula = C2H6

        Empirical formula = CH3

Here are some more examples:

NameMolecular formulaEmpirical Formula
penteneC5H10CH2
buteneC4H8CH2
glucoseC6H12O6CH2O
hydrogen peroxideH2O2HO
propaneC3H8C3H8

Notice from the table that several different molecules can have the same empirical formula, which means that it is not possible to deduce the molecular formula from the empirical formula without some additional information. Also notice that sometimes it is not possible to simplify a molecular formula into simpler whole-number ratio, in which case the empirical formula is equal to the molecular formula.

 

1:33 calculate empirical and molecular formulae from experimental data

Calculating the Empirical Formula

Example: What is the empirical formula of magnesium chloride if 0.96 g of magnesium combines with 2.84 g of chlorine?

Step 1: Put the symbols for each element involved at the top of the page.

Step 2: Underneath, write down the masses of each element combining.

Step 3: Divide by their relative atomic mass (Ar).

Step 4: Divide all the numbers by the smallest of these numbers to give a whole number ratio.

Step 5: Use this to give the empirical formula.

(If your ratio is 1:1.5 then multiple each number by 2

If your ratio is 1:1.33 then x3. If your ratio is 1:1.25 x4)

 

Calculating the Molecular Formula

If you know the empirical formula and the relative formula mass you can work out the molecular formula of a compound.

Example: A compound has the empirical formula CH2, and its relative formula mass is 56. Calculate the molecular formula.

Step 1: Calculate the relative mass of the empirical formula.

Step 2: Find out the number of times the relative mass of the empirical formula goes into the Mr of the compound.

Step 3: This tells how many times bigger the molecule formula is compared to the empirical formula.

 

Empirical formula calculations involving water of crystallisation

When you heat a salt that contains water of crystallisation, the water is driven off leaving the anhydrous (without water) salt behind. For example, barium chloride crystals contain water of crystallisation, and therefore would have the formula  BaCl2.nH2O  where the symbol ‘n’ indicates the number of molecules of water of crystallisation. This value can be calculated using the following method.

Example: If you heated hydrated barium chloride (BaCl2.nH2O) in a crucible you might end up with the following results.

     

Step 1: Calculate the mass of the anhydrous barium chloride (BaCl2) and the water (H2O) driven off.

     

Step 2: Use the empirical formula method to find the value of n in the formula.

     

1:36 practical: know how to determine the formula of a metal oxide by combustion (e.g. magnesium oxide) or by reduction (e.g. copper(II) oxide)

The formulae of metal oxides can be found experimentally by reacting a metal with oxygen and recording the mass changes.

Example
When magnesium is burned in air, it reacts with oxygen (O2) to form magnesium oxide (MgO).
Method:
• Weigh a crucible and lid
• Place the magnesium ribbon in the crucible, replace the lid, and reweigh
• Calculate the mass of magnesium
   (mass of crucible + lid + Magnesium – mass of crucible + lid)
• Heat the crucible with lid on until the magnesium burns
   (lid prevents magnesium oxide escaping therefore ensuring accurate results)
• Lift the lid from time to time (this allows air to enter)
• Stop heating when there is no sign of further reaction
   (this ensures all Mg has reacted)
• Allow to cool and reweigh
• Repeat the heating , cooling and reweigh until two consecutive masses are the same
   (this ensures all Mg has reacted and therefore the results will be accurate)
• Calculate the mass of magnesium oxide formed (mass of crucible + lid + Magnesium oxide – mass of crucible + lid)

Select a set of flashcards to study:

     Terminology

     Skills and equipment

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Section 1: Principles of chemistry

      a) States of matter

      b) Atoms

      c) Atomic structure

     d) Relative formula masses and molar volumes of gases

     e) Chemical formulae and chemical equations

     f) Ionic compounds

     g) Covalent substances

     h) Metallic crystals

     i) Electrolysis

 Section 2: Chemistry of the elements

     a) The Periodic Table

     b) Group 1 elements: lithium, sodium and potassium

     c) Group 7 elements: chlorine, bromine and iodine

     d) Oxygen and oxides

     e) Hydrogen and water

     f) Reactivity series

     g) Tests for ions and gases

Section 3: Organic chemistry

     a) Introduction

     b) Alkanes

     c) Alkenes

     d) Ethanol

Section 4: Physical chemistry

     a) Acids, alkalis and salts

     b) Energetics

     c) Rates of reaction

     d) Equilibria

Section 5: Chemistry in industry

     a) Extraction and uses of metals

     b) Crude oil

     c) Synthetic polymers

     d) The industrial manufacture of chemicals