Chemistry: Calculations and formulae

Chemistry: Calculations and formulae

​

Remember that

• Mr = Molecular mass of a formulae (relative formula mass)

• Ar = Atomic mass of an element

ions

Sodium

In an atom, the number of positively-charged protons is always the same as the number of negatively-charged electrons

State the overall charge of a sodium atom. You should make reference to the sub-atomic particles in a sodium atom in your answer (2 marks)

Answer

The overall charge of a sodium atom is neutral because it contains 11 positively-charged protons and 11 negatively-charged electrons

Electrons in a sodium ion????

f sodium loses an electron, it now has 11 protons, 11 neutrons, and only 10 electrons.

What is an ion?

• Ions contain a different number of protons when compared to electrons and as a result, ions are particles with a charge

Open Ended

There are 10 electrons in a sodium ion.

State the charge of a sodium ion and explain your answer with reference to the number of sub-atomic particles (2 marks)

ANSWER

A sodium ion has a 1+ charge because it contains 11 positively-charged protons but only 10 negatively-charged electrons

What is the Negative charge of a sulfide ion?

Sulphur has a valency of 6

• therefore needs to gain 2 electrons to fill its octet. 

• As electrons are negative, the overall charge of the ion will be 2-.

• Therefore the charge on a sulfide ion is 2-, which can be written as S2− .

Multiple Choice

A sulfide ion has the same electronic structure as which of the following noble gases? (1 mark)

• Helium

• Neon

• Argon

• Krypton

Multiple Choice

Of the remaining 3 noble gases, which one has the same electronic structure as a sodium ion (1 mark)

• Helium

• Neon

• Krypton

Key points to remember

• Ions containing more protons than electrons will have a positive charge 

• ions containing more electrons than protons will have a negative charge. 

• All ions have the same electronic structure as the noble gases

Could be useful

• At the start of your Chemistry exam, you could write 1+, 2+, 2- and 1- at the top of groups 1, 2, 6 and 7 of the Periodic table. These charges can come in very handy in a number of topics and one particular topic is the writing of chemical formulae for ionic compounds…..

Fill in the Blank

Aluminium: number of protons

Fill in the Blank

Aluminium: number of 13 neutrons

Fill in the Blank

electron structure of Aluminium

Fill in the Blank

Fluorine: number of protons

Fill in the Blank

Fluorine: number of: neutrons

Fill in the Blank

Florine: number of electrons

Fill in the Blank

electronic structure of a fluorine ion

Fill in the Blank

Which ion has 4 protons, 5 neutrons and 2 electrons?

chemical formula for sodium chloride

• 1. Write the formulae for each of the ions

• 2. Na1+         Cl1-

  
  

• If there is the same amount of positive charge as negative charge, simply cancel out and write out what is left

  
  

• 3. Sodium chloride = NaCl

• 
  

  
  

When writing chemical formulae

• when there isn’t the same amount of charge on both ions…….

• use the transfer technique

Writing chemical formulae magnesium chloride

• If there is a different amount of positive charge to negative charge, TRANSFER the numbers between the substances

  
  

• Mg2+ Cl-

• = MgCl2

Fill in the Blank

Using the technique that you’ve just seen, write down the chemical formula for sodium oxide (1 mark)

fairly important……

• You’ve recalled how to use the group of an atom to work out the ion charge.  

• However, some ions don’t have an element in a (specific) group and therefore their charges will need to be recalled…

• Hydrogen = H+

  Hydroxide = OH-

  Carbonate = CO32-

  Sulfate = SO42-

  Nitrate = NO3-

  
  

• Unlike the examples we saw earlier, these ions are charged molecules which contain more than one type of atom but the charge actually applies to the whole ion. Therefore, if there are more than one of them in a chemical formula, in order to make sure that the number applies to the whole ion, brackets must be included

  
  

• 
  

• 
  

Magnesium Nitrare: Mg2+     NO3-

• As the amount of charge is different, transfer the numbers and use brackets to ensure that any number greater than one applies to the whole ion

  
  

• Mg(NO3)2

  
  

Fill in the Blank

Chemical formula for magnesium hydroxide

Fill in the Blank

Chemical formula for Calcium Nitrate

Isotopes

• Isotopes are different atoms of the same element containing the same number or protons and electrons the but different numbers of neutrons. Therefore, isotopes have the same Atomic number but different Mass numbers

  
  

Isotopes

• When isotopes are represented in a question, they are written with the chemical symbol of the element and then their respective mass number such as C-14.

  
  

Fill in the Blank

Use the statement above and the diagrams to write the formulae of these two isotopes (2 marks)

Avagadro's law

• Avogadro’s law states that one mole of a substance will contain the same number of particles (atoms, ions, formulae or molecules) and that amount is 6.02 x 10-23

• But you only use this if it is included in the question.

• other wise you use...

Mr first!

• K= 39, O= 16, H= 1

• =56

• (Formula mass has no units)

Apply to the triangle

• M= n X Mr

• Mass = 0.25 X 56

• Mass = 14g

Fill in the Blank

Calculate the mass of 0.5 moles of Cu

Fill in the Blank

Calculate the mass of 0.75 moles of water

Fill in the Blank

How many moles in are 65g of sodium chloride?

Fill in the Blank

Calculate the number of moles in 375g of CaCO3

Fill in the Blank

Calculate the mass of 1.5 moles of Na2O

Fill in the Blank

Calculate the relative formula mass of a compound when a mass of 2.6g is equal to 0.1 moles

Molar ratio

• As well as being able to balance symbol equations, you will need to be able to identify a molar ratio in the equation when asked to calculate a mass….

  
  

A POTENTIAL EXAM QUESTION

• Calculate the mass of lithium oxide that is produced when 8g of oxygen reacts”

  
  

• 4Li + O2 -> 2Li2O

  
  

1.

Calculate the amount of moles of the substance given in g

moles

• Mr of O2 = 16 x 2 = 32

  amount (mol) = mass ÷ Mr

  amount (mol) = 8 ÷ 32

  amount = 0.25 moles

  
  

2.

Use the balanced symbol equation to identify the molar ratio and then calculate the amount of the other substance

4Li + O2 -> 2Li2O

O2 : 2Li2O

1 : 2

amount = 0.25 x 2 = 0.5 moles

3.

Use the answer to step 2 and the relative formula mass (Mr) to calculate the mass

4Li + O2 -> 2Li2O

• Mr of Li2O = (7 x 2) + 16 = 30

  mass = amount x Mr

  mass = 0.5 x 30

  mass = 15g

  
  

Fill in the Blank

Calculate the mass of iron needed to make 16.25g of iron chloride

Worked problem

• Mr of FeCl3 = 162.5

  amount (mol) = 16.25 ÷ 162.5

  amount = 0.1 mole

  2Fe + 3Cl2 -> 2FeCl3

   

  The ratio of Fe : FeCl3 is 2 : 2

   

  0.1 mole of Fe is needed

  Mr of Fe = 56

  mass = 0.1 x 56

  mass = 5.6g

gas produced

• By applying a similar approach to the calculating masses questions, answer the gas calculation question

  
  

• The volume occupied by one mole of molecules of any gas at RTP is 24dm3 or 24000cm3

gas

1.31g of zinc reacts with excess sulphuric acid. Calculate the volume of hydrogen produced at RTP

Zn (s) + H2SO4 (g) -> ZnSO4 (aq) + H2 (g)

amount = mass ÷ Mr

• amount (Zn)= 1.31 ÷ 65.4 = 0.02 moles

• Zn : H2

  1 : 1

• 0.02 moles of H2

• volume = 0.02 x 24 = 0.48dm3

converting units

To convert a volume in cm3 to dm3, you have to divide by 1000

• The concentration of a solution can be measured in either g/dm3 or mol/dm3. 

  When the question requires to give you the concentration in mol/dm3, you need to:

  • use moles = mass ÷ Mr to work out the number of moles

  •

  •then use concentration = moles ÷ volume to work out the concentration

Atom economy

atom economy = (Mr of desired product ÷ sum of Mr of all reactants) x 100

calculate the atom economy for the production of calcium chloride

• CaCO3 + 2HCl -> CaCl2 + CO2 + H2O

  
  

• Mr of CaCl2 = 40 + (35.5 x 2) = 111

  
  

• Mr of CaCO3 + 2HCl = 100 + 73 = 173

  
  

• Atom economy = (111 ÷ 173) x 100 = 64.2% 

  
  

Multiple Choice

• A: 11.g

• B: 13.8g

• C: 15.0g

• D: 22.0g

This equation calculates the % yield

• 
  

  The % yield is rarely 100% because:

  the reaction may not go to completion because it is reversible

   some of the product may be lost when it is separated from the reaction mixture

  some of the reactants may react in ways different to the expected reaction

mass made ÷ theoretical mass x 100

• 2Na + Cl2 à 2NaCl

  
  

• calculate percentage yield

mass made ÷ theoretical mass x 100

5.75g of sodium is reacted with chlorine to produce sodium chloride. 

If the actual yield of sodium chloride is 10.2g, calculate the percentage yield. 

Leave your answer to 3 significant figures (4 marks)

1.

5.75 ÷ 23 = 0.25 moles of sodium

  Na : NaCl

2 : 2

1 : 1

2.

amount of sodium chloride = 0.25 moles

mass = 0.25 x 58.25 = 14.625g

3.

% yield = (10.2 ÷ 14.625) x 100 = 69.7%

calculating percentage of an element in a compound

• Look at the formula in a compound

• Find relative atomic masses (Ar) of each element

• Calculate the relative formula mass (Mr) of the compound

• Write the mass of the element you are looking for as fraction of the total relative mass.

• Find the percentage by multiplying your fraction by 100.

What percentage of Mg is in MgO?

• MgO

• Ar Mg= 24

• Ar O=16

• Mr = 40

• 24/40 = 0.6

• 0.6x100= 60%

find the percentage

• Find the % of C in CO₂

• Find the % of H in H₂O

• Find the % of Pb in PbO₂

Fill in the Blank

Find the % of C in CO₂

Fill in the Blank

Find the % of H in H₂O

Fill in the Blank

Find the % of Pb in PbO₂

empirical formula

finding the formula

4.8g of magnesium are reacted with 32g of bromine to form magnesium bromide, calculate the empirical formula.

1.

• 1)  Get the masses of each element,    Mg-4.8g,         Br-32g

• 2)  Find the moles of each one using moles = mass/molar mass.

• i.      Moles of Mg = 4.8/24 = 0.2 moles

  ii.    Moles of Br = 32/80 = 0.4 moles

2.

• 3) Find the simplest ratio between the elements by dividing by the lowest number, in this case 0.2 moles

• i.      Mole ratio of Mg = 0.2/0.2 = 1

  ii.    Mole ratio of Br = 0.4/0.2 = 2

• 4)  Write the ratio into the empirical formula; each mole of Mg is combined with two moles of bromine.

   So the formula of magnesium bromide is MgBr₂.

Fill in the Blank

1. Iron oxide, in which 11.2g of iron combine with3.2g of oxygen gas.

Fill in the Blank

2. Carbon fluoride, where 24g of carbon react with 152g of fluorine.

Fill in the Blank

3. Methane, in which 2.4g of carbon combine with 0.8g of hydrogen gas.