3. Quantitative Chemistry

• Law of Conservation of Mass


  No matter is lost or gained during a chemical reaction
• Mass is always conserved, therefore the total mass of the reactants is equal to the total mass of the products, which is why all chemical equations must be balanced
• The sum of the relative atomic/molecular masses of the reactants will be the same as the sum of the relative atomic/molecular masses of the products
• Precipitation reaction

  Two solutions react to form an insoluble solid called a precipitate
• If the reaction flask is closed and no other substance can enter or leave the system, then the total mass of the reaction flask will remain constant
• If carried out in a closed system then the mass before and after the reaction will be the same
• Balanced equation

  CaCl2 (aq) + Na2SO4 (aq) ⟶ CaSO4 (s) + 2NaCl (aq)
• Diagram showing the conservation of mass in a precipitation reaction

  
• • If the reaction flask is open and a gaseous product is allowed to escape, then the total mass of the reaction flask will change as product mass is lost when the gas leaves the system
  • For example, the reaction between hydrochloric acid and calcium carbonate produces carbon dioxide gas:

  2HCl (aq) + CaCO3 (s) ⟶ CaCl2 (aq) + H2O (l) + CO2 (g)

  • Mass will be lost from the reaction flask unless it is closed
  • If the mass of a reaction flask is found to increase then it may be due to one of the reactants being a gas found in the air and all of the products are either solids or liquids
• Chemical formulae and equations


  Provide information about the chemicals involved
• Chemical formulae

  • If there is no subscript number after an element, then there must be one of that particular element
  • If there is a subscript number after an element, then that number belongs to the element just before it
  • If there is a subscript number after brackets, then that number belongs to all of the elements inside the bracket
  • The most complicated examples contain a subscript number inside the bracket as well as outside
• Chemical formulae examples


  • CO
  • CO2
  • Ca(OH)2
  • Ca(NO3)2
• Ca(NO3)2 contains one calcium atom, two nitrogen atoms, and six oxygen atoms
• Chemical equation


  Uses the chemical symbols of each reactant and product
• Balancing equations

  • There has to be the same number of atoms of each element on either side of the equation in accordance with the Law of Conservation of Mass
• Non-metals written as molecules

  • H2
  • N2
  • O2
  • F2
  • Cl2
  • Br2
  • I2
• Balancing an equation

  Work across the equation from left to right, checking one element after another
• If there is a group of atoms, for example, a nitrate group (NO3–) that has not changed from one side to the other, then count the whole group as one entity rather than counting the individual atoms
• Acid-base neutralisation reaction


  • NaOH (aq) + HCl (aq) ⟶ NaCl (aq) + H2O (l)
• Redox reaction

  • 2Fe2O3 (aq) + 3C (s) ⟶ 4Fe (s) + 3CO2 (g)
• In each equation there are equal numbers of each atom on either side of the reaction arrow so the equations are balanced
• Chemical equation


  Uses the chemical symbols of each reactant and product
• Balancing equations

  • There has to be the same number of atoms of each element on either side of the equation in accordance with the Law of Conservation of Mass
• Non-metals written as molecules

  • H2
  • N2
  • O2
  • F2
  • Cl2
  • Br2
  • I2
• Balancing an equation

  Work across the equation from left to right, checking one element after another
• If there is a group of atoms, for example, a nitrate group (NO3–) that has not changed from one side to the other, then count the whole group as one entity rather than counting the individual atoms
• Acid-base neutralisation reaction


  • NaOH (aq) + HCl (aq) ⟶ NaCl (aq) + H2O (l)
• Redox reaction

  • 2Fe2O3 (aq) + 3C (s) ⟶ 4Fe (s) + 3CO2 (g)
• In each equation there are equal numbers of each atom on either side of the reaction arrow so the equations are balanced
• Balancing Equations

  • The best approach is to practice lot of examples of balancing equations
  • By trial and error change the coefficients (multipliers) in front of the formulae, one by one checking the result on the other side
  • Balance elements that appear on their own, last in the process
• Worked example

  Example 1

  Balance the following equation:

  aluminium + copper(II) oxide ⟶ aluminium oxide + copper 

  Unbalanced symbol equation:

  Al + CuO ⟶ Al2O3 + Cu
• answer for the question

  
• Worked example

  Example 2

  Balance the following equation:

  magnesium oxide + nitric acid ⟶ magnesium nitrate + water 

  Unbalanced symbol equation:

  MgO + HNO3 ⟶ Mg(NO3)2 + H2O
• answer for example

  
• answer for example 2

  
• Relative Formula (Molecular) MassHow to work out relative formula mass

  • The symbol for the relative atomic mass is Ar
  • This is calculated from the mass number and relative abundances of all the isotopes of a particular element
  • The symbol for the relative formula mass is Mr and it refers to the total mass of the molecule
  • To calculate the Mr of a substance, you have to add up the relative atomic masses of all the atoms present in the formula
• Relative Formula Mass Calculations Table

  
• • In accordance with the Law of Conservation of Mass, the sum of the relative molecular masses of the reactants will be the same as the sum of the relative molecular masses of the products Calculating % Mass of an Element in a Compound
  • The percentage by mass of an element in a compound can be calculated using the following equation:

  
• Worked example

  Calculate the percentage by mass of calcium in calcium carbonate, CaCO3.

  
• Gases in Reactions

  1. Some chemical reactions may appear to involve a change in mass due to the presence of a gaseous reactant or product

  2. If the reaction flask is open and a gaseous product is allowed to escape, then the total mass of the reaction flask will decrease as product mass is lost when the gas leaves the system