C3 — Quantitative Chemistry

• Relative formula mass

  You can calculate the relative formula mass (Mr) of compounds, which is just the relative atomic masses of all the atoms in the molecular formula added together. For example…

  
• Calculating percentage by mass

  You can also calculate the percentage mass of an element in a compound by using this formula:

  
• The mole

  The mole is the name given to an amount of a substance.

  One mole of any substance is just an amount of that substance that contains an Avogadro number of particles: so 6.02 x10^23 particles.

  The particles could be atoms, molecules, ions or electrons.
• Why is the value of the avogadro constant so large?

  It is because the mass of that number of atoms or molecules of any substance is exactly the same number of grams as the relative atomic mass (Ar) or relative formula mass (Mr) of the element or compound.

  In other words, one mole of atoms or molecules of any substance will have a mass in grams equal to the relative formula mass (Ar or Mr) for that substance.

  For example…

  
• Calculating the number of moles in a given mass

  You can use this formula to calculate the number of moles in a given mass:

  
• You can rearrange the equation n=m/Mr using a handy formula triangle. You could use it to find the mass of a known number of moles of a substance, or to find the M, of a substance from a known mass and number of moles. Just cover up the thing you want to find with your finger and write down what's left showing.

  
• Conservation of mass

  During a chemical reaction, no atoms are destroyed, and no atoms are created. This means that there are the same number and types of atoms on each side of a reaction equation. Because of this, we say that mass is conserved during a reaction.

  For example…

  
• By adding up the relative formula masses of the substances on each side of a balanced symbol equation, you can see that mass is conserved. Remember that:

  🟨 The total Mr of all the reactants = the total Mr of the products.
• Why may mass change in a reaction?

  In some experiments, you may observe a change of mass of an unsealed reaction vessel during a reaction. There are usually two explanations for this.
• Explanation 1: If the mass increases, it's probably because one of the reactants is a gas that's found in air (e.g. oxygen) and all the products are solids, liquids or aqueous.

  Before the reaction, the gas is floating around in the air. It's there, but it's not contained in the reaction vessel, so you can't account for its mass.

  • When the gas reacts to form part of the product, it becomes contained inside the reaction vessel — so the total mass of the stuff inside the reaction vessel increases.
• EXPLANATION ONE example, when a metal reacts with oxygen in an unsealed container, the mass of the container increases.

  The mass of the metal oxide produced equals the total mass of the metal and the oxygen that reacted from the air.

  metal(s) + oxygen(g) → metal oxide(s)
• Explanation 2: If the mass decreases, it's probably because one of the products is a gas and all the reactants are solids, liquids or aqueous.

  • Before the reaction, all the reactants are contained in the reaction vessel.
  • If the vessel isn't enclosed, then the gas can escape from the reaction vessel as it's formed. It's no longer contained in the reaction vessel, so you can't account for its mass — the total mass of the stuff inside the reaction vessel decreases.
• EXPLANATION TWO example, when a metal carbonate thermally decomposes to form a metal oxide and carbon dioxide gas, the mass of the reaction vessel will decrease if it isn't sealed. But in reality, the mass of the metal oxide and the carbon dioxide produced will equal the mass of the metal carbonate that decomposed.

  metal carbonate(s) → metal oxide(s) + carbon dioxide(g)

  Remember from the particle model (see more in C2) that a gas will expand to fill any container it's in. So, if the reaction vessel isn't sealed, the gas expands out from the vessel, and escapes into the air around.
• The Mole and Equations

  Balanced symbol equations can be used to tell you how many moles of each substance takes part or is formed during the reaction. The big numbers in front of the chemical formulas of the reactants and products tell you how many moles of each substance takes part or is formed during the reaction. The little numbers tell you how many atoms of each element there are in each of the substances.

  For example…

  
• Balancing equations using reacting masses

  If you know the masses of the reactants and products that took part in a reaction, you can work out the balanced symbol equation for the reaction.
• Here are the steps you should take:

  1. Divide the mass of each substance by its relative formula mass to find the number of moles.
  2. Divide the number of moles of each substance by the smallest number of moles in the reaction.
  3. If any of the numbers aren't whole numbers, multiply all the numbers by the same amount so that they all become whole numbers.
  4. Write the balanced symbol equation for the reaction by putting these numbers in front of the chemical formulas.

  
• Limiting reactants

  When some magnesium, carbonate (MgCO3) is placed in a beaker of hydrochloric acid (HCl), you can tell a reaction is taking place because you see lots of bubbles of gas being given off.

  After a while, the amount of fizzing slows down and the reaction eventually stops.
• 1. This is because the reaction will stop when all of one of the reactants is used up. Any other reactants are in excess. They are usually added in excess to make sure that the other reactant is used up.
  2. The reactant that is used up in a reaction is called the limiting reactant (because it limits the amount of product that is formed).
• 3. The amount of product formed is directly proportional to the amount of limiting reactant. For example, if you halve the amount of limiting reactant, the amount of product formed will also halve. If you double the amount of limiting reactant, the amount of product will double (as long as it is still the limiting reactant).
• This is because if you add more reactant there will be more reactant particles to take part in the reaction, which means more product particles.

  
• Calculating the mass of product formed in a reaction

  You can calculate the mass of a product formed in a reaction by using the mass of the limiting reactant and the balanced reaction equation. You can also use this method to find the mass of a reactant needed to produce a known mass of a product.
• Here are the steps you should take:

  1. Write out the balanced equation.
  2. Work out relative formula masses (M,) of the reactant and product you want.)
  3. Find out how many moles there are of the substance you know the mass of.
  4. Use the balanced equation to work out how many moles there'll be of the other substance. In this case, that's how many moles of product will be made of this many moles of react.
  5. Use the number of moles to calculate the mass.

  
• ALT METHOD

  1. Draw a table; with mass (m), moles (n) and relative formula mass (Mr) on the right-hand side and your known and unknown products/reactants on the top.
  2. Work out relative formula masses (M,) of the reactant and product you want.) Find out how many moles there are of the substance you know the mass of.In this case, that's how many moles of product will be made of this many moles of react.
  3. Use the balanced equation to work out how many moles there'll be of the other substance.
  4. Use the number of moles to calculate the mass.

  
• The mass of the product is called the yield of the reaction. Masses you calculate in this way are called theoretical yields. In practice, you never get 100% of the yield, so the amount of product you get will be less than you calculated.
• Concentration

  The amount of substance (For example, the mass or the number of moles) in a certain volume of a solution is called its concentration.

  The more solute (the substance that is dissolved) there is in a given volume, the more concentrated the solution.

  One way to measure the concentration of a solution is by calculating the mass of a substance in a given volume of the solution.

  The units will be the units of mass/units of volume.
• Use this equation to calculate the concentration of a solution in g/dm3

  You can calculate the mass of a solute in solution by rearranging this formula to: mass = concentration x volume.

  
• Use this equation to calculate the concentration of a solution in mol/dm3

  This equation can be used to give the concentration in mol/dm3.

  You can calculate the number of moles in a solute by rearranging this formula to: number of moles = concentration x volume.

  Remember the equation: n = m/Mr. This equation can be used with this equation as well.

  
• Concentration calculations

  Titrations experiments that let you find the volumes needed for two solutions to react together completely.

  If you know the concentration of one of the solutions, you can use the volumes from the titration experiment, along with the reaction equation, to find the concentration of the other solution.

  Finding the concentration in mol/dm3. For example…

  
• Converting mol/dm3 to g/dm3

  To find the concentration in g/dm3, start by finding the concentration in mol/dm3 using the steps above.

  Then convert the concentration in mol/dm3 to g/dm3 using the equation n = m/Mr.

  
• Similarly to the limiting reactant calculations, you can also use a tabular format to calculate the concentration of an unknown substance:

  Concentration of a solution in g/dm3

  1. Draw a table; with mass (m), volume (dm3) and concentration (g/dm3) on the right-hand side and your known and unknown products/reactants on the top.
  2. Work out How many moles of the ‘known’ substance you have using the formula n= c x v.
  3. Use the reaction equation to work out how many moles of the “unknown” stuff you must have had
  4. Work out the concentration of the “unknown“ stuff.

  
• Concentration of a solution in mol/dm3

  1. Draw a table; with number of moles (mol), volume (dm3) and concentration (mol/dm3) on the right-hand side and your known and unknown products/reactants on the top.
  2. Work out how many moles of the 'known' substance you have using the formula n= c x v.
  3. Use the reaction equation to work out how many moles of the "unknown" stuff you must have had
  4. Work out the concentration of the "unknown" stuff.