Specifications Core Practicals

# Chemical Calculations

## Relative Atomic Mass (RAM or Ar)

This is the average relative mass of the atoms of different isotopes in an element. It is the number of times heavier an atom is than one-twelfth of a carbon-12 atom.

An atom’s mass number is the sum of its protons and neutrons. Carbon has 6 neutrons and 6 protons so we say it has a mass of 12. You can find this information on a Periodic Table.

However, relative atomic mass takes into account that some elements have isotopes. These are atoms of the same element, but with different numbers of neutrons. The Periodic Table contains a list of every element, with their relative atomic masses.

We can take an average of all an element's isotope mass numbers to work out the relative atomic mass of that element for ourselves (see diagram). Relative formula mass (RFM or Mr) is like relative atomic mass, but we are working out the mass of a compound. You have to add all of the relative atomic masses of each atom together to calculate an RFM, for example water (H₂O):

• there are two hydrogen atoms, each with an atomic mass of 1... so 1 × 2 = 2

• there is one oxygen atom, which has an atomic mass of 16

• in total the relative formula mass of water is 16 + 2 = 18

## Empirical Formula

You can calculate the formulae of simple compounds from reacting masses or percentage composition. These formula are called empirical formulae

An empirical formula is the simplest whole number ratio of atoms in a substance.

Experimental evidence

It's possible to complete a practical to work out the empirical formula of a substance. For example, calculating the empirical formula of magnesium oxide, by reacting magnesium with oxygen in the air:

• record the mass of a crucible with, and without magnesium

• complete the reaction, then record the mass of crucible with product (magnesium oxide)

• calculate the mass of oxygen used

• using the mass of magnesium and oxygen used to make magnesium oxide, we can work out its empirical formula ## Conservation of Mass

The law of conservation of mass states that no atoms are created or destroyed during a chemical reaction, they are only rearranged. This means that the mass of the products must be the same as the mass of the reactants.

Closed systems

No substances can enter or exit a closed system. A simple closed system in the lab could just be a sealed flask. Sometimes reactions that happen in open beakers are still closed systems (because nothing enters or exits the system). These include:

• acid-alkali neutralisation reactions, which produce salt solutions

• precipitation reactions, which produce an insoluble precipitate (solid)

Non-enclosed systems

Substances can enter or exit a non-enclosed system. These systems are often open flasks, or crucibles, that let gases enter or exit.

If a gas escapes, it can look like the total mass has decreased. If a gas is added, the total mass will look as if it has increased. However, the total mass stays the same if the mass of the gas is included in calculations. ## Concentration

solution is formed when a solute dissolves in a solvent.

The concentration of a solution is a measure of the mass, or amount of solute, dissolved in a given volume of solvent. The more concentrated the solution, the more particles it contains in a given volume.

Calculating concentration

The concentration of a solution can be calculated using:

• the mass of dissolved solute (in g)

• the volume of solvent (in dm³)

concentration = mass of solute  ÷ volume of solvent

The units for concentration are g/dm³, but they may also be written as gdm⁻³ - don't worry as these mean the same thing.​ Volume unit conversions

Sometimes volumes can be quoted in ml, rather than cm³. These units describe the same volume. For example, 250 ml = 250 cm³.

If your volume is given in cm³, then you will need to convert it into dm³ before it can be used in this calculation.

• divide by 1000 to convert from cm³ to dm³

• multiply by 1000 to convert from dm³ to cm³

## Moles and Molar Quantities (Higher Only)

Chemical amounts are measured in moles (symbol: mol). The mass of one mole of substance in grams is equal to the substance’s RAM/RFM.

One mole of a substance contains the same number of particles, atoms, molecules or ions as one mole of any other substance.

The number of atoms, molecules or ions in a mole of a given substance is the Avogadro constant. The value of the Avogadro constant is 6.02×10²³ particles per mole. This means that for every one mole of substance (no matter the substance), it will always contain 6.02×10²³ particles. Substance
Type
RAM/RFM
1 mole (g)
1 mole (particles)
carbon
element
12
12
6.02×10²³
sodium
element
23
23
6.02×10²³
water
compound
18
18
6.02×10²³
carbon dioxide
compound
44
44
6.02×10²³

moles = mass (g) ÷ RFM

We can use this equation to calculate the number of moles of a chemical in a given amount of mass.

## Limiting Reactants (Higher Only)

Reactions stop when one of the reactants is used up. This is because the other reactant has nothing more to react with, and so some of it will be left over.

The substance that runs out is called the limiting reactant. The one left over we say has been added in excess.

The stoichiometry of a reaction is the ratio of the amounts of each substance in the balanced equation. It can be worked out using masses found by experiment.

Action
Mg
O₂ This means that 2 moles of Mg reacts with 1 mol of O₂, so the left-hand side of the equation is:        2Mg + O₂

Then balancing the equation gives us:        2Mg + O₂ → 2MgO