Introduction to Chemical Calculations

Welcome to one of the most important parts of Chemistry! If you have ever followed a recipe to bake a cake, you already understand the basics of this chapter. In chemistry, we need to know exactly how much of each "ingredient" (reactant) to use so we don't waste materials and so we know exactly how much "food" (product) we will get at the end.

Don't worry if you aren't a "maths person"—we will break every calculation down into simple, repeatable steps. Let's get started!

1. Relative Formula Mass (\(M_r\))

Before we can calculate masses in a reaction, we need to know how heavy different molecules are. Every element has a Relative Atomic Mass (\(A_r\)) found on the Periodic Table (it is usually the larger of the two numbers).

The Relative Formula Mass (\(M_r\)) is simply the sum of the relative atomic masses of all the atoms shown in a chemical formula.

How to calculate \(M_r\):

  1. Identify how many atoms of each element are in the formula.
  2. Look up the \(A_r\) for each element on the Periodic Table.
  3. Multiply the \(A_r\) by the number of atoms.
  4. Add them all together.

Example: Find the \(M_r\) of Water (\(H_2O\))
Hydrogen (\(H\)) has an \(A_r = 1\). There are 2 Hydrogen atoms.
Oxygen (\(O\)) has an \(A_r = 16\). There is 1 Oxygen atom.
Calculation: \((2 \times 1) + (1 \times 16) = 18\).
So, the \(M_r\) of \(H_2O = 18\).

Quick Review: The \(M_r\) has no units! It is a "relative" number compared to other atoms.

2. Percentage by Mass

Sometimes we want to know what percentage of a compound's total mass comes from just one specific element. We use this formula:

\(\text{Percentage mass} = \frac{\text{Total } A_r \text{ of the element}}{\text{Total } M_r \text{ of the compound}} \times 100\)

Common Mistake: Forgetting to multiply the \(A_r\) by the number of atoms. If you are finding the % of Oxygen in \(CO_2\), you must use \(32\) (which is \(2 \times 16\)) for the top part of the fraction!

3. Empirical and Molecular Formulae

There are two ways to write a chemical formula:

  • Molecular Formula: The actual number of atoms of each element in a molecule (e.g., \(C_2H_4\)).
  • Empirical Formula: The simplest whole-number ratio of atoms in a compound (e.g., \(CH_2\)).

Calculating Empirical Formula from Masses:

If you are given the masses of elements that reacted together, follow these steps:

  1. Write down the Mass of each element.
  2. Divide each mass by the element's \(A_r\) (this gives you the number of moles).
  3. Divide all the results by the smallest number you just calculated.
  4. If the results aren't whole numbers, multiply them up (e.g., \(1.5\) becomes \(3\)) to get the Ratio.

4. Conservation of Mass

The Law of Conservation of Mass states that no atoms are lost or made during a chemical reaction. Therefore:
Total mass of reactants = Total mass of products.

Why does mass sometimes "change" in experiments?

If you perform a reaction in a non-enclosed system (like an open beaker), the mass might seem to change:

  • Mass increases: This usually happens because a gas from the air (like Oxygen) has reacted with the substance inside the beaker and is now part of the solid product.
  • Mass decreases: This usually happens because one of the products is a gas (like Carbon Dioxide) and it has escaped into the surrounding air.

5. Concentration of Solutions

Concentration tells us how "crowded" the solute particles are in a liquid. For this topic, we measure it in grams per cubic decimetre (\(g\ dm^{-3}\)).

\(\text{Concentration} = \frac{\text{mass of solute (g)}}{\text{volume of solution (dm}^3\text{)}}\)

Important Unit Conversion: Chemistry volumes are often given in \(cm^3\), but concentration uses \(dm^3\).
\(1\ dm^3 = 1000\ cm^3\)
To turn \(cm^3\) into \(dm^3\), divide by 1000.

6. The Mole and Avogadro Constant (HIGHER TIER ONLY)

In Chemistry, a mole is just a specific number of particles. It's like the word "dozen" means 12; the word "mole" means \(6.02 \times 10^{23}\). This massive number is called the Avogadro Constant.

The Golden Rule: One mole of any substance has a mass in grams equal to its Relative Formula Mass (\(M_r\)).
Example: The \(M_r\) of Water is 18. Therefore, 1 mole of water weighs exactly 18g.

The Formula Triangle:

You can use this triangle to switch between mass and moles:

\(\text{Mass (g)} = \text{Moles} \times M_r\)

\(\text{Moles} = \frac{\text{Mass (g)}}{M_r}\)

7. Amounts in Equations (HIGHER TIER ONLY)

Balanced equations tell us the molar ratio of the reactants and products. We can use this to calculate exactly how much product we will make.

Step-by-Step Method:

  1. Calculate Moles: Find the moles of the substance you know the mass of using \(\text{Moles} = \frac{\text{Mass}}{M_r}\).
  2. Use the Ratio: Look at the big numbers in the balanced equation to find the moles of the "unknown" substance.
  3. Calculate Mass: Turn those moles back into mass using \(\text{Mass} = \text{Moles} \times M_r\).

8. Limiting Reactants (HIGHER TIER ONLY)

In most reactions, we use an excess of one reactant to make sure the other one is completely used up. The reactant that gets used up first is called the limiting reactant.

The amount of product formed is directly proportional to the amount of the limiting reactant used. If you half the amount of limiting reactant, you half the amount of product made.

Did you know? It's like making sandwiches. If you have 10 slices of bread and 2 slices of cheese, the cheese is the "limiting reactant"—you can only make 2 sandwiches, no matter how much bread you have left over!

9. Deducing Stoichiometry (HIGHER TIER ONLY)

If you are given the masses of all reactants and products, you can work out the balanced equation (the stoichiometry):

  1. Find the moles of every substance (\(\text{Mass} \div M_r\)).
  2. Divide all the mole values by the smallest mole value.
  3. The resulting whole numbers are the "big numbers" used to balance the equation.

Key Takeaway: Always convert mass to moles first! Moles are the "universal language" of chemical equations.