Quantitative Chemistry: Mass, Moles and Concentrations
What Are Moles?
A mole is the unit chemists use to count atoms, molecules and ions. Just like a dozen equals 12 items, one mole equals 6.02 × 10²³ particles. This huge number is called Avogadro's constant.
One mole of any element has a mass in grams equal to its relative atomic mass. For example, one mole of carbon (relative atomic mass 12) has a mass of 12g.
The molar mass connects the microscopic world of atoms to the macroscopic world we can measure. For compounds, we add up the relative atomic masses of all atoms present.
Calculating Moles from Mass
The fundamental equation linking moles, mass and molar mass is:
\(\text{number of moles} = \frac{\text{mass}}{\text{molar mass}}\)
This can be rearranged to find mass or molar mass depending on what information you're given.
Calculate the number of moles in 44g of carbon dioxide (CO₂).
Step 1: Find the molar mass of CO₂
Carbon: 1 × 12 = 12g/mol
Oxygen: 2 × 16 = 32g/mol
Total molar mass = 12 + 32 = 44g/mol
Step 2: Apply the formula
\(\text{moles} = \frac{44}{44} = 1 \text{ mole}\)
Concentration of Solutions
When substances dissolve in water, we create solutions. The concentration tells us how much solute is dissolved in a given volume of solution.
Concentration can be measured in g/dm³ (mass per volume) or mol/dm³ (moles per volume). Combined Science calculations only need g/dm³; mol/dm³ belongs to separate Chemistry.
The two main concentration equations you need to know are:
$$\text{concentration (g/dm³)} = \frac{\text{mass of solute (g)}}{\text{volume of solution (dm³)}}$$
\(\text{concentration (mol/dm³)} = \frac{\text{moles of solute}}{\text{volume of solution (dm³)}}\)
Remember these volume conversions:
- 1 dm³ = 1000 cm³ = 1000 ml = 1 litre
- To convert cm³ to dm³: divide by 1000
- To convert dm³ to cm³: multiply by 1000
Calculating Masses in Reactions
Chemical equations show the molar ratios between reactants and products. We can use these ratios along with molar masses to calculate the masses of substances involved in reactions.
The process follows these steps:
- Write the balanced chemical equation
- Identify the molar ratio from the equation
- Calculate moles of the known substance
- Use the molar ratio to find moles of unknown substance
- Convert moles back to mass using molar mass
Calculate the mass of water produced when 16g of methane burns completely.
\(CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O\)
Step 1: Calculate moles of methane
Molar mass of CH₄ = 12 + (4 × 1) = 16 g/mol
\(\text{moles of CH}_4 = \frac{16}{16} = 1 \text{ mole}\)
Step 2: Use molar ratio
From equation: 1 mole CH₄ produces 2 moles H₂O
Therefore: moles of H₂O = 1 × 2 = 2 moles
Step 3: Convert to mass
Molar mass of H₂O = (2 × 1) + 16 = 18 g/mol
\(\text{mass of H}_2\text{O} = 2 × 18 = 36\text{g}\)
Limiting Reactants
In many reactions, one reactant runs out before the others. This limiting reactant determines how much product can be formed.
To identify the limiting reactant, calculate how many moles of each reactant you have, then compare this to the molar ratios in the balanced equation. The reactant that would be used up first is the limiting reactant.
Common Calculation Mistakes
Students often make errors when working with quantitative chemistry. Always check your balanced equations are correct before starting calculations. Make sure you convert units properly — especially converting cm³ to dm³ for concentration calculations. Remember that molar mass uses the relative atomic mass from the periodic table, and for compounds you must add up all the atoms present.