Calculate reacting masses in simple proportions. Calculations will not involve the mole concept

Stoichiometry – Relative masses of atoms and molecules

What is a relative mass?

Think of a relative mass as the “weight” of an atom compared to a standard unit – the hydrogen atom, which we set to 1.0. It’s like comparing the weight of a feather to a rock; the numbers tell you how many times heavier one is than the other. ⚛️

Atomic masses – the “mass number”

The relative mass of an element is simply the sum of the number of protons and neutrons in its nucleus.

Examples:

• Hydrogen (H): 1 proton + 0 neutrons = 1
• Carbon (C): 6 protons + 6 neutrons = 12
• Oxygen (O): 8 protons + 8 neutrons = 16

Calculating relative masses of molecules

To find the relative mass of a molecule, add up the relative masses of all its atoms.

Example – Water (H₂O):
$$ M_{\text{H}_2\text{O}} = 2 \times M_{\text{H}} + M_{\text{O}} = 2 \times 1 + 16 = 18 $$ So, one molecule of water has a relative mass of 18. 🧪

Simple proportion calculations

When two substances react, the masses that combine are in a simple proportion equal to the ratio of their relative masses.

General rule:
If substance A has relative mass $M_A$ and substance B has relative mass $M_B$, then $$ \frac{\text{mass of A}}{\text{mass of B}} = \frac{M_A}{M_B} $$ This is the same idea as mixing equal volumes of two liquids – the ratio of their “weights” tells you how much of each you need. 📐

Common element masses (quick reference)

Example problems

1. Problem 1: 10 g of hydrogen reacts with oxygen to form water. How many grams of water are produced?
   Solution: $$ \frac{M_{\text{H}_2\text{O}}}{M_{\text{H}_2}} = \frac{18}{2} = 9 $$ So, for every 2 g of H₂ you get 18 g of H₂O. $$ \text{Mass of H₂O} = 10\,\text{g} \times \frac{18}{2} = 90\,\text{g} $$ 📚
2. Problem 2: 12 g of carbon reacts with 24 g of oxygen. How much CO₂ is produced?
   Solution: $$ \frac{M_{\text{CO}_2}}{M_{\text{C}}} = \frac{44}{12} = 3.\overline{6} $$ $$ \text{Mass of CO₂} = 12\,\text{g} \times \frac{44}{12} = 44\,\text{g} $$ ??
3. Problem 3: 5 g of nitrogen reacts with 20 g of hydrogen to form ammonia. What is the mass of NH₃ produced?
   Solution: $$ \frac{M_{\text{NH}_3}}{M_{\text{N}}} = \frac{17}{14} \approx 1.21 $$ $$ \text{Mass of NH}_3 = 5\,\text{g} \times 1.21 \approx 6.05\,\text{g} $$ 🎯