Explain Avogadro's law in relation to molar quantities

$n = \frac{V}{V_m}$

Where:

• $n$ = number of moles (mol)
• $V$ = volume of gas (dm³)
• $V_m$ = molar volume (22.4 dm³/mol at STP)

Example 1: Converting volume to moles

Calculate the number of moles in 44.8 dm³ of nitrogen gas (N₂) at STP.

Solution:

$n = \frac{V}{V_m} = \frac{44.8 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 2.0 \text{ mol}$

Example 2: Converting moles to volume

Calculate the volume occupied by 1.5 mol of oxygen gas (O₂) at STP.

Solution:

$V = n \times V_m = 1.5 \text{ mol} \times 22.4 \text{ dm}^3/\text{mol} = 33.6 \text{ dm}^3$

Example 3: Finding mass from gas volume

Calculate the mass of 11.2 dm³ of carbon dioxide (CO₂) at STP. (Molar mass of CO₂ = 44 g/mol)

Solution:

First, find moles: $n = \frac{11.2 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.5 \text{ mol}$

Then, calculate mass: $\text{Mass} = n \times \text{molar mass} = 0.5 \text{ mol} \times 44 \text{ g/mol} = 22 \text{ g}$

• Volume to moles: Divide volume by 22.4
• Moles to volume: Multiply moles by 22.4
• Moles to mass: Multiply moles by molar mass
• Volume to mass: Volume → moles (÷22.4) → mass (× molar mass)

This value (22.4 dm³/mol) is constant for all gases at STP because Avogadro's Law tells us that the number of particles in equal volumes is the same, regardless of the type of gas.

In Tanzania, this principle is used in industries such as brewing and soft drink manufacturing. For example, when carbonating beverages, manufacturers must calculate the exact volume of CO₂ gas needed to dissolve in a given volume of drink to achieve the desired fizziness. Using Avogadro's Law, they can determine how many moles of CO₂ will occupy the required volume at the processing temperature and pressure, ensuring consistent product quality across batches.