Introduction to Molar Mass
To compare the mass of different chemical substances, we rely on the concept of molar mass (the mass of one mole of a substance) and Avogadro's number ($6.022 \times 10^{23}$ particles per mole). This guide walks you through the steps to calculate the mass of substances given in moles, grams, or particle counts.
Solving Part (a): Comparing CO₂ and SO₂
We need to determine which has a higher mass: 0.5 mole of CO₂ or 16 g of SO₂.
Step 1: Calculate mass of 0.5 mole of CO₂
- Atomic masses: C = 12, O = 16
- Molar mass of CO₂ = $12 + (2 \times 16) = 44 \text{ g/mol}$
- Mass = $\text{moles} \times \text{molar mass} = 0.5 \times 44 = 22 \text{ g}$
Step 2: Compare
- Mass of CO₂ = 22 g
- Mass of SO₂ = 16 g
- Conclusion: 0.5 mole of CO₂ has a higher mass than 16 g of SO₂.
Solving Part (b): Comparing Hydrogen and Oxygen
We compare 2 g of Hydrogen ($H_2$) and $6.023 \times 10^{21}$ molecules of Oxygen ($O_2$).
Step 1: Mass of 2 g of Hydrogen
This value is already given as 2 g.
Step 2: Mass of $6.023 \times 10^{21}$ molecules of O₂
- Molar mass of $O_2 = 2 \times 16 = 32 \text{ g/mol}$
- Number of moles = $\text{Number of molecules} / (6.023 \times 10^{23})$
- $ ext{Moles of } O_2 = (6.023 \times 10^{21}) / (6.023 \times 10^{23}) = 0.01 \text{ moles}$
- Mass of $O_2 = 0.01 \times 32 = 0.32 \text{ g}$
Step 3: Compare
- Mass of Hydrogen = 2 g
- Mass of Oxygen = 0.32 g
- Conclusion: 2 g of Hydrogen has a higher mass than $6.023 \times 10^{21}$ molecules of Oxygen.