Step 1: Context - Electrolysis of Water:
Electrolysis of water decomposes H₂O into hydrogen and oxygen gases.
- Hydrogen gas (H₂) is collected at the cathode.
- Oxygen gas (O₂) is collected at the anode.
Step 2: Mole Ratio from Reaction:
The balanced chemical equation is:
\[
2H_2O \rightarrow 2H_2 + O_2
\]
This indicates:
- 2 moles of H₂ are produced.
- 1 mole of O₂ is produced.
Step 3: Molar Mass Calculation:
- Molar mass of H₂ = 2 g/mol.
- Molar mass of O₂ = 32 g/mol.
Step 4: Mass Ratio Calculation:
Based on the equation:
- 2 moles of H₂ = 2 × 2 = 4 g.
- 1 mole of O₂ = 32 g.
The mass ratio of hydrogen to oxygen is therefore:
\[
\text{Hydrogen : Oxygen} = 4 : 32 = 1 : 8
\]
Step 5: Conclusion:
The mass ratio of gases collected at the cathode (H₂) to the anode (O₂) is 1 : 8.