Calculate the volume of oxygen produced at room temperature when a concentrated H2SO4 is electrolyzed for 30 min using a current.

Steps to Solve

1. Understand the Electrolysis Reaction

When concentrated sulfuric acid (H₂SO₄) undergoes electrolysis, water decomposition occurs, producing oxygen (O₂) at the anode. The balanced half-reaction for oxygen generation is: $$ 4OH^- \rightarrow 2H₂O + O₂ + 4e^- $$

2. Determine the Quantity of Electric Charge (Coulombs)

Use the formula for electric charge: $$ Q = I \times t $$ Where:

• ( Q ) is the electric charge in coulombs (C)
• ( I ) is the current in amperes (A)
• ( t ) is time in seconds

Given ( t = 30.0 , \text{min} = 30.0 \times 60 , \text{s} = 1800 , \text{s} ).

3. Calculate the Moles of Oxygen Produced

Using Faraday's laws, we find that 4 moles of electrons produce 1 mole of O₂:

• First, calculate the number of moles of electrons using Faraday's constant ( F \approx 96500 , \text{C/mol} ): $$ n = \frac{Q}{F} $$ Then, the moles of O₂ produced is: $$ n_{O₂} = \frac{n_{e^-}}{4} $$

4. Convert Moles of Oxygen to Volume

At room temperature and 1 atm, the molar volume of a gas is approximately ( 24.0 , \text{dm}^3 ). The volume of oxygen produced is calculated as: $$ V_{O₂} = n_{O₂} \times 24.0 , \text{dm}^3 $$