Final answer:
To calculate the oxygen volume produced at STP during the electrolysis of aqueous sodium sulfate, the charges passed through the electrolyte are found using the current and time given. The moles of oxygen are then calculated based on the number of transferred electrons, and using the standard molar volume of gas at STP, the oxygen volume is determined to be 0.334 liters.
Step-by-step explanation:
To calculate the volume of oxygen produced at STP (standard temperature and pressure) during the electrolysis of aqueous sodium sulfate, we need to understand the process of electrolysis and the reaction involved. Given the reaction 2H2O → O2 + 2H2, we see that the mole ratio between oxygen and water is 1:2. This means for every mole of oxygen produced, two moles of water are consumed.
Using Faraday's laws of electrolysis, we can first determine the moles of electrons transferred. The charge (Q) passed through the electrolyte is calculated by multiplying the current (I) by the time (t), Q = I × t. Hence, Q = 3.20 A × 1800 s (since 30 minutes is 1800 seconds) = 5760 Coulombs. With Faraday's constant being approximately 96500 Coulombs per mole of electrons, the moles of electrons are 5760 C / 96500 C/mol = 0.0597 moles of electrons.
From the half-reaction, we know that it takes four moles of electrons to produce one mole of oxygen. Therefore, the moles of oxygen produced n(O2) = 0.0597 moles of electrons / 4 = 0.0149 moles of O2. At STP, one mole of gas occupies 22.4 liters. Therefore, the volume of oxygen gas produced at STP is V(O2) = 0.0149 moles × 22.4 L/mol = 0.334 liters.