This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Write the half-reaction for the production of magnesium. Magnesium ions (Mg^2+) gain two electrons to form solid magnesium (Mg). Mg^2+ + 2e^- Mg Step 2: Calculate the total charge (Q) passed through the cell. The current (I) is 500 amperes and the time (t) is 24 hours. First, convert time to seconds: t = 24 hours × 60 minutes/hour × 60 seconds/minute = 86400 s Now, calculate the charge: Q = I × t Q = 500 A × 86400 s = 43200000 C Step 3: Calculate the moles of electrons (n_e) transferred. Using Faraday's constant (F = 96500 C/mol): n_e = (Q)/(F) n_e = 43200000 C96500 C/mol ≈ 447.668 mol Step 4: Determine the moles of magnesium (n_Mg) produced. From the half-reaction, 2 moles of electrons are required to produce 1 mole of magnesium. n_Mg = (n_e)/(2) n_Mg = 447.668 mol2 ≈ 223.834 mol Step 5: Calculate the mass of magnesium (m_Mg) produced. The molar mass of magnesium (Mg) is 24 g/mol. m_Mg = n_Mg × Molar Mass of Mg m_Mg = 223.834 mol × 24 g/mol = 5372.016 g Step 6: Convert the mass from grams to kilograms. m_Mg = 5372.016 g1000 g/kg ≈ 5.372 kg The mass of magnesium produced is 5.372 kg. That's 2 down. 3 left today — send the next one.