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: Convert time to seconds. The given time is 50 minutes. t = 50 min × 60 s/min t = 3000 s Step 2: Calculate the total charge (Q) passed. The given current is I = 3 A. Q = I × t Q = 3 A × 3000 s Q = 9000 C Step 3: Write the half-reaction for zinc deposition. Zinc(II) ions (Zn^2+) gain electrons to form solid zinc. Zn^2+(aq) + 2e^- Zn(s) This reaction shows that 2 moles of electrons are required to deposit 1 mole of Zn. Step 4: Calculate the moles of electrons transferred. Faraday's constant is F = 96500 C/mol e^-. Moles of electrons = Charge (Q)Faraday's constant (F) Moles of electrons = 9000 C96500 C/mol e^- Moles of electrons ≈ 0.093264 mol e^- Step 5: Calculate the moles of zinc deposited. From the half-reaction, 1 mole of Zn requires 2 moles of electrons. Moles of Zn = Moles of electrons2 Moles of Zn = 0.093264 mol2 Moles of Zn ≈ 0.046632 mol Step 6: Calculate the mass of zinc deposited. The molar mass of Zn is 65 g/mol. Mass of Zn = Moles of Zn × Molar mass of Zn Mass of Zn = 0.046632 mol × 65 g/mol Mass of Zn ≈ 3.031 g The mass of zinc deposited is approximately 3.031 g. 3 done, 2 left today. You're making progress.