Final answer:
To calculate the grams of chromium metal deposited at the cathode, we use Faraday's Law of Electrolysis. We calculate the charge passed through the circuit and convert it to moles of electrons. Finally, we convert the moles of chromium metal to grams using the molar mass of chromium.
Step-by-step explanation:
To calculate the number of grams of chromium metal deposited at the cathode, we need to use Faraday's Law of Electrolysis, which states that the mass of a substance deposited on an electrode is directly proportional to the amount of charge passing through the circuit.
First, we need to calculate the charge (Q) passed through the circuit using the current (I) and time (t) given:
Q = I × t = 5.00 A × (30.0 minutes x 60 seconds/minute) = 9000 C
Next, we need to convert the charge to moles of electrons using Faraday's constant (F) which is 96485 C/mol. Since the reduction of chromium(III) requires 3 moles of electrons to produce 1 mole of chromium metal, we can calculate the moles of electrons (n) as:
n = Q / (3F) = 9000 C / (3 × 96485 C/mol) = 0.0984 mol
Finally, we can convert the moles of chromium metal to grams using the molar mass of chromium (Cr), which is 51.996 g/mol:
Mass = n × molar mass = 0.0984 mol × 51.996 g/mol ≈ 5.10 grams