Question

zinc is used as a coating for steel to protect the steel from environmental corrosion. if a piece of steel is submerged in an electrolysis bath for 24 minutes with a current of 6.5 amps, how many grams of zinc will be plated out? the molecular weight of zn is 65.38, and zn^+2 + 2e^- → zn. a) 3.17 g of zn b) 1.09 g of zn c) 12.68 g of zn d) 6.34 g of zn

Explanation:

Step1: Calculate total charge (Q)

Current \( I = 6.5 \, \text{A} \), time \( t = 24 \, \text{min} = 24 \times 60 = 1440 \, \text{s} \).
Charge \( Q = I \times t = 6.5 \, \text{A} \times 1440 \, \text{s} = 9360 \, \text{C} \).

Step2: Moles of electrons

1 mole of electrons = \( 96485 \, \text{C} \) (Faraday's constant, \( F \)).
Moles of \( e^- = \frac{Q}{F} = \frac{9360}{96485} \approx 0.0970 \, \text{mol} \).

Step3: Moles of Zn

From reaction \( \text{Zn}^{2+} + 2e^-
ightarrow \text{Zn} \), 2 moles \( e^- \) produce 1 mole Zn.
Moles of Zn = \( \frac{\text{moles of } e^-}{2} = \frac{0.0970}{2} \approx 0.0485 \, \text{mol} \). Wait, no—wait, recalculate \( Q \): \( 6.5 \times 1440 = 9360 \). Wait, maybe miscalculation. Wait, let's redo Step2: \( 9360 / 96485 \approx 0.0970 \)? No, 9360 ÷ 96485 ≈ 0.097? Wait, 96485 × 0.1 = 9648.5, so 9360 is ~0.097? Wait, no, 9360 / 96485 ≈ 0.097? Wait, 96485 × 0.097 ≈ 9359. So yes, ~0.097 mol e⁻. Then moles Zn: 0.097 / 2 ≈ 0.0485? Wait, no, that can't be. Wait, maybe I messed up time. Wait, 24 minutes is 24×60=1440 seconds. 6.5 A × 1440 s = 9360 C. Correct. Then Faraday's constant: 96485 C/mol e⁻. So moles e⁻: 9360 / 96485 ≈ 0.097 mol e⁻. Then Zn: 1 mol Zn per 2 mol e⁻, so moles Zn = 0.097 / 2 ≈ 0.0485 mol. Then mass Zn = moles × molar mass = 0.0485 × 65.38 ≈ 3.17 g? Wait, but that's option A. Wait, but let's check again. Wait, maybe I made a mistake in moles e⁻. Wait, 6.5 A × 24 min × 60 s/min = 6.5 × 1440 = 9360 C. Moles e⁻: 9360 / 96485 ≈ 0.097 mol e⁻. Then Zn: 1 mol Zn needs 2 mol e⁻, so moles Zn = 0.097 / 2 ≈ 0.0485 mol. Mass: 0.0485 × 65.38 ≈ 3.17 g. So option A? Wait, but let's check again. Wait, maybe I messed up the current or time. Wait, 6.5 A, 24 minutes. 24 minutes is 24×60=1440 s. 6.5×1440=9360 C. Faraday: 96485 C/mol e⁻. Moles e⁻: 9360 / 96485 ≈ 0.097 mol. Moles Zn: 0.097 / 2 ≈ 0.0485 mol. Mass: 0.0485 × 65.38 ≈ 3.17 g. So answer A? Wait, but let's check the calculation again. Wait, maybe I made a mistake in the number of electrons. The reaction is Zn²⁺ + 2e⁻ → Zn, so 2 moles e⁻ per 1 mole Zn. So moles Zn = (Q / F) / 2. So Q = It = 6.5 A 2460 s = 6.51440 = 9360 C. Then moles e⁻ = 9360 / 96485 ≈ 0.097 mol. Then moles Zn = 0.097 / 2 ≈ 0.0485 mol. Mass = 0.0485 65.38 ≈ 3.17 g. So option A. Wait, but let's check with another approach. Let's use the formula: mass = (I t M) / (n F), where M is molar mass, n is moles of electrons per mole of substance. Here, n=2 (since Zn²⁺ gains 2 e⁻). So mass = (6.5 1440 65.38) / (2 96485). Let's calculate numerator: 6.51440=9360; 936065.38 ≈ 936065 = 608400, 93600.38=3556.8, total ≈ 611,956.8. Denominator: 296485=192,970. Then 611956.8 / 192970 ≈ 3.17 g. Yes, so that's option A.

Answer:

A) 3.17 g of Zn