Question

a current of 5.25 a is applied to the aluminum sulfate solution for 112 minutes. what mass of al is plated onto the part?
al³⁺ + 3e⁻ → al
mass = ? g al

Explanation:

Step1: Calculate the total charge (Q)

The formula for charge is \( Q = I \times t \), where \( I \) is current in amperes (A) and \( t \) is time in seconds (s). First, convert time from minutes to seconds: \( 112 \, \text{min} \times 60 \, \text{s/min} = 6720 \, \text{s} \). Then, \( Q = 5.25 \, \text{A} \times 6720 \, \text{s} = 35280 \, \text{C} \) (since \( 1 \, \text{A} = 1 \, \text{C/s} \)).

Step2: Find moles of electrons

Faraday's constant \( F = 96485 \, \text{C/mol e}^- \). Moles of electrons \( n_{e^-} = \frac{Q}{F} = \frac{35280 \, \text{C}}{96485 \, \text{C/mol e}^-} \approx 0.3656 \, \text{mol e}^- \).

Step3: Relate moles of electrons to moles of Al

From the reaction \( \text{Al}^{3+} + 3\text{e}^-
ightarrow \text{Al} \), 3 moles of electrons produce 1 mole of Al. So moles of Al \( n_{\text{Al}} = \frac{n_{e^-}}{3} = \frac{0.3656 \, \text{mol e}^-}{3} \approx 0.1219 \, \text{mol} \).

Step4: Calculate mass of Al

Molar mass of Al is \( 26.98 \, \text{g/mol} \). Mass \( m = n_{\text{Al}} \times \text{molar mass} = 0.1219 \, \text{mol} \times 26.98 \, \text{g/mol} \approx 3.29 \, \text{g} \).

Answer:

\( \approx 3.29 \)