a current of 5.25 a is applied to the aluminum sulfate solution for 112 minutes. what mass of al is plated…

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}^- \rightarrow \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 )