Question

How long (in hours) will a current of 2.00 A need to be applied to produce 50.0 grams of aluminum metal from molten Al2O3

Answer 1

`t=74.5hr`

Step-by-step explanation:

Hello!

In this case, given the mass of aluminum metal which can undergo the following reduction from aluminum oxide:

`Al^(3+)+3e^-\rightarrow Al`

We can see three moles of electrons are transferred per mole of aluminum, thus, we obtain:

`mole^-=50.0gAl*(1molAl)/(26.98gAl)*(3mole^-)/(1molAl) =5.56mole^-`

Next, we compute the charge carried by those electrons via the faraday's constant:

`q=5.56mole^-*(96,485C)/(1mole^-) =536,425C`

Finally, considering the applied current, we compute the elapsed time in hours to achieve such electrolysis:

`t=536,425C*(s)/(2.00C) *(1hr)/(3600s) \\\\t=74.5hr`

Best regards!