How many hours will it take to produce 78.0 g of Al metal by the reduction of Al3+ in an electrolytic cell with a current of 2.00 Amperes? [Enter only a number for your answer.]

78.0 g Al.

96,485 coulombs will reduce 26.98/3 g Al or 96,485 C will reduce approximately 9 g (but you need to do it more accurately). We want to reduce 78.0; therefore, we will need
96,485C x 78.0/9 = about 836,200 C.
Amperes x seconds = C
Substitute and solve for seconds, then convert to hours.

Well, it really depends on how motivated that Aluminum ion is to become a metal. Some ions are just lazy, you know? But let's assume this Aluminum ion is feeling particularly ambitious.

So, to calculate the time it takes, we can use Faraday's law. One Faraday is equal to 96,485 Coulombs, which is the amount of charge needed to produce one mole of a substance during electrolysis.

Now, let's find out how many moles of Aluminum we need. The molar mass of Aluminum is 26.98 g/mol, so if we divide 78.0 g by that, we get approximately 2.89 moles.

Next, we need to find out how many Coulombs are needed to produce 2.89 moles of Aluminum. Since the charge of one mole of Aluminum ions is 3 times the charge of one electron (3e-), we multiply the amount of moles by Avogadro's number (6.02 x 10^23) and the charge of one electron (1.60 x 10^-19 Coulombs). Phew, that's a lot of math!

So, multiplying all those numbers together, we get approximately 2.89 x 6.02 x 10^23 x 3 x 1.60 x 10^-19 Coulombs, which is about 8.81 x 10^5 Coulombs.

Now, we can finally determine the time it takes with our current of 2.00 Amperes. We divide the charge (in Coulombs) by the current (in Amperes) to get the time. So, 8.81 x 10^5 Coulombs divided by 2.00 Amperes gives us approximately 4.40 x 10^5 seconds.

And there you have it! The answer is approximately 4.40 x 10^5 hours. Just remember, this calculation assumes that our ambitious Aluminum ion works hard and doesn't take any coffee breaks.

To determine the time required to produce 78.0 g of Al metal, we need to calculate the number of moles of Al using the molar mass of Al and then use Faraday's law of electrolysis.

1. Determine the number of moles of Al:
The molar mass of Al is 26.98 g/mol.
78.0 g of Al is equivalent to:
78.0 g / 26.98 g/mol = 2.894 mol

2. Use Faraday's law of electrolysis:
Faraday's constant (F) is 96,485 C/mol (coulombs per mole).
The current (I) is given as 2.00 Amperes.

The charge (Q) required to produce 1 mole of Al is:
Q = n * F
= 2.894 mol * 96,485 C/mol
= 279,262.39 C

The time (t) required to produce 78.0 g of Al can be calculated using the formula:
t = Q / I

Plugging in the values:
t = 279,262.39 C / 2.00 A
= 139,631.195 s

Converting seconds to hours:
139,631.195 s / 3600 s/h = 38.79 hours

Therefore, it will take approximately 38.79 hours to produce 78.0 g of Al metal.

To determine the number of hours it will take to produce 78.0 g of Al metal, you need to use the concept of Faraday's law of electrolysis. Faraday's law states that the amount of substance produced or consumed in an electrolytic cell is directly proportional to the quantity of electricity passed through the cell.

The formula to calculate the amount of substance produced is:

Amount of substance (in moles) = (Electric charge (in Coulombs) / Faraday's constant) * (1 / number of electrons transferred during the reaction)

Given:
Mass of Al = 78.0 g
Current (I) = 2.00 Amperes
Time (t) = ? (in hours)

First, we need to convert the mass of Al to moles using its molar mass (26.98 g/mol).

Number of moles of Al = 78.0 g / 26.98 g/mol

Next, we need to calculate the quantity of electricity passed through the cell using the formula:

Electric charge (in Coulombs) = Current (I) * Time (t) * 3600 seconds

Here, we multiply the current (I) by time (t) in seconds (3600 seconds = 1 hour) to convert the time to seconds.

Electric charge (in Coulombs) = 2.00 A * t * 3600 s

Now, we know that the number of moles of Al produced is equal to the electric charge passed through the cell divided by Faraday's constant (96485 C/mol) and the number of electrons transferred during the reaction (which is 3 for Al3+ to Al):

Number of moles of Al = (Electric charge (in Coulombs) / Faraday's constant) * (1 / 3)

Setting these two expressions for the number of moles equal to each other, we can solve for time (t):

(78.0 g / 26.98 g/mol) = [(2.00 A * t * 3600 s) / 96485 C/mol] * (1 / 3)

Now, we can solve this equation to find the value of time (t) in seconds and then convert it to hours.

Once we calculate the value of time (t), we can convert it to hours by dividing by 3600 seconds:

Time (t in hours) = (t in seconds) / 3600

By following these steps and performing the necessary calculations, you can determine the number of hours it will take to produce 78.0 g of Al metal by the reduction of Al3+ in an electrolytic cell with a current of 2.00 Amperes.