Respuesta :
In order to determine the mass of aluminum that is plated, we need relationships relating charge to moles of substance. We calculate as follows:
Charge = It = 5.80 (755)(60) = 262740 C
262740 C ( 1 mol e- / 96500 C ) ( 1 mol Al / 3 mol e- ) ( 26.98 g / 1 mol ) = 24.49 g Al can be plated
Hope this helps.
Charge = It = 5.80 (755)(60) = 262740 C
262740 C ( 1 mol e- / 96500 C ) ( 1 mol Al / 3 mol e- ) ( 26.98 g / 1 mol ) = 24.49 g Al can be plated
Hope this helps.
[tex]\boxed{24.{\text{5 g}}}[/tex] of aluminium can be plated onto the object in 755 minutes at 5.80 A of current.
Further Explanation:
The rate of flow of electric charge through any region is known as electric current. It is denoted by I. The SI unit of current is Ampere. It is measured with the help of a device called ammeter. The charge is caused due to the presence of charge carriers. Generally, electrons or electron-deficient species act as charge carriers. Charge is a fundamental property of subatomic particles. The standard unit of charge is Coulomb.
The relationship between the charge and the electric current is expressed as follows:
[tex]{\text{Q}} = {\text{It}}[/tex] …… (1)
Here,
Q is the amount of charge on a substance.
I is the electric current.
t is the time for which the charge is passed through the substance.
Firstly, the time is to be converted into seconds. The conversion factor for this is,
[tex]{\text{1 min}} = {\text{60 sec}}[/tex]
So time can be calculated as follows:
[tex]\begin{aligned}{\text{t}}&=\left({{\text{755 min}}}\right)\left({\frac{{{\text{60 sec}}}}{{{\text{1 min}}}}}\right)\\&={\text{45300 sec}}\\\end{aligned}[/tex]
The value of I is 5.80 A.
The value of t is 45300 seconds.
Substitute these values in equation (1).
[tex]\begin{aligned}{\text{Q}}&=\left({{\text{5}}{\text{.80 A}}}\right)\left({{\text{45300 s}}}\right)\\&=262{\text{740 C}}\\\end{aligned}[/tex]
The reaction occurs as follows:
[tex]{\text{A}}{{\text{l}}^{3 + }}+3{e^ - }\to{\text{Al}}[/tex]
The formula to calculate the equivalent weight of Al is as follows:
[tex]{\text{E of Al}} = \frac{{{\text{Molecular weight of Al}}}}{{{\text{Valency of Al}}}}[/tex] …… (2)
Substitute 26.98 g for the molecular weight of Al and 3 for valency of Al in equation (2).
[tex]\begin{aligned}{\text{E of Al}}&=\frac{{{\text{26}}{\text{.98 g}}}}{3}\\&=8.9{\text{9 g}}\\\end{aligned}[/tex]
The formula to calculate the mass of Al deposited is as follows:
[tex]{\text{W}}=\frac{{\left({\text{E}}\right)\left({\text{Q}}\right)}}{{\text{F}}}[/tex] …… (3)
Here,
W is the mass of Al deposited.
E is the equivalent weight of Al.
Q is the amount of electric charge.
F is Faraday or 96500 C.
Substitute 8.99 g for E, 262740 C for Q and 96485 C for F in equation (3).
[tex]\begin{aligned}{\text{W}}&=\left({{\text{8}}{\text{.99 g}}}\right)\left({\frac{{{\text{262740 C}}}}{{{\text{96485 C}}}}}\right)\\&=24.480{\text{8 g}}\\&\approx 24.{\text{5 g}}\\\end{aligned}[/tex]
Therefore 24.5 g of Al can be plated onto the object in 755 minutes at 5.80 A of current.
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Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Electrochemistry
Keywords: Al, aluminium, Al3+, 3e-, 24.5 g, 96485 C, 755 minutes, 5.80 A, current, charge, molecular weight, equivalent weight, valency, 26.98 g.
