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Answer :
The mass of aluminium that can be plated onto an object in 755 min at 5.8 A of current will be [tex]\boxed{24.5\;{\text{g}}}[/tex].
Further Explanation:
Electrochemistry is the study to determine the relationship between electrical energy and the chemical change that occurs in a redox reaction.
Electrolyte: It is the compound that undergoes decomposition into ions on the passage of electricity.
Electrolysis: It is the process of decomposition of electrolyte into its constituent ions on passage of electricity through its molten or aqueous solution.
The positively charged ions called cations move towards the electrode that is charged negatively and known as cathode and negatively charged ions called anions move towards the electrode that is positively charged known as anode. Oxidation occurs at anode and reduction occurs at cathode.
The oxidation reaction is as follows:
[tex]{{\text{A}}^ - } \to {\text{A}} + {{\text{e}}^ - }[/tex]
The reduction reaction is as follows:
[tex]{{\text{C}}^ + } + {{\text{e}}^ - } \to {\text{C}}[/tex]
The reduction equation of is as follows:
[tex]{\text{A}}{{\text{l}}^{ + 3}} + 3{{\text{e}}^ - } \to {\text{Al}}[/tex] ……(1)
The amount of substance deposited due to flow of current through the electrolyte depends upon the quantity of electricity passed through the electrolyte. It is known as first law of electrolysis. The formula of first law of electrolysis is as follows:
[tex]{\text{W}} = {\text{ZQ}}[/tex] ……(2)
Here,
W is mass of substance liberated or deposited at electrode,
Z is electrochemical equivalence,
Q is charge flow.
The formula to calculate charge flow(Q) is as follows:
[tex]{\text{Q}} = {\text{I}} \times {\text{T}}[/tex] ……(3)
The formula to calculate electrochemical equivalence (Z) is as follows:
[tex]{\text{Z}} = \dfrac{{\text{E}}}{{\text{F}}}[/tex] …… (4)
Here, E is equivalent mass of the substance, and F is faraday constant.
The formula to calculate the equivalent mass (E) is as follows:
[tex]{\text{E}} = \dfrac{{\text{M}}}{{\text{V}}}[/tex] …… (5)
Here, M is molar mass of substance and V is valency of substance.
Substitute equation (5) in (4).
[tex]{\text{Z}} = \dfrac{{\text{M}}}{{{\text{V}\times{F}}}}[/tex] …… (6)
Substitute Z and Q from (6) and (3) in (2).
[tex]{\text{W}} = \dfrac{{{\text{M} \times {I} \times {T}}}}{{{\text{V} \times {F}}}}[/tex] …… (7)
Substitute [tex]27\;{\text{g/mol}}[/tex] for M, 3 for V, [tex]5.8\;{\text{A}}[/tex] for I, [tex]755\;{\text{min}}[/tex] for T, and [tex]96500\;{\text{C/mol}}[/tex] for F in equation (7).
[tex]\begin{aligned}{\text{W}}&= \frac{{\left( {27\;{\text{g/mol}}}\right)\left( {5.8\;{\text{A}}}\right)\left( {755\;{\text{min}}}\right)\left({\frac{{60\;\sec }}{{{\text{1}}\;{\text{min}}}}}\right)}}{{\left( 3 \right)\left({96500\;{\text{C/mol}}}\right)\left( {\frac{{1\;{\text{A}}\cdot {\text{s}}}}{{{\text{1}}\;{\text{C}}}}} \right)}}\\&= 24.5\;{\text{g}}\\\end{aligned}[/tex]
The mass of aluminium that can be plated onto an object in 755 min at 5.8 A of current will be
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Answer details:
Grade: Senior Secondary School
Subject: Chemistry
Chapter: Electrochemistry
Keywords: electrochemistry, electrolysis, faraday, oxidation, reduction, equivalent mass, electrochemical equivalence, electrolyte, 755 min and 24.5 g
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Answer: 24.5 g
Explanation:
[tex]Q=I\times t[/tex]
where Q= quantity of electricity in coloumbs
I = current in amperes = 5.80 A
t= time in seconds =755 min =[tex]755\times 60=45300s[/tex]
[tex]Q=5.80A\times 45300s=262740C[/tex]
[tex]Al^{3+}+3e^{-1}\rightarrow Al[/tex]
[tex]96500\times 3=289500Coloumb[/tex] of electricity deposits 1 mole of Al.
262740C of electricity deposits =[tex]\frac{1}{289500}\times 262740=0.90mole[/tex] of Zn.
Mass of aluminium=[tex]moles\times {\text {Molar mass}}=0.90\times 27=24.5g[/tex]
