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Calculate the cost to deposit 24 g of Copper, given that the cost to deposit 1 g of Aluminium is N40, M(Al)=27 g/mol, M(Cu)=64 g/mol, valency of Al=3, and valency of Cu=2.
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Step-by-step solution
3 stepsTo solve this problem, we will use Faraday's laws of electrolysis, which relate the mass of a substance deposited to the quantity of electricity passed and its equivalent mass.
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Given Information:
- Cost to deposit 1 g of Aluminium (Al) = N40
- Molar mass of Al () = 27 g/mol
- Molar mass of Copper (Cu) () = 64 g/mol
- Mass of Copper to be deposited () = 24 g
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Assumptions for Valency:
- Aluminium typically forms Al³⁺ ions, so its valency () = 3.
- Copper typically forms Cu²⁺ ions in electrodeposition, so its valency () = 2.
Calculate the equivalent mass for Aluminium and Copper.
The equivalent mass () is given by the formula: .
For Aluminium:
For Copper:
Determine the cost per equivalent for Aluminium.
We are given that it costs N40 to deposit 1 g of Aluminium.
First, find how many equivalents are in 1 g of Aluminium:Now, we can find the cost to deposit 1 equivalent of Aluminium:
Calculate the cost to deposit 24 g of Copper.
According to Faraday's second law, the same quantity of electricity (and thus the same cost) will deposit one equivalent of any substance. Therefore, the cost per equivalent for Copper will also be N360.
First, find how many equivalents are in 24 g of Copper:
Now, calculate the total cost to deposit 24 g of Copper:
Comparing this to the given options, the correct answer is N270.00.
The final answer is .
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