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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.

Chemistry

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Answer

N270.00\text{N}270.00

Step-by-step solution

3 steps

To 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.

  • Given Information:

    • Cost to deposit 1 g of Aluminium (Al) = N40
    • Molar mass of Al (MAlM_{Al}) = 27 g/mol
    • Molar mass of Copper (Cu) (MCuM_{Cu}) = 64 g/mol
    • Mass of Copper to be deposited (mCum_{Cu}) = 24 g
  • Assumptions for Valency:

    • Aluminium typically forms Al³⁺ ions, so its valency (nAln_{Al}) = 3.
    • Copper typically forms Cu²⁺ ions in electrodeposition, so its valency (nCun_{Cu}) = 2.
  1. Calculate the equivalent mass for Aluminium and Copper.

    The equivalent mass (EE) is given by the formula: E=Molar massValencyE = \frac{\text{Molar mass}}{\text{Valency}}.

    For Aluminium:

    EAl=MAlnAl=27 g/mol3=9 g/equivalentE_{Al} = \frac{M_{Al}}{n_{Al}} = \frac{27 \text{ g/mol}}{3} = 9 \text{ g/equivalent}

    For Copper:

    ECu=MCunCu=64 g/mol2=32 g/equivalentE_{Cu} = \frac{M_{Cu}}{n_{Cu}} = \frac{64 \text{ g/mol}}{2} = 32 \text{ g/equivalent}
  2. 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:

    Equivalents of Al=Mass of AlEAl=1 g9 g/equivalent=19 equivalents\text{Equivalents of Al} = \frac{\text{Mass of Al}}{E_{Al}} = \frac{1 \text{ g}}{9 \text{ g/equivalent}} = \frac{1}{9} \text{ equivalents}

    Now, we can find the cost to deposit 1 equivalent of Aluminium:

    Cost per equivalent=Cost for 1 g AlEquivalents of Al in 1 g=N4019 equivalents=N40×9=N360 per equivalent\text{Cost per equivalent} = \frac{\text{Cost for 1 g Al}}{\text{Equivalents of Al in 1 g}} = \frac{\text{N}40}{\frac{1}{9} \text{ equivalents}} = \text{N}40 \times 9 = \text{N}360 \text{ per equivalent}
  3. 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:

    Equivalents of Cu=Mass of CuECu=24 g32 g/equivalent=34 equivalents\text{Equivalents of Cu} = \frac{\text{Mass of Cu}}{E_{Cu}} = \frac{24 \text{ g}}{32 \text{ g/equivalent}} = \frac{3}{4} \text{ equivalents}

    Now, calculate the total cost to deposit 24 g of Copper:

    Cost for Cu=Equivalents of Cu×Cost per equivalent\text{Cost for Cu} = \text{Equivalents of Cu} \times \text{Cost per equivalent} Cost for Cu=34×N360\text{Cost for Cu} = \frac{3}{4} \times \text{N}360 Cost for Cu=3×N90\text{Cost for Cu} = 3 \times \text{N}90 Cost for Cu=N270\text{Cost for Cu} = \text{N}270

    Comparing this to the given options, the correct answer is N270.00.

    The final answer is N270.00\text{N}270.00.

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