This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
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 (M_Al) = 27 g/mol Molar mass of Copper (Cu) (M_Cu) = 64 g/mol Mass of Copper to be deposited (m_Cu) = 24 g Assumptions for Valency: Aluminium typically forms Al³⁺ ions, so its valency (n_Al) = 3. Copper typically forms Cu²⁺ ions in electrodeposition, so its valency (n_Cu) = 2. Step 1: Calculate the equivalent mass for Aluminium and Copper. The equivalent mass (E) is given by the formula: E = Molar massValency. For Aluminium: E_Al = M_Aln_Al = 27 g/mol3 = 9 g/equivalent For Copper: E_Cu = M_Cun_Cu = 64 g/mol2 = 32 g/equivalent Step 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 AlE_Al = 1 g9 g/equivalent = (1)/(9) 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 = N40(1)/(9) equivalents = N40 × 9 = N360 per equivalent Step 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 CuE_Cu = 24 g32 g/equivalent = (3)/(4) equivalents Now, calculate the total cost to deposit 24 g of Copper: Cost for Cu = Equivalents of Cu × Cost per equivalent Cost for Cu = (3)/(4) × N360 Cost for Cu = 3 × N90 Cost for Cu = N270 Comparing this to the given options, the correct answer is N270.00. The final answer is N270.00.