How do you do the math for this? I know cost of Zinc is $5.30/100 g, Silver is $

Question

How do you do the math for this? I know cost of Zinc is $5.30/100 g, Silver is $0.56/g, and Lead is $2.45/100g..

The construction of a cell with maximum voltage

Use metal strips and solutions of your choice to determine which combination will give the largest potential. Several different metals and metal salt solutions will be available. In general, the solid metal should be the same metal as that in the salt solution it is in contact with. Utilize a table of standard reduction potentials to help decide which cells to construct. Keep in mind that you can connect more than one cell together. You can also vary the concentration of the metal salt solutions. A minimum of 3 different batteries should be made and tested. Your grade will not be based solely on the number of batteries you make, but also on the strategy used for choosing battery designs and the thoroughness of your investigation. In addition to finding the highest voltage you can achieve, determine which battery gives you the best ratio of volts to cost (V/$).

Battery 1.)   HALF CELL ONE: 1.0 Mg2+ (aq) and 1.0 Mg (s) HALF CELL TWO: 1.0 M Zn2+ (aq) and Zn (s) observed potential = + 1.12 V

Battery 2.)   HALF CELL ONE: 1.0 Mg2+ (aq) and 1.0 Mg (s) HALF CELL TWO: 1.0 M Ag+ (aq) and Ag (s) observed potential = + 2.39 V

Battery 3.)   HALF CELL ONE: 1.0 Mg2+ (aq) and 1.0 Mg (s) HALF CELL TWO: 1.0 M Pb2+ (aq) and Pb (s) observed potential = + 1.42 V

Explanation / Answer

Now, let us calculate, their costs per mol fisrt,

Cost of 1 mol (65.38 g.) of Zn = 65.38 * 5.30 / 100 = 3.46 $

Cost of 1 mol of (207.2 g. ) Pb = 207.2 * 2.45 / 100 = 5.08 $

Cost of 1 mol (107.8 g.) of Ag = 107.8 * 0.56 / 1 = 60.4 $

Now take the ratio of potential generated to cost,

Battery (1) : V / $ = 1.12 / 3.46 = 0.324

Battery (2) : V / $ = 2.39 / 60.4 = 0.0396

Battery (3) V / $ = 1.42 / 5.08 = 0.280

According to this Battery (1) has best ratio of V / $

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