It took 150 . s for a current of 1.25 \(\mathrm{A}\) to plate out 0.109 g of a metal from a solution containing its cations. Show that it is not possible for the cations to have a charge of \(1+.\)

We need to determine the total charge that passed through the cell in order to calculate the amount of metal deposited. We can calculate the total charge by using the following formula: Total charge (Q) = Current (I) × Time (t) Where I = 1.25 A (amperes) and t = 150 s (seconds).

Plug the given values of current and time into the formula: Q = 1.25 A × 150 s Q = 187.5 C (coulombs)

According to Faraday's law of electrolysis, the amount of metal deposited (in moles) is proportional to the total charge passed through the cell. The relation can be written as: Amount of metal deposited (in moles) = Total charge (Q) / (Charge of cations (z) × Faraday's constant (F)) Where z = charge of cations and F = Faraday's constant, approximately 96485 C/mol.

Now let's assume the charge of the cations is \(1+,\) which means z = 1. We can calculate the number of moles of metal deposited using the total charge obtained in step 2: Amount of metal deposited (in moles) = 187.5 C / (1 × 96485 C/mol) Amount of metal deposited (in moles) ≈ 0.00194 mol

To find the theoretical mass of the metal deposited, we need to know the molar mass of the metal (M). However, we do not have this information. So, we can write a general equation for the theoretical mass: Theoretical mass of metal = Amount of metal deposited (in moles) × Molar mass of metal (M) Theoretical mass of metal ≈ 0.00194 mol × M

We know that 0.109 g of metal was actually deposited. Since we don't have the molar mass of the metal, it is difficult to reach a definite conclusion. However, we can analyze the results by assuming that the metal is from Group 1 of the periodic table. If we assume that the metal is Lithium (the lightest Group 1 element) with a molar mass of approximately 6.94 g/mol: Theoretical mass of metal ≈ 0.00194 mol × 6.94 g/mol ≈ 0.0135 g This theoretical mass is less than the actual mass of metal deposited (0.109 g). This indicates that, if the metal is from Group 1, our assumption that the charge of the cations is \(1+\) is incorrect, since a charge of \(1+\) would have led to less mass being deposited. Therefore, it's not possible for the cations to have a charge of \(1+.\)