An electrochemical cell is created using gold and magnesium half-cells.
a. Determine which half-cell will undergo oxidation and which will undergo reduction,
identify anode and cathode, and calculate the voltage for the cell. You do not need to
diagram the cell.
b. If the mass of the magnesium electrode changes by 5.0 g, what will be the change in
mass of the gold electrode, and will its mass increase or decrease?
Mg ==> Mg^+2 + 2e
Au^+3 + 3e ==> Au
3Mg + 2Au^+3 ==> 3Mg^+2 + 2Au
a. To determine which half-cell will undergo oxidation and reduction, we need to compare the standard reduction potentials of the two half-reactions involved.
The half-reaction with the higher reduction potential will undergo reduction and will be the cathode. The half-reaction with the lower reduction potential will undergo oxidation and will be the anode.
Let's look up the standard reduction potentials for the half-reactions involving gold and magnesium.
Standard reduction potential for gold:
Au^3+ + 3e^- -> Au: E° = +1.50 V
Standard reduction potential for magnesium:
Mg^2+ + 2e^- -> Mg: E° = -2.37 V
Since the gold reduction potential is higher than the magnesium reduction potential, gold will undergo reduction and is the cathode. Therefore, the magnesium half-cell will undergo oxidation and is the anode.
The anode is where oxidation occurs, and the cathode is where reduction occurs.
Now, to calculate the voltage for the cell, we need to subtract the reduction potential of the anode from the reduction potential of the cathode. In this case, we are given the reduction potentials, so we don't need to multiply by the number of electrons involved.
Cell voltage (E°cell) = E°cathode - E°anode
= (+1.50 V) - (-2.37 V)
= +1.50 V + 2.37 V
= +3.87 V
Therefore, the voltage for the cell is +3.87 V.
b. To determine the change in mass of the gold electrode, we need to use Faraday's law of electrolysis, which states that the mass change is directly proportional to the charge passed through the electrode.
The equation to calculate the change in mass is:
Change in mass (gold) = (Change in mass (magnesium) * Molar mass (gold)) / Molar mass (magnesium)
Given:
Change in mass (magnesium) = 5.0 g
Molar mass (gold) = 197 g/mol
Molar mass (magnesium) = 24.31 g/mol
Change in mass (gold) = (5.0 g * 197 g/mol) / 24.31 g/mol
= 40.69 g
Therefore, the change in mass of the gold electrode will be 40.69 g. Since the change in mass is positive, it means that the mass of the gold electrode will increase.