Consider the voltaic cell illustrated in the figure, which is based on the cell reaction:
Zn(s)+Cu^2+(aq) -> Zn^2+(aq)+Cu(s)
Under standard conditions, what is the maximum electrical work, in joules, that the cell can accomplish if 52.0g of copper is plated out?
90
To determine the maximum electrical work that can be accomplished by the cell, we need to calculate the cell potential (Ecell) using the standard reduction potentials (E°) of the half-reactions involved in the cell reaction.
In the given cell reaction, we have the oxidation half-reaction:
Zn(s) -> Zn2+(aq) + 2e-
And the reduction half-reaction:
Cu2+(aq) + 2e- -> Cu(s)
The standard reduction potentials for these half-reactions can be obtained from a standard reduction potential table. The reduction potential for the Zn2+(aq) + 2e- -> Zn(s) half-reaction is -0.76 V, and the reduction potential for the Cu2+(aq) + 2e- -> Cu(s) half-reaction is +0.34 V.
Now, the standard cell potential (E°cell) can be calculated by subtracting the reduction potential of the oxidation half-reaction from the reduction potential of the reduction half-reaction:
E°cell = E°reduction - E°oxidation
= (+0.34 V) - (-0.76 V)
= 1.10 V
The maximum electrical work that can be accomplished by the cell is equal to the product of the cell potential and the total charge transferred (Q). The total charge transferred can be calculated using Faraday's law:
Q = n * F
Where n is the number of moles of electrons transferred and F is the Faraday constant (96,485 C/mol e-).
To calculate the number of moles of electrons transferred, we need to use the stoichiometry of the balanced cell reaction. The balanced cell reaction shows that for every 2 moles of electrons transferred, 1 mole of copper is plated out. Therefore, the number of moles of electrons transferred (n) is equal to half the number of moles of copper plated out.
First, we need to convert the mass of copper plated out (52.0 g) to moles:
Mass of copper = 52.0 g
Molar mass of copper (Cu) = 63.55 g/mol
Number of moles of copper = (52.0 g) / (63.55 g/mol)
Now, we can calculate the number of moles of electrons transferred:
Number of moles of electrons transferred = (1/2) * (Number of moles of copper)
Finally, we can calculate the maximum electrical work:
Maximum electrical work = E°cell * Q
= E°cell * (n * F)
Substituting the values and performing the calculations will give you the answer in joules.