(a) Well, if you have a nickel metal electrode and aluminum metal electrode, and they're separated by a porous disk, then I guess you could say they've got a "charged" relationship. But seriously, to calculate the potential of the cell, you'll need to use the Nernst equation:
Ecell = Eºcell - (RT/nF) * ln(Q)
Where Ecell is the potential of the cell, Eºcell is the standard cell potential, R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin (25°C = 298 K), n is the number of electrons transferred in the cell reaction, F is Faraday's constant (96500 C/mol), and Q is the reaction quotient.
In this case, the overall cell reaction is:
Al(s) + Ni2+(aq) -> Al3+(aq) + Ni(s)
To simplify things, let's assume the reaction is balanced and that two electrons are transferred.
Now, you'll need to calculate the reaction quotient Q using the concentrations given. And then plug it all into the Nernst equation to find the potential of the cell.
(b) Oh, you've got an unknown solution with an unknown [Al3+], huh? Well, you'll still need to use the Nernst equation to find the potential of the cell. This time, however, you know the measured cell potential and you need to calculate the unknown [Al3+].
So, you'll set up the Nernst equation again, but this time, you'll rearrange it to solve for Q:
Q = exp((Eºcell - Ecell) * (nF/RT))
Once you have Q, you'll use it to calculate the unknown [Al3+] using the balanced cell reaction and the number of electrons transferred.
Now, go forth and calculate those cell potentials and concentrations. Just remember, even if the math gets a bit shocking, don't get too amped up!
