For the galvanic cell that uses the reaction
2 Al(s) + 3 Ni2+(aq) → 2 Al3+(aq) + 3 Ni(s)
the value of n in the relationship ΔG° = -nFE° is ________.
Note Al goes from zero oxidation state to 3+ so each Al loses 3e. For 2Al that will be 6 electrons. To check that, Ni^2+ gains 2 electrons for each Ni or 6e for 3 Ni. 6 electrons again. So n is 6.
To determine the value of n in the relationship ΔG° = -nFE° for the given galvanic cell, we need to understand the components of the equation and how they relate to each other.
ΔG° represents the standard Gibbs free energy change of the reaction, which is a measure of the spontaneity of the reaction at standard conditions (defined as 1 atm pressure, 298 K temperature, and 1 M concentration for all species involved).
F represents Faraday's constant, which is the amount of charge carried by one mole of electrons. Its value is 96,485 C/mol.
E° represents the standard cell potential, which is a measure of the driving force or voltage of the cell. It is obtained by subtracting the standard reduction potential of the species being reduced from the standard reduction potential of the species being oxidized in the cell.
In the given galvanic cell reaction, 2 Al(s) is being oxidized to 2 Al3+(aq), and 3 Ni2+(aq) is being reduced to 3 Ni(s).
The reduction half-reaction is 3 Ni2+(aq) + 6e- → 3 Ni(s), and its standard reduction potential, which can be found in a table of standard reduction potentials, is -0.25 V.
The oxidation half-reaction is 2 Al(s) → 2 Al3+(aq) + 6e-, and its standard reduction potential is not needed for this calculation since we only consider the absolute value of the reduction potential.
Now, to find the value of n, we need to consider the stoichiometric coefficients of electrons in the balanced half-reactions. In the reduction half-reaction, 6 electrons are involved, while in the oxidation half-reaction, 6 electrons are produced.
Therefore, n = 6 electrons.
Substituting this value into the equation ΔG° = -nFE°, we get:
ΔG° = -(6)(96,485 C/mol)(-0.25 V) = 144,727.5 J/mol
So, the value of n in the relationship ΔG° = -nFE° for the given galvanic cell reaction is 6.