Calculate the standard cell emf for galvanic
cells for the cell reaction
3 Zn(s) + 2 Bi3+(aq) → 3 Zn2+(aq) + 2 Bi(s)
Answer in units of V.
To calculate the standard cell emf (E°) for the given galvanic cell reaction, we can use the Nernst equation. The Nernst equation relates the cell emf to the standard cell emf, the reaction quotient, and the temperature.
The Nernst equation is given by:
E = E° - (RT/nF) * ln(Q)
Where:
E = Cell emf
E° = Standard cell emf
R = Gas constant (8.314 J/mol·K)
T = Temperature in Kelvin
n = Number of electrons transferred in the balanced cell reaction
F = Faraday's constant (96485 C/mol)
ln = Natural logarithm
Q = Reaction quotient
In this case, we are given the balanced cell reaction:
3 Zn(s) + 2 Bi3+(aq) → 3 Zn2+(aq) + 2 Bi(s)
Let's consider the half-reactions for this reaction:
Zn(s) → Zn2+(aq) + 2e- (Oxidation half-reaction)
Bi3+(aq) + 3e- → Bi(s) (Reduction half-reaction)
From the balanced equation, we can see that 2 electrons are transferred in the reduction half-reaction, so n = 2.
Now, we need to determine the reaction quotient (Q) for the given system. The general formula for Q is:
Q = [C]^c[D]^d / [A]^a[B]^b
Where [C], [D], [A], and [B] represent the concentrations of the respective species, and a, b, c, and d are the stoichiometric coefficients of the species in the balanced equation.
In this case, the reaction quotient Q is:
Q = [Zn2+]^3/[Bi3+]^2
Since we are interested in the standard cell emf, the concentrations of the species involved are taken to be 1 M.
Now that we have all the necessary information, we can proceed to calculate the standard cell emf (E°) using the Nernst equation.