Question

BU
1
L3
C01 -
Calculate the voltage in a galvanic cell that contains a manganese electrode
immersed in a 2.0 M solution of MnCl2 as the cathode, and a manganese
electrode immersed in a 5.2 x 10-2 M solution of MnSO4 as the anode (T = 25°C)
C06​

Answer 1

Answer:

Recall that the actual free-energy change for a reaction under nonstandard conditions, ΔG , is given as follows:

ΔG=ΔG°+RTlnQ(20.6.1)

We also know that ΔG=−nFEcell (under non-standard confitions) and ΔGo=−nFEocell (under standard conditions). Substituting these expressions into Equation 20.6.1 , we obtain

−nFEcell=−nFEocell+RTlnQ(20.6.2)

Dividing both sides of this equation by −nF ,

Ecell=E∘cell−(RTnF)lnQ(20.6.3)

Equation 20.6.3 is called the Nernst equation, after the German physicist and chemist Walter Nernst (1864–1941), who first derived it. The Nernst equation is arguably the most important relationship in electrochemistry. When a redox reaction is at equilibrium ( ΔG=0 ), then Equation 20.6.3 reduces to Equation 20.6.4 and 20.6.5 because Q=K , and there is no net transfer of electrons (i.e., Ecell = 0).

Ecell=E∘cell−(RTnF)lnK=0(20.6.4)

since

E∘cell=(RTnF)lnK(20.6.5)

Substituting the values of the constants into Equation 20.6.3 with T=298K and converting to base-10 logarithms give the relationship of the actual cell potential (Ecell), the standard cell potential (E°cell), and the reactant and product concentrations at room temperature (contained in Q ):