Final answer:
To calculate the Ecell for the given electrochemical cell reaction, we need to apply the Nernst equation using the provided concentrations and standard cell potential; the reaction quotient Q is determined by the concentrations of reactants and products, resulting in the cell's operating potential.
Step-by-step explanation:
To find the Ecell for the given electrochemical cell reaction, we need to apply the Nernst equation, which is a way to calculate the cell potential Ecell under non-standard conditions. In this case, the reaction is:
MnO4−(aq) +4H+(aq) + 3Ag(s) → MnO2(s) + 2H2O(l) + 3Ag+(aq)
The standard cell potential (E°cell) is given as +0.88 V. To calculate the actual cell potential under the given concentrations, we use the Nernst equation in the form:
Ecell = E°cell - (RT/nF) * lnQ
Here, R is the gas constant, T is the temperature in Kelvin (assumed to be 25°C or 298K for standard conditions), n is the number of moles of electrons transferred in the balanced equation (which is 3 for this reaction), F is Faraday's constant, and Q is the reaction quotient. The concentrations given are [MnO4−] = 2.0M, [H+] = 1.0M, and [Ag+] = 0.010M. Since solids and liquids do not appear in the reaction quotient, and we are provided with the concentrations of the aqueous species only, Q can be calculated as follows:
Q = [Ag+]^3 / ([MnO4−] * [H+]^4)
Upon substituting into the Nernst equation with the given concentrations and constants, we can find the value of Ecell, which would give us the potential at which the cell operates under these conditions.