For what concentration of Ag+(aq). will the emf of given cell be zero at 25 °C . if the concentration ofCu(s) I Cu2+ (0.1M) II Aa+(aq.)1Ag(s)? Given. E° Ag+/Ag = 0.80V: E° Cu2+/Cu = 0.34V.

The cell reaction is:

Cu(s) + 2Ag+(aq) -> Cu2+(aq) + 2Ag(s)

The cell potential (E) is given by the Nernst equation:

E = E° - (0.0592/n)logQ

where E° is the standard cell potential, n is the number of electrons transferred in the balanced redox reaction, and Q is the reaction quotient.

The standard cell potential (E°) is the difference between the standard reduction potentials of the two half-reactions:

E° = E°(Ag+/Ag) - E°(Cu2+/Cu) = 0.80V - 0.34V = 0.46V

The number of electrons transferred in the balanced redox reaction (n) is 2.

The reaction quotient (Q) is given by:

Q = [Cu2+]/[Ag+]^2 = (0.1)/[Ag+]^2

We want to find the concentration of Ag+ ([Ag+]) when the cell potential (E) is zero. Setting E = 0 in the Nernst equation gives:

0 = 0.46V - (0.0592/2)log((0.1)/[Ag+]^2)

Solving this equation for [Ag+] gives:

[Ag+] = sqrt((0.1)/10^(2*0.46V/0.0592)) = 0.01 M

So, the concentration of Ag+ that will make the emf of the cell zero at 25 °C is 0.01 M.

To find the concentration of Ag+(aq) when the emf of the cell is zero, we can use the Nernst equation. The Nernst equation is used to calculate the potential of a half-cell in an electrochemical cell, or to calculate the total voltage (electromotive force) for a full electrochemical cell.

The Nernst equation is: E = E° - (RT/nF) * lnQ

Where: E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons exchanged in the electrochemical reaction (the reaction quotient), F is Faraday's constant, and Q is the reaction quotient.

Given: E° Ag+/Ag = 0.80V E° Cu2+/Cu = 0.34V Temperature T = 25 °C = 298.15 K R = 8.314 J/(mol*K) F = 96485 C/mol n = 2 (since the reaction involves the transfer of two electrons)

The standard cell potential E° for the cell reaction is the difference between the standard reduction potentials of the two half-cells. So, E° = E° Ag+/Ag - E° Cu2+/Cu = 0.80V - 0.34V = 0.46V

When the emf of the cell is zero (E = 0), we can rearrange the Nernst equation to solve for Q:

0 = E° - (RT/nF) * lnQ lnQ = nFE°/RT Q = e^(nFE°/RT)

The reaction quotient Q for the cell reaction is [Ag+]/[Cu2+]. Since the concentration of Cu2+ is given as 0.1M, we can write Q = [Ag+]/0.1.

Substituting Q into the equation gives:

[Ag+] = 0.1 * e^(nFE°/RT) [Ag+] = 0.1 * e^(2964850.46/8.314*298.15)

Calculating the above expression will give the concentration of Ag+ when the emf of the cell is zero.