A galvanic cell is constructed at 298 K using a zinc rod dipped in a 0.1 M zinc sulfate solution and a silver wire dipped in a silver nitrate solution of concentration 10^ -x M . If the measured cell potential is 1.4715 V , the value of x is _________. [Given: E^ _ Ag ^+/ Ag = 0.80 V , E^ _ Zn ²⁺/ Zn = -0.76 V , 2.303RT F = 0.059 V ]

Step-by-step solution

From the standard reduction potentials, zinc acts as the anode and silver acts as the cathode. The half-cell reactions are: Anode: Zn ( s ) Zn ²⁺( aq ) + 2 e ^- Cathode: 2 Ag ^+( aq ) + 2 e ^- 2 Ag ( s ) Overall cell reaction: Zn ( s ) + 2 Ag ^+( aq ) Zn ²⁺( aq ) + 2 Ag ( s ) Number of electrons transferred, n = 2 . Standard cell potential: E^ _ cell = E^ _ cathode - E^ _ anode = 0.80 - (-0.76) = 1.56 V Using the Nernst equation: E_ cell = E^ _ cell - 0.059 2 [ Zn ²⁺] [ Ag ^+]^2 Substitute the given values: 1.4715