A galvanic cell consists of a magnesium electrode dipped in a 0.1 M Mg ²⁺ solution and a silver electrode dipped in an Ag ⁺ solution of unknown concentration. The measured cell potential at 298 K is 3.01 V . Given: E^ _ Mg ²⁺/ Mg = -2.36 V E^ _ Ag ⁺/ Ag = 0.80 V 2.303RT F = 0.06 V If the concentration of Ag ⁺ is 10^ -x M , the value of x is _____.

Step-by-step solution

First, calculate the standard cell potential E^ _ cell : E^ _ cell = E^ _ cathode - E^ _ anode E^ _ cell = 0.80 - (-2.36) = 3.16 V The balanced cell reaction is: Mg + 2 Ag ⁺ Mg ²⁺ + 2 Ag Here, the number of electrons transferred is n = 2 . According to the Nernst equation: E_ cell = E^ _ cell - 0.06 n [ Mg ²⁺] [ Ag ⁺]² Substitute the given values into the equation: 3.01 = 3.16 - 0.06 2 0.1 [ Ag ⁺]² -0.15 = -0.03 0.1 [ Ag ⁺]² 5 = 0.1 [ Ag ⁺]² Taking the antilog on both sides: 10⁵ = 0.1 [ Ag ⁺]² [ Ag ⁺]² = 0.1 10⁵ =