A galvanic cell is constructed as Zn(s) | Zn ²⁺ (1 M ) || Ag ^+ (c) | Ag(s) . The concentration of Ag ^+ is varied, and the cell potential E_ cell is plotted against ₁₀[ Ag ^+] at 298 K . If the plot is a straight line, the magnitude of its slope is ________ mV . (Given: 2.303 RT F = 0.059 V )

Step-by-step solution

The cell reaction is: Zn(s) + 2 Ag ^+( aq ) Zn ²⁺( aq ) + 2 Ag(s) The number of electrons transferred is n = 2 . According to the Nernst equation: E_ cell = E^ _ cell - 0.059 2 ₁₀ [ Zn ²⁺] [ Ag ^+]^2 Substituting [ Zn ²⁺] = 1 M : E_ cell = E^ _ cell - 0.059 2 ₁₀ ([ Ag ^+]⁻²) E_ cell = E^ _ cell + 0.059 2 2 ₁₀ [ Ag ^+] E_ cell = E^ _ cell + 0.059 ₁₀ [ Ag ^+] Comparing this with the equation of a straight line y = mx + c , the slope m is 0.059 V . Converting to millivolts: Slope = 0.059 1000 mV = 59 mV . Answer: 59