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What is the maximum power output of a galvanic cell consisting of a zinc electrode and a copper electrode, with a concentration of 0.1 M Zn2+ and 0.01 M Cu2+? Assume a standard hydrogen electrode (SHE) as the reference electrode and a temperature of 25°C.

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To calculate the maximum power output of a galvanic cell, we first need to determine the cell potential  E_cell  under the given conditions. We can use the Nernst equation to do this:E_cell = E_cell -  RT/nF  * ln Q where E_cell is the standard cell potential, R is the gas constant  8.314 J/molK , T is the temperature in Kelvin  25C = 298.15 K , n is the number of electrons transferred in the redox reaction, F is the Faraday constant  96485 C/mol , and Q is the reaction quotient.For a galvanic cell consisting of a zinc electrode and a copper electrode, the overall redox reaction is:Zn s  + Cu2+ aq   Zn2+ aq  + Cu s The standard reduction potentials for the half-reactions are:Zn2+ + 2e-  Zn s   E = -0.76 VCu2+ + 2e-  Cu s   E = +0.34 VThe standard cell potential  E_cell  is the difference between the reduction potentials of the two half-reactions:E_cell = E_Cu - E_Zn = 0.34 V -  -0.76 V  = 1.10 VThe number of electrons transferred in the redox reaction  n  is 2. The reaction quotient  Q  can be calculated as:Q = [Zn2+]/[Cu2+] =  0.1 M / 0.01 M  = 10Now we can plug these values into the Nernst equation:E_cell = 1.10 V -  8.314 J/molK * 298.15 K / 2 * 96485 C/mol  * ln 10 E_cell  1.10 V - 0.0295 V = 1.0705 VThe maximum power output  P_max  can be calculated using the formula:P_max =  E_cell^2  /  4 * R_cell However, we do not have the internal resistance  R_cell  of the galvanic cell. Without this information, we cannot calculate the maximum power output.

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