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A student wants to calculate the standard cell potential for a galvanic cell that consists of a silver electrode and a copper electrode. The silver electrode has a silver ion concentration of 0.05 M and the copper electrode has a copper ion concentration of 0.1 M. What is the standard cell potential for this cell?

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To calculate the standard cell potential for this galvanic cell, we need to use the Nernst equation. The Nernst equation is given by:E_cell = E_cell -  RT/nF  * ln Q where E_cell is the cell potential, E_cell is the standard cell potential, R is the gas constant  8.314 J/molK , T is the temperature in Kelvin  assuming 298 K for room temperature , 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.First, we need to determine the standard cell potential, E_cell. The standard reduction potentials for silver and copper are:Ag + e  Ag s   E = +0.80 VCu + 2e  Cu s   E = +0.34 VSince the silver electrode is the cathode  reduction occurs  and the copper electrode is the anode  oxidation occurs , we can write the overall cell reaction as:2Ag + Cu s   2Ag s  + CuNow, we can calculate the standard cell potential, E_cell, by subtracting the standard reduction potential of the anode from the standard reduction potential of the cathode:E_cell = E_cathode - E_anode = 0.80 V - 0.34 V = 0.46 VNext, we need to determine the reaction quotient, Q. For the given reaction, Q is given by:Q = [Cu]/[Ag]^2Plugging in the given concentrations:Q =  0.1 M / 0.05 M ^2 = 0.1/0.0025 = 40Now, we can use the Nernst equation to calculate the cell potential, E_cell:E_cell = E_cell -  RT/nF  * ln Q E_cell = 0.46 V -   8.314 J/molK  *  298 K  /  2 * 96485 C/mol   * ln 40 Converting R to V by dividing by 1000:E_cell = 0.46 V -   0.008314 V/molK  *  298 K  /  2 * 96485 C/mol   * ln 40 E_cell = 0.46 V -  0.00247 V  * ln 40 E_cell  0.46 V - 0.00247 V * 3.6889E_cell  0.46 V - 0.0091 VE_cell  0.4509 VTherefore, the standard cell potential for this galvanic cell is approximately 0.4509 V.

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