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A student needs to calculate the resistance of an electrochemical cell that has a concentration of 0.1 M for both copper(II) and zinc(II) ions, using an electrochemical sensor that measures 2.5 volts for the cell. Calculate the resistance of the electrochemical cell at room temperature, given that the Faraday constant is 96485 C/mol and the gas constant is 8.314 J/(mol·K).

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To calculate the resistance of the electrochemical cell, we can use the Nernst equation and Ohm's law. First, let's find the standard cell potential  E  for the Cu2+/Cu and Zn2+/Zn redox couples.Cu2+ + 2e- -> Cu  E = +0.34 V Zn2+ + 2e- -> Zn  E = -0.76 V The overall cell reaction is:Cu2+ + Zn -> Cu + Zn2+The standard cell potential  Ecell  is the difference between the reduction potentials of the two half-reactions:Ecell = E Cu2+/Cu  - E Zn2+/Zn  = 0.34 V -  -0.76 V  = 1.1 VNow, we can use the Nernst equation to find the cell potential  Ecell  at the given concentrations:Ecell = Ecell -  RT/nF  * ln Q where R is the gas constant  8.314 J/ molK  , T is the temperature in Kelvin  assume room temperature, 298 K , n is the number of electrons transferred  2 for both Cu2+ and Zn2+ , F is the Faraday constant  96485 C/mol , and Q is the reaction quotient.Since the concentrations of both Cu2+ and Zn2+ are 0.1 M, the reaction quotient  Q  is:Q = [Zn2+]/[Cu2+] = 0.1/0.1 = 1Now, we can plug in the values into the Nernst equation:Ecell = 1.1 V -  8.314 J/ molK  * 298 K /  2 * 96485 C/mol   * ln 1 Ecell = 1.1 V - 0 = 1.1 VHowever, the electrochemical sensor measures 2.5 volts for the cell. This means there is an additional voltage  Vextra  due to the resistance in the cell:Vextra = Vmeasured - Ecell = 2.5 V - 1.1 V = 1.4 VNow, we can use Ohm's law to find the resistance  Rcell  of the electrochemical cell:Vextra = Rcell * IWe need to find the current  I  in the cell. We can use the cell potential  Ecell  and the number of electrons transferred  n  to find the current:I = n * F *  Ecell / Ecell I = 2 * 96485 C/mol *  1.1 V / 1.1 V  = 192970 C/molNow, we can plug the current  I  into Ohm's law to find the resistance  Rcell :1.4 V = Rcell * 192970 C/molRcell = 1.4 V / 192970 C/mol  7.25  10^-6 The resistance of the electrochemical cell is approximately 7.25  10^-6 .

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