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A voltaic cell consists of a standard hydrogen electrode and a copper electrode in a solution of copper(II) sulfate. The measured cell potential is 0.78 V at 25°C. If the concentration of copper(II) sulfate is 0.1 M, what is the resistance of the electrochemical cell?

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To find the resistance of the electrochemical cell, we need to use the Nernst equation, which relates the cell potential to the concentrations of the species involved in the redox reaction. The Nernst equation is: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  25C = 298 K , n is the number of electrons transferred in the redox reaction, F is the Faraday constant  96,485 C/mol , and Q is the reaction quotient.For the given voltaic cell, the redox reaction is:Cu aq  + 2e  Cu s The standard cell potential  E_cell  for this reaction is the difference between the standard reduction potentials of the two half-reactions:E_cell = E Cu/Cu  - E H/H  = 0.34 V - 0 V = 0.34 VThe number of electrons transferred  n  in the redox reaction is 2. The reaction quotient  Q  for this reaction is:Q = [Cu]/[H]Since the standard hydrogen electrode has a concentration of 1 M for H ions, and the concentration of Cu is given as 0.1 M:Q =  0.1 / 1  = 0.1Now we can plug these values into the Nernst equation:0.78 V = 0.34 V -  8.314 J/molK * 298 K /  2 * 96,485 C/mol   * ln 0.1 Solving for the resistance  R  in the equation:R =   0.34 V - 0.78 V  * 2 * 96,485 C/mol  /  8.314 J/molK * 298 K * ln 0.1  R  -0.44 * 192,970 C/mol /  2,464.972 J/mol * ln 0.1  R  -86,179.8 C/mol /  -10,791.7 J/mol R  7.98 The resistance of the electrochemical cell is approximately 7.98 ohms.

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