Question

Given the following electrochemical equation:Cu(s) | Cu²⁺(aq, 0.0100 M) || Cr³⁺(aq, 1.00 M) | Cr(s)At 298 K, the standard reduction potential for Cu²⁺/Cu is +0.34 V and for Cr³⁺/Cr is -0.74 V. Calculate the equilibrium constant (K) for the above electrochemical reaction.

Answer 1

To calculate the equilibrium constant  K  for the given electrochemical reaction, we first need to determine the overall cell potential  E  and the balanced redox reaction.The balanced redox reaction is:Cu s  + 2Cr aq   Cu aq  + 2Cr s The cell potential  E  can be calculated using the standard reduction potentials:E = E cathode  - E anode Since Cu/Cu has a more positive standard reduction potential, it will act as the cathode, and Cr/Cr will act as the anode.E =  +0.34 V  -  -0.74 V  = +1.08 VNow we can use the Nernst equation to relate the cell potential to the equilibrium constant  K . The Nernst equation is:E = E -  RT/nF  * ln Q At equilibrium, the cell potential  E  is 0, and Q becomes K:0 = E -  RT/nF  * ln K We can rearrange the equation to solve for K:ln K  = nFE/RTWhere:n = number of electrons transferred in the balanced redox reaction  2 in this case F = Faraday's constant  96,485 C/mol R = gas constant  8.314 J/mol K T = temperature  298 K ln K  =  2 * 96,485 C/mol * 1.08 V  /  8.314 J/mol K * 298 K ln K   52.6Now, we can take the exponent of both sides to find K:K  e^52.6  4.7  10^22So, the equilibrium constant  K  for the given electrochemical reaction is approximately 4.7  10^22.