A concentration cell based on the following half reaction at 289 K has initial concentrations of 1.39 M , 0.312 M , and a potential of 0.037206 V at these conditions. After 9.1 hours, the new potential of the cell is found to be 0.0095376 V. What is the concentration of at the cathode at this new potential

The concentration at the cathode is  

Explanation:

From the question we are told that

   The initial concentration is  

     The reaction is  

 At Cathode  

  At anode    

     The initial potential is  

The complete reaction is

                       (Cathode)   -----------------  (anode)

 Looking the reaction above we can see that after the reaction   at cathode loss some concentration and  will gain some concentration

 Let say the amount of concentration lost/gained is = z M

The after the reaction the concentration of  at the cathode would be

While the concentration at the anode would be  

At initial the condition the net potential of the cell is

    After time

     The potential  of the cell is  

Generally this potential is defined by Nernst equation as

Where R is the gas constant with a value of  

           T is the temperature given as  

          n is the number of mole of electron which

           F is the farad constant with a value of  

Substituting values

      Taking exponent of both sides

The concentration at the cathode is