An experiment was constructed to determine the passive diffusion of thallium ions Ti+ across the membrane of E.coli bacteria. A suspension of E.coli was prepared and incubated with Ti+ and used as the left half-cell solution in the electrochemical cell constructed as follow:
Ti(s) I Ti+(aq) I H+ (aq) I H2(g) I Pt(s)
(i) Initially the cell potential was +0.297V at 298K. Given that E0(Ti(s), Ti+(aq)) = -0.074V and E0(H2(g), H+(aq)) = 0.000V, calculate the initial concentration of Ti+ added to the solution containing the bacteria. All other species on the right half cell were at their standard state.
(ii) After some time the cell potential stabilised to a new value of +0.302V, calculate the final concentration of Ti+ outside and inside the bacteria, given that the total volume of the solution is 300cm3 and the volume fraction of the bacteria cells was 0.012.