Need help to calculate results of an electrochemistry cell potential lab work

Question

So, the lab work is this. I made an AgCl electrode of a silver wire by coating it with AgCl. This was done by electrolysis by immersing the wire in HCl and using platinum as a counter electrode and applying current to the system. After that, the AgCl electrode was immersed into HCl dilutions of different molalities and the cell potential was measured against a hydrogen gas electrode (normal hydrogen electrode NHE).

The measurements were done at temperature of 25 °C. The results of the measurements are as follows:

\begin{array}{llc} \hline c\,(\pu{mol/kg}) &\sqrt{c}\, (\sqrt{\pu{mol/kg}}) & \mathrm{E\,(V)} \\ \hline 0.001 & 0.032 & 0.6322 \\ 0.002 & 0.045 & 0.6815 \\ 0.004 & 0.063 & 0.6497 \\ 0.006 & 0.077 & 0.6280 \\ 0.008 & 0.089 & 0.6153 \\ 0.010 & 0.100 & 0.6049 \\ 0.020 & 0.141 & 0.5700 \\ 0.050 & 0.224 & 0.5030 \\ \hline \end{array}

Because the cell potential can be calculated by (as the pressure gradient of the hydrogen electrode was 0): $$ E(m)= E^0 + \frac{2ART}{F} \sqrt{\frac{m_{\text{HCl}}}{m^0}} $$

By plotting the table values we get (excluding the first data point as an outlier):

We can see from the equation that the $E^0$ would be about 0,708 V. However, literature references say the standard potential of the AgCl electrode is about 0,222 V. Any idea what I am doing wrong here?

Then I also should plot the HCl mean activity coefficient values calculated from the formula: $$ E(m) = E^0 - \frac{2RT}{F} \ln \left[ \gamma_{\text{HCl}} \left( \frac{m_{\text{HCl}}}{1\ \text{mol/kg}} \right) \right] \\ \Leftrightarrow \ \gamma_{\text{HCl}} = e^{ \frac{(E^0-E)F}{2RT} } / \frac{m_{\text{HCl}}}{1\ \text{mol/kg}} $$

Thus I get values:

\begin{array}{cc} \hline m & \gamma_\ce{HCl} \\ \pu{mol/kg} \\ \hline 0.001 & 4371.98 \\ 0.002 & 837.44 \\ 0.004 & 777.51 \\ 0.006 & 790.73 \\ 0.008 & 759.33 \\ 0.01 & 743.74 \\ 0.02 & 733.46 \\ 0.05 & 1080.77 \\ \hline \end{array}

But literature references (CRC Handbook of Chemistry and Physics - 97th Edition, p. 5-101) gives greatly different values:

\begin{array}{cc} \hline m & \gamma_\ce{HCl} \\ \pu{mol/kg} \\ \hline 0.001 & 0.965 \\ 0.002 & 0.952 \\ 0.004 & 0.929 \\ 0.01 & 0.905 \\ 0.02 & 0.876 \\ 0.05 & 0.832 \\ \hline \end{array}

Any help would be greatly appreciated.

Answer 1

The silver-silver chloride is a half cell. When the silver wire coated with AgCl is dipped into HCl solutions with no Ag$^+$ cations, as confirmed by the OP, it is not a half cell with AgCl in equilibrium with silver and silver chloride, but a half cell that is a silver anode corroding in acid solution (with oxygen from air?).

After some time (hours?), with stirring of the solution, enough AgCl may dissolve, still leaving enough on the silver wire, dropping the 0.5-0.7 V to wind up with the desired 0.222 V. Perhaps the HCl solutions need to be saturated with AgCl and deoxygenated before the immersion of the wire electrode.