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.