$($a$)$ Estimate the junction potential for the following situation $(T=298K)(10pt)$

$HCl\frac{0\mathrm{.}1M}{N}$aCl$(0\mathrm{.}01M)$

Note the Henderson equation:

$E_j=\frac{{\displaystyle \underset{i}{\overset{?}{}}}\frac{|z_i|u_i}{z_i}[C_i()-C_i()]}{{\displaystyle \underset{i}{\overset{?}{}}}|z_i|u_i[C_i()-C_i()]}\frac{RT}{F}ln(\frac{{\displaystyle \underset{i}{\overset{?}{}}}|z_i|u_i{C}_i()}{{\displaystyle \underset{i}{\overset{?}{}}}|z_i|u_i{C}_i()})$

$($b$)$ Derive the membrane potential below. $(5$pt$)$

$E_m=-\frac{RT}{z_{i}F}ln(\frac{a_1^{}}{a_i^{}})$