# What is the equation for solving the concentration of the unknown from a Single-point Standard Addition Calibration for Potentiometry?

I know how to use the standard addition equation for a single-point analysis from an equation I got from the Analytical Chemistry book "Quantitative Chemical Analysis" 9ed by D. Harris.

However, solving for a potentiometry problem, the equation doesn't seem to be effective anymore. I keep on getting negative value for the initial concentration of the unknown sample.

The problem goes like this:

The Na+ concentration of a solution was determined by measurement with a sodium ion-selective electrode. The electrode system developed a potential of -0.2462 V when immersed in 10.0 mL of the solution of unknown concentration. After addition of 1.00 mL of 2.00 x 10-2 M NaCl, the potential changed to -0.1994 V. Calculate the Na+ concentration of the original solution.

Is there a specific equation I can use so I can correctly solve for the concentration of the unknwon solution?

If we consider the simplified Nernst equation in context of parameters $$A, B$$,
and if we consider $$c, c_\mathrm{0}$$ as unknown concentration and concentration increment, respectively,
\begin{align} E_\mathrm{1} &= A + B \cdot \log c\\ E_\mathrm{2} &= A + B \cdot \log ( c + c_\mathrm{0} )\\ E_\mathrm{2}- E_\mathrm{1} &= B . \log( 1 + \frac {c_\mathrm{0}}{c} )\\ 10^{\frac{E_\mathrm{2}- E_\mathrm{1}}{B}} &= 1 + \frac {c_\mathrm{0}}{c}\\ c &= \frac {c_\mathrm{0}}{10^{\frac{E_\mathrm{2}- E_\mathrm{1}}{B}} -1} \end{align}
where $$B = \frac{RT}{nF} \cdot \ln(10)$$