- #1
H Smith 94
Gold Member
- 55
- 1
Hi! I am currently trying to determine how the salinity ##S## of a sample of seawater (or, objectively, a salt-water solution) changes its electrical conductivity ##\sigma##.
It is clear that they are proportional since the mobility of the ##\text{Na}^{+}## and ##\text{Cl}^{-}## ions plays a huge role but I am unable to find any conclusive models which describe relationship between ##\sigma## and ##S##. Does anyone have any pointers or know of any existing relations? It would also be useful to understand in what way these factors depend on the temperature ##T##.
I have previously discovered the Kohlrausch ionic model (see also: Molar conductivity), which provides a semi-empirical determination of the specific conductivity. From this I determined that
Making the assumption that ##\nu_+ = \nu_- = \nu## and using the substitution for ##C_n(S)## we find that
Have I made any fatal assumptions/errors in deriving this? What are its limitations? Does anyone know of a way to expand this model to incorporate temperature, rather than simply being a specific conductivity?
It is clear that they are proportional since the mobility of the ##\text{Na}^{+}## and ##\text{Cl}^{-}## ions plays a huge role but I am unable to find any conclusive models which describe relationship between ##\sigma## and ##S##. Does anyone have any pointers or know of any existing relations? It would also be useful to understand in what way these factors depend on the temperature ##T##.
I have previously discovered the Kohlrausch ionic model (see also: Molar conductivity), which provides a semi-empirical determination of the specific conductivity. From this I determined that
[tex] \sigma_{25^\text{o}\text{C}}(C_n) = \left(\nu_+\lambda_+^{(0)}+\nu_-\lambda_-^{(0)}\right)\,C_n - KC_n^{3/2} [/tex]
where:##\nu_\pm## is the number of moles of each ion;
##\lambda_\pm^{(0)}## is the limiting molar conductivities of each ion,
##\lambda_\pm^{(0)}## is the limiting molar conductivities of each ion,
for ##\text{Na}^{+}## and ##\text{Cl}^{-}##:
##C_n(S) = S\rho_\text{water}/N_Am_i## is the number concentration (i.e. number of ions per unit volume,) in which:##\lambda_+^{(0)} = 5.011\, \text{mS}\,\text{m}^2\,\text{mol}^{-1}##,
##\lambda_-^{(0)} = 7.634\, \text{mS}\,\text{m}^2\,\text{mol}^{-1}##;
##\lambda_-^{(0)} = 7.634\, \text{mS}\,\text{m}^2\,\text{mol}^{-1}##;
##S## is salinity;
##\rho_\text{water}## is the density of water;
##m_i## is the mass of each salt particle (##m_i = m_\text{Na} + m_\text{Cl}##;)
##N_A## is Avagadro's constant.
##\rho_\text{water}## is the density of water;
##m_i## is the mass of each salt particle (##m_i = m_\text{Na} + m_\text{Cl}##;)
##N_A## is Avagadro's constant.
Making the assumption that ##\nu_+ = \nu_- = \nu## and using the substitution for ##C_n(S)## we find that
\begin{equation} \sigma_{25^\text{o}\text{C}}(S) = \left(\lambda_{\text{Na}^{+}}^{(0)}+\lambda_{\text{Cl}^{-}}^{(0)}\right)\left(\frac{\rho_\text{water}}{N_Am_i}S\right)\nu - K\left(\frac{\rho_\text{water}}{N_Am_i}S\right)^{3/2}. \end{equation}
Although this model is great and seems to cover most bases it still has that pesky empirical ##K## value (the Kohlrausch constant,) so it's really not perfect.Have I made any fatal assumptions/errors in deriving this? What are its limitations? Does anyone know of a way to expand this model to incorporate temperature, rather than simply being a specific conductivity?
Last edited: