Calculation of NaOH and HNO3 solution strengths based on Conductivity

[RobbyI]

I currently have graphs that show conductivity measurements of NaOH and NNO3 solutions at fixed temperatures. I was after an equation (or graphs) that can calculate conductivity of varying NaOH and or HNO3 solutions (between 5 - 0.5%) at varying temperatures (say within 80-10 *C.

Any assistance would be much appreciated

 

[m777182]

Hello RobbyI,
You could do it in an Excel spreadsheet:the idea is to construct a best fit function that represents conductivity (=kapa)of NaOH (or HNO3) as a function of concentration and temperature, kapa(NaOH)=f(C(NaOH,T). The most simple equation would be kapa= constant + a*conc(NaOH).As the relationship is not entirely linear, a better approximation would be kapa= constant + a*C(NaOH)+b*C(NaOH)^2, or to my experiences, a third degree polynom will be optimal :
kapa= constant + a *C(NaOH)+b *C(NaOH)^2+c *C(NaOH)^3, where C(NaOH) stays for concentration of NaOH.Of course you can have a 5th degree polynom or more , but usually you will be not much more happy with it.Your function now works for a certain chosen temperature.
If you want to expand it over a T range, you should include temperature into you equation,now for the 1st approximation
as
kapa=constant1 + a1*C(NaOH)+ b1*T.
A better approximation will include some mixed terms,
kapa=constant1 + a1*C(NaOH)+ b1*T +c1*C(NaOH)*T or even better a model that would include a polynom of C(NaOH) to a third degree,a polynom of T to a second degree (or more)and a mixed term to a second degree.There are some other more complex ways, but you have to start somewhere.
How to do it?
For a model, that will include C(NaOH) up to the power of 3, a mixed term C(NOH)*T up to the power 2 and a T term up to the power of 2 form a spreadsheet where the first column(let it be "A&quotcontains values of particular concentrations of NaOH. Into column "B" write the same concentrations to power of 2 and into column "C" write values of C(NaOH)^3.Into column "D" write the temperatures T, into "E" write values of T^2.Into column "F" write values of the mixed term C(NaOH)*T and into"G" values of (C(NaOH)*T)^2. A lot of work, isn't it? Now into "H" finally write the corresponding values of the conductivities from your tables.Goto Excel.Tools.DataAnalysis.Regression,
correctly select the range of independent varaiables ["A1" :"G..."]and the range of dependant variable ["H1":"H..."] and GO. On a new sheet you will find the result.The first coefficient is the constant; next belong to the terms as you wrote them in columns "A"..."G".
Start with the simplest case to get practice and you will later enjoy with the full termed model!
m777182

 

[25362]

From data taken from Lange's Handbook of Chemistry, the conductivities on large dilutions, expressed as
Ohm^-1.cm²/equivalent:


temperatures, ^oC 0 18 25
NaOH 143.65 219.3 249.31
HNO₃ 264.3 377.5 421.52

The same book -table 8.36- gives the conductivities for various concentrations from 0.001 N to 5.0 N at 18^oC for various electrolytes (including the above) in aqueous solutions.