# Temperature Dependence of The Conductivity of Electrolytic Solutions

I have learned in my chemistry text books that the conductivity of electrolytic solutions increase with the increasing of temperature because the ions of electrolytic solution move faster by getting more thermal energy. But a question arose in my mind if there exist any mathematical equation which can describe the conductivity of electrolytic solutions as a function of temperature. I searched about it on internet but I got nothing satisfactory. Does any equation exist which can model the electrolytic conductivity as a function of temperature?

• I suppose there would be just some empirical equations, applicable just for particular cases. Mar 17 at 15:50

One useful approximate relationship that can be used to predict the temperature dependence of the conductivity can be obtained by relating the electrical mobility to the viscosity.

For a $$z_+:z_-$$ electrolyte the limiting molar conductivity can be expressed as

$$\Lambda^\circ _m = F^2\left(\frac{z_+^2\nu_+}{f_+} + \frac{z_-^2\nu_-}{f_-} \right)$$

where the $$f_i$$ are frictional coefficients for each ion, z is the ionic charge, $$\nu$$ is the stoichiometric coefficient, and F is the Faraday constant (for instance, for $$\ce{Al2O3}$$, $$z_+=3$$,$$\nu_+=2$$,$$z_-=2$$,and $$\nu_-=3$$.

The frictional coefficients can be related to the viscosity, for instance using Stokes' relation $$f=6\pi \eta r$$ for a sphere being driven through a uniform viscous medium with a low Reynold's number. From the temperature dependence of the viscosity, and assuming the ion radii are independent of T, you can derive a relation for the T dependence of the limiting conductivity:

$$\Lambda^\circ _m = \frac{F^2}{6\pi\eta (T)}\left(\frac{z_+^2\nu_+}{r_+} + \frac{z_-^2\nu_-}{r_-} \right)$$

The equations so far apply to dilute solutions where the viscosity is independent of the concentration of electrolyte and ion-ion interactions can be neglected.

Note that even simpler theories predict a somewhat complex dependence of the molar conductivity on temperature. One can however attempt to fit an expression inspired by those above, of the sort

$$\Lambda _m = A \times \eta (T)^{-1}$$

where A is assumed independent of T. This might work over a narrow T range and could be used to assess the importance of ion-ion interactions.

• Thanks for your answer. But I haven't understood what 'z' means in your answer. Does it mean valency? Please make it clear with some examples. And do you mean Faraday's constant with 'F'? And is this formula only applicable for limiting molar conductivity but not for any molar conductivity? Please make me clear about these. Mar 18 at 4:08
• @Md.HasibulHossain Please see the modifications to the answer. Mar 18 at 8:01
• What does 'z' represent in that equation? Please explain that term with some examples. Suppose, what is the value of 'z' for Al₂O₃? Mar 18 at 15:27
• Thanks for editing your answer and making it clear. Mar 19 at 2:47

Conductor are generally two types .Electronic conductor and electrolytic conductor. In case of electronic conductor conduction occur by moving of free electron but in case of electrolytic conductor the conduction occur by moving of ions. so with increasing the temperature, in case of electrolytes the solvent jacket surrounding the ions are destroyed as a result mobility if ions increase and conductivity increase. From Debye Huckle limiting law K=√((F . I)/(∈ R T)) K^(-1)= distance of and central ion and solvent jacket. as temperature increase than distance increase so ionic interaction decrease , mobility increase , conductivity increase.