Оборудование:
One mole of substance is the amount of substance that contains $N_A = 6.02\cdot 10^{23} \cdot 1/\mathrm{mol}^{-1}$ moleclues.
At the beginning of the last century, Peter Debye and Erich Hückel developed the first theory describing the behavior of charged particles surrounded by a large number of other charged particles. Although this approach quantitatively explained many phenomena in plasma and electrolytes, many fundamental questions related to the behavior of ions in solutions remain unresolved.
For the theoretical description of microsopic phenomena in an electrolyte, it's convenient to use the specific conductance $\kappa$ instead of the specific resistance $\rho$. The resistance $R$ of a long wire of length $L$ and cross-sectional area $S$ is expressed in terms of specific conductivity as:
\[ R = \frac{L}{\kappa S}.\]
If the current $I$ uniformly flows through the cross-sectional area $S$ the current density $j=I/S$ is introduced.
Note that there is always a parasitic voltage at the solution-electrode interfaces due to various chemical phenomena, which may change slowly over time. Your further measurements must take into account the presence of this voltage. It is best not to measure the parasitic voltage directly. nor to include it in formulae for calculations.
Only graphite rods should come into contact with the electrolyte, as their surface is much more inert than metal surfaces.
Measure the dependence of the solution's specific conductance $\kappa$ of the solution on the molar concentration $c$ of the salt. Obtain at least 10 data points.
Note: In the setup for measuring $\kappa$, you must clearly understand how the currents are distributed in the region of space where the most of the applied voltage drops.
In the solution, the salt $\rm NaCl$ dissociates completely into charged ions $\rm Na^+$ and $\rm Cl^-$. That is, in a salt solution of molar concentration $c$, the salt exists as sodium ions $\rm Na^+$ with concentration $c$ and chloride ions $\rm Cl^-$ also with concentration $c$. The charge of the ions is $\pm e$, where $e=1.60\cdot10^{-19}~\mathrm{C}$. Further in the problem, we will refer to the sodium ion simply as a positively charged ion and assign it the index «$+$», and the chloride ion as a negatively charged ion and assign it the inde «$-$».
Both types of ions, begin to move under the influence of an external electric field $\vec{E}$, creating an electric current. Any object moving in a fluid experiences a viscous frictional force $\vec{F} = - \mu \vec{v}$, where the quantity $\mu$ is called the mobility. The viscosity of water is $\eta = 8.9\cdot10^{-4}~\mathrm{Pa}\cdot\mathrm{s}$.
Neglect the influence of the ions on each other.
Express your answers in terms of the ion mobilities $\mu_+$ and $\mu_-$ and their molar concentration $c_+=c_-=c$.
These deviations can be qualitatively explained: in constructing the theory, we did not account for the interaction between ions. As the concentration increases, the average distance between ions decreases, so ions moving in opposite directions begin to pass close to each other at small distances. The interaction between ions is Coulombic in nature, and an analogy with gravity applies: the smaller the impact parameter, the stronger the deflection.
To describe only the mobility of ions (and neglect their interactions), the concept of limiting molar conductivity $\Lambda_0=\Lambda(c=0)$ is useful.
