The proton possesses abnormal mobility in water, but does it behave normally in liquid ammonia? To investigate this question, a moving-boundary technique was used to determine the transport number of \(\mathrm{NH}_{i}\) in liquid ammonia (the analogue of \(\mathrm{H}_{3} \mathrm{O}^{+}\) in liquid water) at \(-40^{\circ} \mathrm{C}(\mathrm{J}\), Buldwin, \(\mathrm{J}\). Evans, and J.B. Gill, \(J\). Chem. Soc. A, 3389 (1971)). A steady current of \(5.000\) mA was passed for \(2500 \mathrm{~s}\), during which time the boundary formed between mercury(II) iodide and ammonium iodide solutions in ammonia moved \(286.9\) \(\mathrm{mm}\) in a \(0.01365 \mathrm{~mol} \mathrm{~kg}^{-1}\) solution and \(92.03 \mathrm{~mm}\) in a \(0.04255 \mathrm{~mol} \mathrm{~kg}^{-1}\) solution. Calculate the transport number of \(\mathrm{NH}_{\text {; }}\) at these concentrations, and comment on the mobility of the proton in liquid ammonia. The bore of the tube is \(4.146 \mathrm{~mm}\) and the density of liquid ammonia is \(0.682 \mathrm{~g} \mathrm{~cm}^{-3}\).

Understanding the peculiar behavior of protons in various solvents is fundamental in the study of electrolyte solutions. In water, protons exhibit abnormal mobility due to the phenomenon of 'proton hopping' or the Grotthuss mechanism. This involves a relay system where a proton is transferred from one water molecule to another, leading to an effective 'movement' of the proton through the liquid. However, when considering a different solvent like liquid ammonia, the scenario changes. Liquid ammonia, similar to water, can form hydrogen bonds but with a different structural arrangement and strength, which could potentially affect how protons move within it.

Investigating the behavior of a proton in ammoniated solutions is crucial for a greater understanding of reaction mechanisms and the physical properties of materials that contain ammonia. Proton mobility affects the conductivity and the transport number, a vital parameter which, as seen in the original exercise, can be measured using experimental techniques like the moving-boundary method. Conductivity and transport numbers provide insights into the solvation and migration abilities of ions in electrolyte solutions. If the transport number and consequent mobility of protons in liquid ammonia is significantly lower than in water, this could imply differences in reactivity and conductivity of ammoniated systems compared to aqueous ones. Thus, it becomes apparent why the research by J. Buldwin et al. was aimed at answering questions regarding this atypical property of protons in non-aqueous solutions.

The moving-boundary technique is a fascinating experimental method used to study the transport of ions in solution. This method involves introducing two different solutions into a tube, with an interface between them, and then applying an electric field across the solutions. The ions start moving according to their charge—cations towards the cathode and anions towards the anode. This motion creates a visible boundary that travels along the tube. By measuring the movement of the boundary, one can infer the transport number of the ions.

For instance, in the provided exercise, the boundary's movement was used to calculate the transport number of \(\mathrm{NH}_4^+\) in liquid ammonia. The volume of solution displaced can be calculated with the boundary's movement and the cross-sectional area of the tube, then using the known concentration and density of the solution, the amount of \(\mathrm{NH}_4^+\) ions

In electrolyte solutions, the conductivity depends on the presence of ions and their ability to move freely through the solvent to carry an electric charge. This movement is related to several factors, including the size and charge of the ions, the viscosity of the solvent, and the temperature of the solution. Conductivity is crucial in the design of batteries, the operation of electrolysis processes, and understanding the behavior of ions in biological systems.

Conductivity is, in a way, a macroscopic indicator of microscopic mobility. The higher the conductivity, the greater the mobility of ions in the solution. This is intrinsically linked to the transport number, which quantifies the fraction of the total electric current carried by a particular ion. A transport number near unity means an ion is highly mobile and predominantly carries the current over other present ions. By linking the transport number obtained from moving-boundary experiments to the ionic conductivity of the solution, scientists can deduce important properties concerning individual ions and overall solution behavior.