A first-order indicator electrode works because the electrode potential is set directly by the redox equilibrium between the solid electrode material and its own ion in solution. In this case, the ion you’re trying to measure is the same element as the metal forming the electrode. The basic relation is E = E° + (RT/zF) ln a(M^z+), so the measured potential tracks the activity of that specific ion directly. A simple example is a zinc electrode measuring Zn2+ activity, where the Zn2+ in solution and the Zn metal on the electrode establish the potential through the Zn2+ + 2e− ⇌ Zn(s) couple. That is why this option is the best: the ion of interest is the same as the metal used in the electrode, giving a straightforward, Nernstian response. Other scenarios, where the ion is not the same as the electrode material or where the electrode isn’t a metal, involve different mechanisms and aren’t considered first-order indicator electrodes.

The key idea is that the equilibrium constant for a reaction and for its reverse are reciprocals. When you reverse a reaction, you swap products and reactants, so the expression inverts. For base reacting with water, the forward hydrolysis is B + H2O ⇌ BH+ + OH−, with Kb = [BH+][OH−]/[B]. If you look at the reverse, BH+ + OH− ⇌ B + H2O, the equilibrium constant is K_reverse = [B][H2O]/([BH+][OH−]). Water is the solvent, so its activity is effectively 1, giving K_reverse ≈ [B]/([BH+][OH−]) = 1/Kb. So the equilibrium constant for the reverse reaction is 1/Kb. (Remark: Ka of the conjugate acid BH+ relates via Ka(BH+) × Kb(B) = Kw, but that detail isn’t needed to answer this question.)

Metric prefixes indicate powers of ten that multiply the base unit. Deci- represents 1/10, i.e., 10^-1. In comparison, milli- is 1/1000 (10^-3), micro- is 1/1,000,000 (10^-6), and nano- is 1/1,000,000,000 (10^-9). So a deci- unit is one tenth of the base unit (for example, a decimeter is 0.1 meters). Therefore, the prefix with the value 10^-1 is deci-.

Reference electrodes provide a stable, known potential that stays essentially constant as current flows in the measurement. In potentiometric experiments, you determine the potential of the working electrode relative to this reference. Because the reference potential is fixed, any change observed at the working electrode directly reflects the analyte’s influence, allowing accurate determination of the unknown potential. The measured cell potential is the difference between the working and reference electrodes, so a steady reference potential makes it possible to relate the reading to the analyte. In practice, reference electrodes are designed to be non-polarizable, with common systems like Ag/AgCl or SCE. The other options aren’t about providing a stable reference potential: measuring pH is done with a pH-sensitive electrode, driving reactions requires applying current through working and counter electrodes, and viscosity isn’t determined from electrochemical potentials.