Chemistry - Why don't the electrons move through the electrolyte (instead of the circuit) in a galvanic cell?
Solution 1:
Not in water. Free electron in water is really unfavorable, so no significant concentration of them can be generated chemically, and it almost immediately reduces water itself to hydrogen (but I heard rumors about generation of solvated electrons in water in very special experiment with short half-life)
In liquid $\ce{NH_3}$, however, solvated electrons can occur, so self-discharge of galvanic cells with $\ce{NH_3}$-based electrolyte may occur through travel of electrons via electrolyte.
Solution 2:
You're questioning the intuitive disconnect caused by most galvanic cell drawings which seem to assume the electrolyte solution in the salt bridge does not conduct electricity, so let's investigate.
Imagine a Zn/Cu$^{2+}$ cell with electrodes 5 cm apart in a 3.5% NaCl solution with a tube (1 cm$^2$ cross-section) of solution as the salt bridge for balancing charge.
The electrical resistance (R = $\rho$l/A) of our NaCl 0.05 m x 1 cm$^2$ salt bridge solution is:
$$\frac{0.2 \ ohms*m}{} * \frac{0.05 \ * m \ (length)}{10^{-4}m^2 \ (cross-section \ area)}= 100 \ ohms$$
Considering the predicted EMF of 1.1 Volts for this cell, the expected current ($I = V/R$) through the salt bridge is: $1.1V/100 \ ohms \ = 0.011 \ amps$
This current may be negligible in a galvanic cell drawing compared to the current through some wire or low-resistance load. However, this would make a terrible battery for most common purposes as a typical AA battery (3000 mAh) would go completely dead in less than 2 weeks if it actually leaked at this rate!
It seems then your intuition is basically right... until you understand what the models leave out. In real alkaline battery designs, the cathode, electrolyte, and anode are sandwiched together very closely with a very large surface area, yielding excellent conductivity through electrolyte (and therefore very low resistance). However, these layers are separated by a membrane which allows ions through but has a very high resistance to electric current.
Sources: https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499 (seawater resistance) https://en.wikipedia.org/wiki/Alkaline_battery (alkaline battery design)
Solution 3:
Electrons cannot survive in aqueous state. Being a charged subatomic particle, the electron has to stay close to protons which are located at the center of the atom. Hence, the electron can move from one atom to another which are closely-packed, what we have in a solid.
Solution 4:
Electron's can travel through the electrolyte solution, however electrons take the pathway with the lowest resistance, the solution has a relatively higher resistance compared to the outer circuit. Hence the electron takes the path of the outer circuit.