# Simulation of a battery with lifting up and role of salt bridge

Usually for explanation of the mechanism of a battery, it is modelled by lifting a mass from lower to higher position. The attached figure shows a mass that goes down due to the gravitational potential and then is lifted up by an external energy (left part). In the right part a galvanic cell is shown in which negative charges goes from anode to cathode due to difference in chemical potential. I would like to know, in comparison to the left part, which force take the negative charges back from cathode half-cell to anode half-cell? Is it the salt bridge? If so, we may say that in fact the salt bridge has the role of a battery! isn't it?

The salt bridge acts like a wire, although it transports ions rather than electrons.

Without the salt bridge, you don't have a circuit and the two solutions may be at different potentials.

The energy source is not the salt bridge, but the chemical reactions happening on the two electrodes.

In the gravitational model, the reactions at the electrodes are trying to lift up and push down a mass. What the salt bridge does is connect one of the levels of each cell together.

• I am still thinking about your last comment "at the electrodes are trying to lift up and push down". How do the reactions lift up the electrons? As far as I know the electrons travels due to the difference in chemical potential! Commented Jun 23 at 15:39
• This is an analogy (en.wikipedia.org/wiki/Hydraulic_analogy). The original question showed a mass moving up or down gaining or losing gravitational potential as referencing this analogy. The chemical reactions at the electrodes in fact move charges up or down an electrical potential. Commented Jun 24 at 2:30
• The tendency to reaction (or equivalently difference in chemical potential) causes the electrons to travel from anode to cathode and some heat (reaction energy) releases in the process. It seems that the difference between the chemical potentials of reactants is already present, and reactions don't lift the charges up the barrier and electrons just slide down it. I think it is the consumption of reactants rather than the reaction energy which keeps the process ongoing. The process stops when the materials are entirely consumed. This consumption occurs by salt bridge. I appreciate any help. Commented Jun 24 at 15:33
• I think also the better gravitational analogy is to consider a large number of masses (already taken at the higher position) which are consequently coming down the hill. Commented Jun 24 at 15:47

There is no direct gravitational analogue of the salt bridge, because it exists to counteract a repulsive force. Gravity is never repulsive.

By introducing the additional force of pressure, we can create a mechanical analogy. Imagine a tank 99% full of water on the table, with a narrow tube running to an air-filled tank on the floor. Both tanks are sealed to be air-tight. Some water will initially flow, but as it does, the air in the bottom tank becomes pressurized, while the air in the top tank becomes depressurized. At some point, probably long before the top tank is empty, the pressure difference will stop the water flow. (In this scenario we'll assume that bubbles are unable to force their way into the narrow tube and flow upwards, perhaps because the outlet is positioned below the water level in the bottom tank.) This is analogous to a battery without a salt bridge. A few electrons can flow "down" from the copper (top of the table), through the wire (the tube), to the silver ions (floor). However, as they do, a repulsive force builds up due to the charge difference, and further electrons cannot flow.

However, if we add an additional tube that connects the two air compartments in the tanks, the pressure buildup is neutralized and the top tank will empty all the way. Because air is so much less dense than water, it takes a lot less energy to lift the air upwards than it does to move the water downwards, so overall, the process is spontaneous. This second tube, which unleashes the ability to drain the entire tank by neutralizing the repulsive force, is the equivalent of the salt bridge. In the battery, the salt bridge neutralizes the electric repulsion by transferring $$\mathrm{NO_3^-}, \mathrm{Na^+},$$ and $$\mathrm{Cu}^{2+}$$ ions to the charged solutions, cancelling out the charge build up.

• If the salt bridge acts as connection between the identical levels in the two half-cells, as mentioned by BowlOfRed, we may consider it's role like kind of pushing the mass, kept at the higher level, to the edge for preparation to fall. Commented Jun 21 at 10:44

I think the analogy between the Galvanic cell and the falling mass as said in my previous post is not a proper one-by-one correspondence. The reaction in the galvanic cell is $$Cu+Ag^{2+} \rightarrow Ag+Cu^{2+}$$ and the better analogy is shown in the following figure in which the reactants"$$Cu+Ag^{2+}$$", already kept at higher chemical potential, convert consequently to the productions "$$Ag+Cu^{2+}$$" with releasing two electrons. In contrast to the previous model, here, the charges are not lifted after losing their energies. The process continues as far as the reactants are consumed. In analogy with falling masses, we may consider the masses already kept at higher position are falling consequently as far as all the masses are used.