[Sammy5124]

I have read a basic explanation of electrolysis but there are small details that i'm not understanding.

Let's say you have a cathode(negative), an anode(positive) both connected to a battery through a wire, and both dipped in solid lead bromide.

My chemistry book says the following will happen.
"As soon as you connect the power source, it pumps any mobile electrons away from the anode, to the cathode. At the moment, the lead(II) bromide is still solid."

Now wait a second, I thought a battery will only supply voltage in a complete circuit, and we don't have a complete circuit if the lead bromide is solid. If we simply attach an anode to the positive end of a battery, and a cathode to the negative end, will the battery really supply voltage to make the anode positive and the cathode negative when the circuit is incomplete? Will sticking a piece of metal to the negative end of a battery really make it negatively charged?

[Borek]

Whether the circuit counts as closed or not is somewhat relative. What is the specific resistance of the lead bromide? (probably very low, but it won't hurt to check).

Note that even if the resistance is very high, there is still a current flowing. It can be very low but for example for 1 GΩ and 1 V you get 1 nA - and back in eighties we routinely registered electrochemical curves with currents lower than that.

[Sammy5124]

Even if electricity could flow through the solid lead bromide, why would that make the cathode have more electrons in it than the anode in this scenario? Wouldn't the electron counts in each rod even out at electricity travels through the cathode, the lead bromide and then the anode?

I'm not sure why the cathode has more electrons in it than the anode

[Borek]

What is the potential difference? Is potential difference between object possible without these objects being charged?

[Sammy5124]

I've always though of potential difference as the difference in voltage between two points

Are you saying that since the voltage is higher in the cathode than in the anode (assuming current it can pass through the solid bromide, otherwise I think the voltage would be 0 due to the circuit being incomplete), that there are more electrons in the cathode than in the anode?

The way the book worded it though suggests that as soon as you connect two pieces of metal to a battery in an incomplete circuit, it will immediately begin pumping electrons out of the anode and into the cathode, positively and negatively charging them respectively.

[Borek]

I've always though of potential difference as the difference in voltage between two points

Then you are missing physics behind.

Existence of potential difference always means there exists an electric field between two points. There is no electric field without separated charges. For the potential difference to exist between two conductors one of them has to be charged relative to the other.