# Water electrolysis, work done, and volume change

1. Jul 8, 2015

### HelloCthulhu

I'm trying to learn more about water electrolysis and the work done on and by the system, but I'm still very confused about a few elements. Knowing the volume of the closed container, the number of moles of water, the amps/volts from the battery, and the initial temperature of the water, I know I can calculate the final temperature of the system using the specific heat capacity formula:

Q=c x m x ΔT

I can also use Faraday's law of electrolysis to solve for gas produced. Assuming the external pressure is standard in a closed system, how can I calculate the change in volume as the gas expands?

2. Jul 8, 2015

### Staff: Mentor

So what is kept constant - pressure, or volume?

3. Jul 8, 2015

### HelloCthulhu

The external pressure is constant. Using the ideal gas law, does this mean I can just divide nRT by standard P now?

Actually, I'm very confused. If the temperature increases inside of the container, won't the pressure inside of the container increase too?

Last edited: Jul 8, 2015
4. Jul 8, 2015

### Staff: Mentor

So the volume of the container changes,. No problem, you just need to be precise.

If the pressure is equilibrated with the outside pressure, then no.

5. Jul 9, 2015

### HelloCthulhu

Let's say 2 moles of water at 20°C undergoes electrolysis at 5A/40V inside of a closed 40mL container for 1 min at standard external/internal pressure. I'll calculate the total temperature of the system first.

Gas Produced
(5A*60s*4g)/(F*4)=0.00311g H2
(5A*60s*32g)/(F*4)=0.024875g O2
0.00311g + 0.024875g = 0.02798g

Temperature of the system
Q=cmΔT
5A*40V*60s=12kJ
Liquid 36g x 4.18J/(g⋅K)=150.48J/(g⋅K)
Gas 0.02798g x 2.080J/(g⋅K)=0.0582J/(g⋅K)
150.48J/(g⋅K) + 0.0582J/(g⋅K)=150.538J/(g⋅K)
12kJ=150.538J/(g⋅K)/(g⋅K)*ΔT
12kJ/150.538J/(g⋅K)=(T2-20°C)
79.7 + 20°C=99.7°C

Does the rise in temperature cause the total volume of the system to increase? If so, how do I calculate the change in volume? I think I'm supposed to use the volume of the container as initial volume and use Charle's law to calculate the change but I'm not sure in this case.

Vi/Ti = Vf/Tf

0.040L/293K=Vf/372.85
Vf=0.05L