Energy needed for the electrolysis of water

[buffordboy23]

I am exploring a problem of my own and am confused by the contradictory info that I am finding.

Problem Statement:

What is the minimum energy required to obtain 32 g of diatomic oxygen (one mole) and 4 g of hydrogen (two mole) via the electrolysis of water in the presence of some electrolyte from an external voltage source of 12 V?

I often see sources quote that the minimum energy is the standard enthalpy of the reaction

2H20 (l) --> 2H2 (g) + 02 (g), $$\Delta$$H = 483.6 kJ
Other sources cite that the minimum energy required for an electrolysis reaction is given by

Energy = Work = nFE_ext,

where n is the number of electron moles forced into the system by the external potential, F is the number of Faradays, and E_ext is the external applied voltage.

The oxygen is produced at the anode and is given by the equation

2H20 (l) --> O2 (g) + 4H$$^{+}$$ (aq) + 4e$$^{-}$$, E_red = +1.23 V

The hydrogen is produced at the cathode and is given by the equation

2H20 + 2e$$^{-}$$ --> H2 (g) + 2OH$$^{-}$$, E_red = -0.83 VThoughts and Questions

For oxygen production electrons are being forced out of the system, and for hydrogen production electrons are being forced into the system. How do I obtain the values for the variable 'n'? If I assume for oxygen that n = -4 and for hydrogen n = 2, it seems evident that I will obtain a negative value for work (or applied energy), which does not make sense. Perhaps, I am simplifying the scenario too much because of the other oxidation-reduction reactions that take place (e.g. OH$$^{-}$$).

What role does the standard enthalpy value play in this electrolysis reaction? Does the voltage have to supply this energy value too, or can be it be independent of the voltage source and come from the environmental surroundings (which would tend to cool the surroundings).

Any advice would be greatly appreciated.

 

[Borek]

First of all, number of electrons taking part in the reaction is never negative. Regardless of wheteher they are consumed or produced, their number is always positive.

Then, to calculate amount of work done you have to relate it to the amount of product, not to the half reaction. 32g of oxygen and 4g of hydrogen both require the same charge.

 

[Blueshift5]

Thank you for sharing your problem and thoughts on the energy needed for the electrolysis of water. This is a complex topic, and it is not uncommon to come across contradictory information. Let me try to address your questions and provide some guidance.

Firstly, it is important to understand that the minimum energy required for an electrolysis reaction is not a fixed value. It depends on various factors such as the nature of the electrolyte, the concentration of the electrolyte, the temperature, and the external voltage source. Therefore, it is not surprising to find different values quoted in different sources.

To address your question about obtaining the values for 'n' in the equation Energy = nFE_ext, it is essential to understand the concept of Faraday's constant (F). Faraday's constant is the amount of electrical charge required to reduce one mole of a substance during an electrolysis reaction. Therefore, the value of 'n' would depend on the number of moles of electrons involved in the reduction or oxidation reaction. In the case of oxygen production, it would be -4 because four moles of electrons are involved in the reduction reaction. Similarly, for hydrogen production, it would be 2. So, your assumption is correct.

However, it is important to note that in an electrolysis reaction, other reactions may also take place, such as the formation of hydroxide ions (OH^-) at the cathode. These reactions can also involve the transfer of electrons and contribute to the overall energy requirement. Therefore, it is not advisable to simplify the scenario too much, as you have mentioned. Instead, it would be best to consider all the possible reactions and their respective electron transfers to calculate the total energy requirement accurately.

Coming to your question about the role of standard enthalpy in an electrolysis reaction, it is important to note that the standard enthalpy value (ΔH) represents the energy change associated with the formation of products from reactants under standard conditions. It is a thermodynamic property and does not directly relate to the energy needed for an electrolysis reaction. However, it can provide a reference point for comparing the energy requirements of different reactions.

Finally, to address your question about the source of energy in an electrolysis reaction, it is essential to understand that the applied voltage is the source of energy for the reaction. The voltage provides the necessary electrical potential for the transfer of electrons and drives the reaction. However, it is also important to consider the