Understanding Bonding Energy in Water for Electrolysis Calculations

[tommyhp2]

Homework Statement

Find the required energy and volt needed for electrolysis of water

Relevant Equations

Coulomb's law: F = k * q_1 * q_2 / r*r
V = W / q

Hello everyone,

I'm just doing a bit of review of math to be used in electrolysis calculations. From the reference:

https://www.ccmr.cornell.edu/wp-con...o_Skyler_splitting-water-with-electricity.pdf

the result for r12 on page 4, the author has 1.5 * 10e-11 m. Google sheets and MS Excel has 1.89e-10 = sin(52) * 2 * 9.6e-11.

Also, for U12 using my result of r12 instead of the author's, I got 1.28e-19 instead of the author's 1.6e-19. If I used the author's result for r12, I got 1.62e-18.

And the covalent bond energy of H-O = 464 kJ / mol to break the bond from:

https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/

The total U from 'splitting water with electricity' is too low 8.54e-19 J (author's) or 8.86e-19 J (based upon my results of r12) from the covalent bond energy above (464 + 464) * 1000 / 6.022e-23 = 1.54e-18 J.

Would someone please check if my findings are correct? Does anyone know where I can get a more accurate than the above for covalent bond energy reference?

Thanks,
Tommy

[Edit] PS: If I use the complete calculation for covalent bond energies for the electrolysis reaction:

2 H-O-H => 2 H-H + O-O

( 2(464 * 2) - (2 * 436) - 140 ) * 1000 / 6.022e23 = 1.4e-18 J

But to get the net energy required for 1 molecule of water, 1.4-18 J / 2 = 7e-19 J.

Which still doesn't equate to electrostatic force result.

 

[DrClaude]

the result for r12 on page 4, the author has 1.5 * 10e-11 m. Google sheets and MS Excel has 1.89e-10 = sin(52) * 2 * 9.6e-11.

The angle is given in degrees. The sin function in the spreadsheet expects radians. That said, the result given is off by a factor of 10. (You can easily see this by considering that, with the numbers as written, the two hydrogen would be about 6 times closer to each other than to the oxygen atom, which wouldn't result in an angle of 104°.)

Also, for U12 using my result of r12 instead of the author's, I got 1.28e-19 instead of the author's 1.6e-19. If I used the author's result for r12, I got 1.62e-18.

The value of U₁₂ in the document is correct.

And the covalent bond energy of H-O = 464 kJ / mol to break the bond from:

https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/

The total U from 'splitting water with electricity' is too low 8.54e-19 J (author's) or 8.86e-19 J (based upon my results of r12) from the covalent bond energy above (464 + 464) * 1000 / 6.022e-23 = 1.54e-18 J.

The model used is completely inadequate. The bond between oxygen and hydrogen is more covalent than ionic, and there is no way that calculating the Coulomb interaction between the partial charges on the atoms will give the right binding energy for water.

Does anyone know where I can get a more accurate than the above for covalent bond energy reference?

https://courses.lumenlearning.com/introchem/chapter/bond-energy/

For instance, the HO-H bond in a water molecule requires 493 kJ/mol to break and generate the hydroxide ion (OH–). Breaking the O-H bond in the hydroxide ion requires an additional 424 kJ/mol. Therefore, the bond energy of the covalent O-H bonds in water is reported to be the average of the two values, or 458.9 kJ/mol. These energy values (493 and 424 kJ/mol) required to break successive O-H bonds in the water molecule are called ‘bond dissociation energies,’ and they are different from the bond energy. The bond energy is the average of the bond dissociation energies in a molecule.

If you have access to the CRC Handbook of Chemistry and Physics, it is always a good reference for these kind of numbers.

 

[tommyhp2]

The angle is given in degrees. The sin function in the spreadsheet expects radians. That said, the result given is off by a factor of 10. (You can easily see this by considering that, with the numbers as written, the two hydrogen would be about 6 times closer to each other than to the oxygen atom, which wouldn't result in an angle of 104°.)The value of U₁₂ in the document is correct.

Thank you for the correction. I saw the 'angle' in the popup tip but didn't read down far enough for the fine print of expecting radians. Correcting that does have the right U₁₂.

The model used is completely inadequate. The bond between oxygen and hydrogen is more covalent than ionic, and there is no way that calculating the Coulomb interaction between the partial charges on the atoms will give the right binding energy for water.

https://courses.lumenlearning.com/introchem/chapter/bond-energy/

If you have access to the CRC Handbook of Chemistry and Physics, it is always a good reference for these kind of numbers.

I understand about the movements in 3-D space and dissociation energy. I've figured a better approximation is to use integral but I'm after peak energy required to break its strongest bond. I was hoping the model I've found would provide that since the O-H bond varies 0.957 A to 1 A and the H-O-H angles varies from 104.52 to 109.5 from my research.

Thanks for the tip on CRC Handbook. I'll see if I can get a copy. By any chance do you know where I can get reference to the formulas to calculate either covalent or ionic bonds? I don't want to reinvent the wheel by reviewing calculus to derive the formula(s) based upon the graph.

 

[tommyhp2]

hmm... After some more research, it seems I need to pick up quantum mechanics due to chosen CS major in college.

 

[DrClaude]

´By any chance do you know where I can get reference to the formulas to calculate either covalent or ionic bonds? I don't want to reinvent the wheel by reviewing calculus to derive the formula(s) based upon the graph.

This is a quantum chemistry problem. You need some specialized quantum mechanics, and even then the problem can only be solved numerically.