Question About Breaking Bonds in Crystal Lattices

[NullusSum]

TL;DR Summary

How do we calculate the bond dissociation energy of compounds in crystal lattices?

I am trying to understand how certain endothermic reactions work as a layman. I found the idea of reducing a rock to separate atoms fascinating, like what you would see in a comic book. However, I struggled to wrap my head around what that process would be like. I did some preliminary research, so I hope I was able to frame the question appropriately.

Question:​

How does the bond dissociation energy of compounds like silicon dioxide (SiO$_2$) and aluminum oxide (Al$_2$O$_3$) differ when they are embedded in a crystal lattice, such as in granite, compared to their isolated molecular forms? What additional interactions (e.g., lattice energy, covalent/ionic bonding) need to be considered when calculating the energy required to break these bonds in the lattice context?

 

[Borek]

Broadly speaking there is no such thing as a "bond dissociation energy of a compound". Bond energy typically refers to bond between two atoms (they can be part of something larger, each atom can be bonded to more than one other atom). We sometimes write more complicated compounds in the oxide form (like Na₂O⋅SiO₂ instead of Na₂SiO₃), but that's mostly notational trick (it does reflect some underlying chemical properties of atoms involved, but doesn't mean "compound is a mixture of oxides"). There are some compounds in which it is possible to "show" separate molecules (and we can calculate energy of forces keeping them together), but these are not very common (and often classifying them as "compounds" blurs the difference between a compound and a mixture).

That being said for every atom energy required to remove it from the lattice is a sum of interactions with all surrounding atoms, so it doesn't matter much if you want to remove Si from SiO₂ or Na₂SiO₃ - calculation will follow the same general principles.

What you ask about can be defined through the process "remove atoms, then create a compound out of them" (that's what the Hess's law is about) - but I don't remember seeing it used in this sense (even if it could be potentially useful in some contexts).

 

[NullusSum]

Broadly speaking there is no such thing as a "bond dissociation energy of a compound". Bond energy typically refers to bond between two atoms (they can be part of something larger, each atom can be bonded to more than one other atom). We sometimes write more complicated compounds in the oxide form (like Na₂O⋅SiO₂ instead of Na₂SiO₃), but that's mostly notational trick (it does reflect some underlying chemical properties of atoms involved, but doesn't mean "compound is a mixture of oxides"). There are some compounds in which it is possible to "show" separate molecules (and we can calculate energy of forces keeping them together), but these are not very common (and often classifying them as "compounds" blurs the difference between a compound and a mixture).

That being said for every atom energy required to remove it from the lattice is a sum of interactions with all surrounding atoms, so it doesn't matter much if you want to remove Si from SiO₂ or Na₂SiO₃ - calculation will follow the same general principles.

What you ask about can be defined through the process "remove atoms, then create a compound out of them" (that's what the Hess's law is about) - but I don't remember seeing it used in this sense (even if it could be potentially useful in some contexts).

Thank you for the detailed answer. My presumption was that because a compound has an enthalpy of formation, it must also have a specific enthalpy of dissociation. Based on your answer, this seems to be an erroneous way of thinking.

So, if we took a simple SiO$_2$ molecule, where the Si atom is covalenty bonded to two O atoms (O=Si=O), would the energy to remove the Si atom be approximately the dissociation energy of an O-Si bond (~799.6 kJ/mol) multiplied by 2? And if SiO$_2$ is a compound in a lattice, would we have to take it a step further and identity every other atom bonded to the Si and O atoms by analyzing the lattice itself?

 

[Borek]

Thank you for the detailed answer. My presumption was that because a compound has an enthalpy of formation, it must also have a specific enthalpy of dissociation. Based on your answer, this seems to be an erroneous way of thinking.

It is not erroneous as such, you can define this number and calculate its value in a strict way. Problem is you were freely jumping between bonding of atoms and "bonding" of molecules, as if they were the same thing. Thermochemically they can be definitely seen as analogous, but atoms are well defined in the context of a lattice, while "molecules" are not (see below).

So, if we took a simple SiO$_2$ molecule, where the Si atom is covalenty bonded to two O atoms (O=Si=O), would the energy to remove the Si atom be approximately the dissociation energy of an O-Si bond (~799.6 kJ/mol) multiplied by 2? And if SiO$_2$ is a compound in a lattice, would we have to take it a step further and identity every other atom bonded to the Si and O atoms by analyzing the lattice itself?

Multiplied by 4 (every Si atom has four bonds with oxygens), but more or less - yes.

Thing is in the lattice Si is actually in the center of a tetrahedron, surrounded by four oxygen atoms, so while it has four bonds to oxygens, there are no double bonds involved (even if O=Si=O seems to be suggesting it). No SiO₂ molecules there.

 

[snorkack]

Broadly speaking there is no such thing as a "bond dissociation energy of a compound". Bond energy typically refers to bond between two atoms (they can be part of something larger, each atom can be bonded to more than one other atom). We sometimes write more complicated compounds in the oxide form (like Na₂O⋅SiO₂ instead of Na₂SiO₃), but that's mostly notational trick (it does reflect some underlying chemical properties of atoms involved, but doesn't mean "compound is a mixture of oxides"). There are some compounds in which it is possible to "show" separate molecules (and we can calculate energy of forces keeping them together), but these are not very common (and often classifying them as "compounds" blurs the difference between a compound and a mixture).

Compounds with separate molecules are abundant. All gases, and most liquids and solids that are capable of evaporating at low temperature.

Thank you for the detailed answer. My presumption was that because a compound has an enthalpy of formation, it must also have a specific enthalpy of dissociation. Based on your answer, this seems to be an erroneous way of thinking.

There are different zero points of enthalpy.
Enthalpy of formation is forming solid SiO₂ lattice out of elemental Si - which is a solid lattice full of Si-Si bonds - and elemental O, which is gas of O₂ molecules containing O=O double bonds.
"Dissociating" the SiO₂ lattice sounds like you want to dissociate the lattice into Si atoms and O atoms.

So, if we took a simple SiO$_2$ molecule, where the Si atom is covalenty bonded to two O atoms (O=Si=O), would the energy to remove the Si atom be approximately the dissociation energy of an O-Si bond (~799.6 kJ/mol) multiplied by 2? And if SiO$_2$ is a compound in a lattice, would we have to take it a step further and identity every other atom bonded to the Si and O atoms by analyzing the lattice itself?

Take simple CO₂ molecule. In O=C=O, both oxygens and both C=O double bonds are initially equal.
You might dissociate it into C and two O atoms, splitting both bonds and divide the total equally. That would give you one value.
Or you could dissociate just one O and leave CO molecule behind. You would get a different value for C=O bond strength.
Which of these two are you regarding as the dissociation energy of C=O bond.
Lattice energy?
It is trivial to split CO₂ lattice into CO₂ molecules. Just let it evaporate at -78 C, and measure the latent heat of evaporation.
I think the latent heat of evaporation is not yet the pure potential energy of lattice bonds because you have to account for the total thermal motion energy of CO₂ lattice versus the total thermal motion energy of gaseous CO₂ (translations, rotations, vibrations).
But a CO₂ molecule in a lattice has a lot of van der Waals bonds. How do you define and measure the energy of each of them? Many of them are distinct. Solid CO₂ lattice is low symmetry because it is trigonal.
As an alternative to splitting the lattice into molecules by evaporating (and then optionally into atoms by dissociating the molecules), you might split the lattice into lattices by cracking it. Just measure the work stored into creating the crack surfaces (as opposed to any dissipated into heat or by making crystal defects inside the shards), and compare the energy that goes into cracking the crystal in different directions. You can then compare the energy with the count and type of bonds that were broken and left dangling across the crack surface.
Can you define the dissociation energy of all distinct bond types by analyzing crack energy in different directions?
Compared to CO₂, SiO₂ is messy. At its boiling point, you have an appreciable amount of SiO₂ molecules, but also appreciable amounts of SiO and O₂ molecules and O atoms in the mix.

 

[Borek]

Compounds with separate molecules are abundant. All gases, and most liquids and solids that are capable of evaporating at low temperature.

That's not what I referred to. Sure, if we put aside ionic solids and infinite lattices what we are left with are compounds that in bulk are a collection of molecules. But what about things like hydrates? These are basically compounds made of separate, individual molecules combined in a stoichiometric ratio. Methane hydrate for example doesn't decompose into atoms, it decomposes cleanly into methane and water, giving well defined "bonding energy" between constituting molecules.