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Excuse my inexperience with chemistry here. I've been poring over papers with terms like "Standard Gibbs free energy of formation", "Hess's Law", "standard enthalpy of formation", "entropy", and several others, and I haven't been able to find an answer to one simple question:

Given I have a system with compounds A, B, and C, and there is an alternative set of compounds X, Y, and Z involving the same amounts of the same elements, how do I calculate how much the ABC system wants* to become XYZ?

As an example, if I have a system with propane and oxygen, with an excess of oxygen, this system wants to combust to become carbon dioxide and water vapor. A quick Wikipedia check reveals the balanced equation for this reaction:

$$\ce{C3H8 + 5O2 \rightleftharpoons 3CO2 + 4H2O}$$

Anyone who's played around with a camp stove knows that propane and oxygen like to burn to become carbon dioxide and water vapor, and that carbon dioxide and water vapor really don't like to "unburn" to become propane and oxygen. How would I measure this tendency for the propane-oxygen system to become the carbon-dioxide-water-vapor system? Similarly, how would I measure the distate for the carbon-dioxide-water-vapor system to become the propane-oxygen system?

If I remember correctly, the tendency of a reaction to happen and the speed of the reaction are entirely unrelated, one being a thermodynamic property and the other a kinetic property, but if you wouldn't mind throwing in just enough info about reaction rate in the above case that I can look up and learn myself on that topic as well, I'd really appreciate it.

*I'm falling victim to the oh-so-elegant abstraction of molecular anthropomorphism here. Yes, I understand that chemicals don't want anything, but given I'm looking for a unit most easily expressed as the degree of desire for chemicals A, B, and C to become X, Y, and Z, these human terms play out quite well. Please do let me know if there's better terminology I could be using

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Depending on the constraints you impose on the system, there are different criteria for spontaneity, however, the commonly running theme is that it is related to minimizing some state function. For example, as a simple example from classical mechanics, the time evolution of the system is such that the potential energy of the mechanical bodies is minimized.

When we do a chemical reaction, we usually do it at constant temperature and pressure. In this case, the evolution of the system is determined by a potential function known as Gibb's free energy. If there is a state in which the system which reduces Gibb's free energy, then the system will evolve to reach that state. When I say evolve I mean to have processes such as chemical reactions.

I had actually written a very detailed answer about this on physics stackexchange, check it out for more information (here)


Refer these notes by MIT for the criteria for spontaneity for different constraints :

MIT ocw notes

Discussion about constant P and T chemical reactions:

Here

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Well, essentially, the Gibb's Free Energy Change of a reaction is the property that determines how much a reaction wants to progress in any particular direction.

It's a property denoted by ΔG.

Basically, the more negative the value of the Gibb's Free Energy change, the more the reaction "wants" to happen. Essentially, the reaction tends to achieve a state of minimum Gibb's Energy

You can calculate ΔG using the enthalpy change, entropy change and temperature by the relation:

ΔG = ΔH - TΔS

ΔH is the enthalpy change

T is the temperature

ΔS is the entropy change

Hope this helps!

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