- #1
davidbenari
- 466
- 18
In class we have been deducing the typical equations for chemical equilibrium. What bothers me was the term ##\Delta Gº## as opposed to ##\Delta G##.
##\Delta G## is fine with me because it takes into account the fact that during a reaction the multiple components find themselves in a mixture, and therefore their chemical potentials are different than ##\mu º##. What bothers me about ##\Delta Gº## is that it doesn't seem that a "standard state reaction" is taking into consideration the mixing aspect.
##\Delta Gº=\sum \nu_p \mu_pº - \sum \nu_r \mu_rº##. With this difference I associate the following picture:
We have all components in different containers at first, mix them, get some products, and separate the products in different containers. ##\Delta Gº## is the difference between having products separated, and having reactants separated.
But it seems that this isn't what is implied by ##\Delta Gº##. What is it really? Why is it useful?
I have one final question. In a mixture each component has its chemical potential ##\mu##. Why is it valid to say that if I wanted to construct a system with ##n_i## moles of each component, I could just say that the Gibbs energy of the system is ##G= \sum_i n_i \mu_i##. I know that the temptation might come because ##\mu_i## has units ##J/mol##. that doesn't mean I can just multiply out moles. I have to integrate. Whats going on here?
You might say that were keeping relative concentration fixed, and integrating yields this result. But consider that at first we have an empty container and thus absolutely no relative concentrations.
You might say we establish this relative concentration after ##dn_i## of each component has been added. Sure okay, but why would the ##\mu## have the same value we are thinking about at first if such a small quantity has been added to the container and therefore we have a completely weird environment where each component is surrounded by an infinite volume. ##\mu## would surely change in such an environment?
Thanks and sorry for the lengthy question.
##\Delta G## is fine with me because it takes into account the fact that during a reaction the multiple components find themselves in a mixture, and therefore their chemical potentials are different than ##\mu º##. What bothers me about ##\Delta Gº## is that it doesn't seem that a "standard state reaction" is taking into consideration the mixing aspect.
##\Delta Gº=\sum \nu_p \mu_pº - \sum \nu_r \mu_rº##. With this difference I associate the following picture:
We have all components in different containers at first, mix them, get some products, and separate the products in different containers. ##\Delta Gº## is the difference between having products separated, and having reactants separated.
But it seems that this isn't what is implied by ##\Delta Gº##. What is it really? Why is it useful?
I have one final question. In a mixture each component has its chemical potential ##\mu##. Why is it valid to say that if I wanted to construct a system with ##n_i## moles of each component, I could just say that the Gibbs energy of the system is ##G= \sum_i n_i \mu_i##. I know that the temptation might come because ##\mu_i## has units ##J/mol##. that doesn't mean I can just multiply out moles. I have to integrate. Whats going on here?
You might say that were keeping relative concentration fixed, and integrating yields this result. But consider that at first we have an empty container and thus absolutely no relative concentrations.
You might say we establish this relative concentration after ##dn_i## of each component has been added. Sure okay, but why would the ##\mu## have the same value we are thinking about at first if such a small quantity has been added to the container and therefore we have a completely weird environment where each component is surrounded by an infinite volume. ##\mu## would surely change in such an environment?
Thanks and sorry for the lengthy question.