# Meaning of small triangle in chemical potential

• etotheipi
In summary, the conversation discusses the meaning of a small triangle symbol in a chemical equation. It is speculated that the symbol may represent an outdated notation for the chemical potential of a solution. The conversation also delves into the difference between the chemical potential of a pure liquid and a solution, and how this relates to activity coefficients and mole fractions. It is concluded that in an ideal solution, with low solute concentration, the chemical potential can be simplified to a function of the mole fraction of the solvent.
etotheipi
It is given that the solution is ideal, i.e. that we can take ##\gamma_A = 1##.

I wondered what that small triangle signifies in the second definition? Thanks!

Good question. I've never seen that before. But it looks like in the first equation the reference state is a solution with [A] = 1M, while in the second, the reference state is xA = 1, i.e. pure A. But I've never seen the little triangle symbol.

etotheipi
Thanks, that's probably what's intended. It's likely just outdated notation . If I stumble across the small-print sometime in the future, then I'll post an update

etotheipi said:
It's likely just outdated notation

I am outdated and I have never seen it as well, so more like an obscure notation

berkeman and etotheipi
etotheipi said:
I wondered what that small triangle signifies in the second definition?
Where is that screenshot from?

etotheipi
It's from the Oxford Chemistry Primers series, there are some really nice undergrad-level overviews of different subjects in Chemistry; if you like you can have a look at some of the titles here .

berkeman
I got my PhD in chemistry in 2018 so I believe my knowledge on recent textbooks is rather updated, but me too have never seen that kind of symbol.

That being said, considering that xA is a notation used for Mole fraction, I believe μA equals to μA* (chemical potential of a pure A solvent), and the only difference is that the former notation is not what the IUPAC recommends. This is the chemical potential of the solution based on vapor pressure.

Chemical potential (Gibbs energy) for mixed gas is:
$\mu=\mu^{\ominus}+RTln\frac{p}{p^{\ominus}}$
where $p^{\ominus}$ is the standard pressure (1 bar) and IUPAC recommends using this symbol. Now turning to solution case, the chemical potential of the vapor pressure of fully pure liquid A (which in equilibrium, this is identical to the chemical potential of the liquid) is:
$\mu _{A}^{*}=\mu _{A}^{\ominus}+RTln \frac{p _{A}^{*}}{p^{\ominus}}$
If the liquid is not pure A, then:
$\mu _{A}=\mu _{A}^{\ominus}+RTln \frac{p _{A}}{p^{\ominus}}$
So combining these two equation gives:
$\mu _{A}=\mu _{A}^{*}+RTln\frac{p _{A}}{p _{A}^{*}}$
We can write this in terms of chemical activity $a_{A}=\frac{p _{A}}{p _{A}^{*}}$, which gives:
$\mu _{A}=\mu _{A}^{*}+RTlna _{A}$
And using activity coefficient and mole fraction,
$\mu _{A}=\mu _{A}^{*}+RTln\gamma _{A}x_{A}$
Ideal solution with sufficiently low solute B and pure solvent A (Roult's Law) means that $\gamma _{A}=1$ so,
$\mu _{A}=\mu _{A}^{*}+RTlnx_{A}$
This is now identical to the second equation of the OP's question.

Last edited:
etotheipi

## 1. What is the small triangle symbol in chemical potential?

The small triangle symbol, ∆, represents the change in a physical quantity, in this case the change in chemical potential.

## 2. How is the small triangle symbol used in chemical potential calculations?

The small triangle symbol is used to indicate a change in chemical potential, which is the measure of the energy required to add or remove a particle from a system at constant temperature and pressure.

## 3. What does a positive small triangle in chemical potential indicate?

A positive small triangle in chemical potential indicates that the energy required to add a particle to the system is greater than the energy released when removing a particle, resulting in an overall increase in chemical potential.

## 4. How does the small triangle symbol relate to the Gibbs free energy equation?

The small triangle symbol is used in the Gibbs free energy equation, ∆G = ∆H - T∆S, to represent the change in chemical potential (∆μ) as a result of changes in enthalpy (∆H) and entropy (∆S).

## 5. Can the small triangle symbol be used for other physical quantities besides chemical potential?

Yes, the small triangle symbol can be used to represent the change in any physical quantity, such as temperature, pressure, or volume, in various scientific equations and calculations.

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