operation oaxaca: langmuir models.

pre-lab jargon, extra (010)

Carlos Manuel Jarquín Sánchez
5 min readFeb 8, 2024

this is carlos.

been in talks for a lab.

i won’t rush the process.

it will be complete when it needs to.

for now, i shall progress on the technicality of the material,

more isotherm models, pseudo-models,

and explain the problem of water in united states (this time).

as always, imma explain what the things i’m researching are & why it’s relevant for my thang.

enjoy, imma just go dive into it.



this word is of greek origin.

so imma break the word down.

iso stems from the greek word ίσος, meaning “equal”.

therms stems from the greek word θερμός, meaning “heat”.

these words define a huge chunk of the definition.

the formal definition (for chemists) is:

An isotherm is the relationship between the concentrations of a solid and fluid, used to describe states of no change in the sorption process. (source)

but i like this (general statement):

isotherms are imaginary lines that connect points or places on a map that have the same atmospheric temperature. (source)

but the isotherms i care about are adsorption isotherms.

remember, the target of the mango peels is to adsorb metal ions (aka make the ions stick to the surface of the peel.)

and imma use an oven to dry these peels out, and temperature of environment can affect properties.

so, that’s why i care.

this is how i would define an adsorption isotherm:

it’s a graph that shows how much the adsorbate gets adsorbed on the surface of the adsorbent as pressure changes, but temperature stays the same.

in our case:

adsorbate → heavy metal ions

adsorbent → anionic-loaded mango peel

how would it be graphed?

well, it would be your typical xy-plane, with an x & y axis.

but this is liquid we are dealing with.

so granted, on one axis, we want to know how much metal we adsorbed (removed from contaminated water.)

the other axis, would be what’s remaining of the metal ions.

this can tell us if our filter is doing its task.

and guess what?

there’s a name for this type of adsorption model.

it’s known as the langmuir isotherm model.

the specifics on this model are as follows.

langmuir says this:

it assumes that adsorption occurs at specific homogeneous sites at the adsorbent surface.

and saturation is reached when the adsorbate fills up the homogeneous bonding sites…

and adsorption can no longer happen at the homogeneous sites.

homogenous → “evenly distributed” in every direction. (aka, ur cup of coffee, no sugar, cream, milk)

saturation → full, no more space (aka, the parking lot is saturated)

note: for chemicals, the mango peel won’t have extra bonding sites on the middle of the peel. all sites are evenly disributed across the peel.

see? coffee doesn’t have extra coffee on one side of the cup lol.

on a graph, the x-axis will have the variable: 1/Ce

and on the y-axis will look have the variable: 1/Qe

but why that?

and what does C,Q, & e mean?

these pieces are actually what define the langmuir isotherm model.

this is the equation and variable used to define it.

thanks to them.

so what do these symbols mean?

note: the majority of defined terms have the word “equilibrium” in it. i’ll define that too (in terms of this context).

equilibrium → where the rate of adsorption (of metal ions) equals the rate of desorption.

q(e) → the amount of adsorbate that’s adsorbed when equilibrium is acheived, measured in milligrams per gram (mg/g)

q(m) → a constant, the maximum monolayer adsorption capacity of our adsorbent (peels), measured in (mg/g)

maximum monolayer means this:

the langmuir model also assumes that it the adsorbate molecules (our metal ions) adsorb onto the surface until a full, single layer (of these ions) is formed.

plus, maximum monolayer adsorption capacity is when the adsorption process reaches equilibrium.

C(e) → the concentration of the adsorbate under equilibrium conditions, measured in (mg/L)

K(l) → the langmuir constant, measured in (L/mg)

btw, the langmuir constant describes the strength of the interaction between the adsorbate (ions) and the adsorbent (peel).

the higher the value is for the constant, there’s a strong interaction between adsorbate and adsorbent.

and if constant smaller, then interaction is weaker.

a good choice of anionic groups on the adsorbent will help with that interaction bring stronger lol.

the last piece of the langmuir isotherm model, is its nature.

in its intuitive sense, it can describe certain features of equilibrium of the adsorbate & adsorbent.

time to introduce the last piece:

R(l)… also known as the equilibrium constant for adsorption.

we defined R(l) was already defined above.

K(l) was the langmuir constant.

C(0) is the inital concentration of adsorbate (ions) in our solution (dirty water).

the constant has specific outcomes between 0 & 1, greater than 1, at 1, and at 0. (0 < R(l) < 1, R(l) = 1, or R(l) = 0)

when R(l) = 0:

desorption can’t happen.

once the adsorbate (ions) is adsorbed onto the surface of the adsorbent (peel), it cannot be easily desorbed. this is irreversible adsorption.

when R(l) is 0 < R(l) < 1:

adsorption will be effective to our cause.

the concentration (number) of ions was just right for the ions to adsorb onto the surface of the peels...


the concentration of the adsorbate is approximately the same as adsorbent sites, leading to efficient adsorption.

when R(l) = 1:

this is a linear adsorption.

the adsorption process is neither favorable nor unfavorable and follows a simple linear relationship. (i like to think of this as “equilibrium”, but in terms of how effective adsorption will happen).

when R(l) > 1:

the adsorption process is unfavorable. the concentration (number) of ions is too much for the peel.


this can also be ’cause of the anionic compounds that are used to force the ions to bond to the peel.

either way, this will leading to less efficient adsorption.

© 2024–2100 by Carlos Manuel Jarquín Sánchez. All Rights Reserved.