November 28, 2021, 07:07:59 AM
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### Topic: Henry’s Law  (Read 1072 times)

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#### Borek

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##### Re: Henry’s Law
« Reply #15 on: June 14, 2021, 02:42:31 PM »
Have you tried to get it right first without the Van 't Hoff corrections?

Your formula uses two constants - 29.42 and -2400 - that are not clear to me.

I mean: I could probably attempt to guess where they came from, but it would be better if you explain everything from the very beginning. So far I am guessing my way through things you have never stated, it is a waste of time
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#### JarredAwesome

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##### Re: Henry’s Law
« Reply #16 on: June 14, 2021, 04:44:42 PM »
Have you tried to get it right first without the Van 't Hoff corrections?

Your formula uses two constants - 29.42 and -2400 - that are not clear to me.

I mean: I could probably attempt to guess where they came from, but it would be better if you explain everything from the very beginning. So far I am guessing my way through things you have never stated, it is a waste of time

Yeah, when I run the numbers without altering the temp (aka, just using Henry's constant as-is), the amounts change slightly, but nothing notable

Sorry, I take for granted that I have figured parts out, and haven't expressly shared the logic I am using
Also, I am reviewing my code, I made some mistakes when I "translated" my code to an equation

The Equation should read like this:

C = (P/10^6) / 29.76 * exp(2400/8.314*(1/(T+273.15)-1/298.15))
C(ppm) = C * 44.1 * 1000

C = Concentration in Water
P = PPM of co2 in cup
C(ppm) = Concentration in PPM
T = Temp in Celsius

Here is where I got the constants from:
29.76 is Henry's constant for CO2 with STP. I can't find the exact resource I used to learn that, but this website confirms it (I had a slightly different number but this seems to be the correct one)
8.314 is the Molar Gas Constant
2400 is the value given as the constant on the same page I listed above

also, after going over some of the resources, I altered Henry's Constant by using the equation below, opposed to the van't Hoff equation:

kH(T) = k°H exp(d(ln(kH))/d(1/T) ((1/T) - 1/(298.15 K)))

Sorry, I REALLY didn't want to make so many mistakes, but this is a project I have been working on for a while, andI got a little confused

#### Borek

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##### Re: Henry’s Law
« Reply #17 on: June 14, 2021, 06:15:20 PM »
29.76 is Henry's constant for CO2 with STP.

This is misleading - as we told you, CO2 solubility heavily depends on the solution pH. The higher the pH, the more CO2 will react with bases present, producing HCO3- and CO32- - this is indistinguishable from just increased dissolution. My bet is that the constant as listed is for dissolution in pure water - but that's not your case. What you need is the "effective" constant, one that takes into account changes in solubility caused by the acid/base equilibrium occurring in the solution.

Quote
2400 is the value given as the constant on the same page I listed above

I don't see it on the page. It should be the dissolution enthalpy. But I strongly recommend you leave the temperature dependence for now, it will be easy to add later, once you get the basics right. Temperature corrections will be most likely in single percent range, order(s) of magnitude lower than the error you have now.
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#### JarredAwesome

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##### Re: Henry’s Law
« Reply #18 on: June 14, 2021, 06:52:43 PM »
Ah, I understand.

So is there a way to figure out what a  ‘effective’ constant?

What information would I need?

Also, what do I do about my other problem?

The co2 raises in the cup along side when I start inject co2, but it doesn’t seem to lower at the same rate as the tank.

I’m looking at the raw data of the sensor, and I don’t think that aspect is a mathematical error.
« Last Edit: June 14, 2021, 08:07:39 PM by JarredAwesome »

#### Borek

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##### Re: Henry’s Law
« Reply #19 on: June 15, 2021, 06:18:58 PM »
So is there a way to figure out what a  ‘effective’ constant?

What information would I need?

Sigh, this is tricky and difficult to explain without a long lecture on the acid/base equilibria.

Imagine you start with a pure water and measure Henry's constant for an inert gas - you get some number, that tells you how much gas will dissolved for a given pressure. Simple.

Now we do the same, but we dissolve CO2 in pure water. CO2 is not inert, it reacts with water, producing carbonic acid, which dissociates, acidifying water. When it dissociates it technically "disappears" from the solution, making room for more CO2 to dissolve. So, what we measure is already kind of "effective constant".

Things get even more complicated when the starting pH is not neutral, as then the carbonic acid either can't dissociate (if pH is low) and the amount of gas that can get dissolved gets lowered, or gets neutralized (if pH is high) making room for more gas.

But, the pH itself is still not enough, as solutions with the same pH can be capable of neutralizing/acidifying different amounts of the acid (broadly speaking it depends on the parameter known as a buffer capacity of the solution).

These things can be calculated using methods for acid/base equilibrium. My bet is the result can be easily fit into some reasonably simple and convenient to use approximated form, but the derivation would be tedious.

Quote
Also, what do I do about my other problem?

The co2 raises in the cup along side when I start inject co2, but it doesn’t seem to lower at the same rate as the tank.

I’m looking at the raw data of the sensor, and I don’t think that aspect is a mathematical error.

No idea and yes, it sounds unexpected.
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