To calculate the boiling point elevation of a pure substance, the ebullioscopic constant (Kb) can be used to used.
ΔT = i * Kb * m
To determine the ebullioscopic constant for butane, we can use
K b = R · T(b)^2 / L(v)
where
|Kb| Ebullioscopic constant (K*kg/mol)|
|R| molar gas constant|
|Tb| Boiling point of liquid (K)|
|Lv| Latent heat of vaporisation per gram (enthalpy of vaporization) (J/kg)|
Kb (butane) =1.6
THCA is 314.45 g/mol
for every 314.45g of THCA dissolved in a kilogram of butane we have boiling point elevation of 1.6 Celsius.
lets say you wanted a to boil off butane till you reached 75% THCA 25% butane
(Mols of THCA * 314.45)/(mols of THCA * 314.45 + 1000g(butane))
Its around 9.55 mols of THCA/Kg butane. This concentration elevates the boiling point of butane by 15.28 degrees celsius.
so how do you know you got to 9.55mol/kg with out being at -0.4 celsius?
Antoine equation
log 10 p = (A - B )/ (C + T)
where
| p | vapor pressure (dimensionless) |
|---|---|
| A | component-specific constant |
| B | component-specific constant |
| C | component-specific constant) |
| T | temperature(K) |
lets rearrange this with butane’s physical properties so we can look at a standard graph in x=celsius and y=psi
f(x) = 10^(4.355-(1175.6/(-2.071+(x+273))))*14.7)-14.7
Lets take a second version of this to account for the horizontal (x axis) transformation created by our boiling point elevation
f(x) = 10^(4.355-(1175.6/(-2.071+(x+273-15.28))))*14.7)-14.7
now lets assume you have a standard temperature you like to keep your miner. for instance 45 celsius. in order to find out what the pressure is for 9.55mol/kg butane solution at 45 celsius we can solve for f(x) at x=45 we get 26.6 psi
Therefore, a solution with a concentration by weight of 3:1 THCA to butane will sit at about {edit} 26.2 PSI at 45 celsius. This relationship can be used to estimate the temperature and pressure you need to achieve the level of saturation you require.
Im leaving out the specifics for setting this up practically. nerds only post
{edit} i removed the difference between functions for pure and solution cause that was actually just for verifying accuracy across a large span due to exponential nature of functions.
