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I'm working with some hobby-level gas sensors and I've run across a "calibration" system I don't understand. A general description of this kind of gas sensor is described a bit more in this question and also here. They have some selectivity between gases, but anything that will react with atomic oxygen at elevated temperature in the presence of a catalyst ($\ce{CO}$, $\ce{H2}$, $\ce{CH4}$, etc.) will register.

Since I don't want to mess with explosive gases, the alcohol sensor is a convenient place to begin. Many hobbyists become voluntary test subjects, and heroically subject themselves to alcohol, then breath on the sensors. Since I'm not so brave, I thought I'd try the recommended calibration test setup below. I'm not interested in doing a careful calibration, but just get some kind of ballpark quantitative agreement.

Henry's law suggests a proportionality between the concentration of a dissolved gas and the partial pressure of the gas above the liquid, and the van 't Hoff equation provides for a temperature dependence within some limited range of variation. However it's of the form $exp(\frac{1}{T}-\frac{1}{T_0})$ and the equation shown below is only a straight exponential of temperature.

This is described more thoroughly in this excellent answer:

Henry's law works for small concentrations of ideal mixtures at equilibrium. Henry's Law constant varies with temperature according to the Van't Hoff equation:

$$ k(T)=k(T_0)exp\left[-C\left(\frac{1}{T}-\frac{1}{T_0}\right)\right] $$

Here $C$ is a constant related to the enthalpy of solvation for each gas, and $T_0$ represents the standard state, T = 298 K and 1 atm.

Is Dubowski’s formula just a further approximation, or does this method contain something new and/or different that I should be paying attention to?


below: Screenshot from Adafruit's AN4 Using MiCS Sensors for Alcohol Detection.pdf

enter image description here

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