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How can I convert a reaction rate $k$ with units of $\mathrm{1\over M~~s}$ to $\mathrm{1\over ppm~~s}$?

For context: I want to make a numerical simulation of a system of reactions that happens in air (and in water droplets suspended in the air), I have already built a part of the model for which I used $\mathrm{ppm}$ for my concentrations and thus, e.g., $\mathrm{1\over ppm~~s}$ as the units for the $k$ values of second-order reactions in the system. (Reactions of different orders have different units, obviously, but those details are irrelevant to the question.) The article I have on hand lists a $k$ value for the reaction I need in $\mathrm{1\over M~~s}$ and the reaction takes place in the liquid phase.I assume that the PPM is weight-based although the article in question does not actually specify this.

I am asking the above question because I am not sure if this conversion is necessarily as straightforward as a simple factor of $10^{-6}$.

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  • $\begingroup$ ppm to moles conversion factor is 1E-6. Similarly, for ppb to moles you need a conversion factor of 1E-9. Since this is just a conversion factor related question and doesn't involve any critical thinking, I think it's OK to help the OP here even if it's a HW problem. $\endgroup$
    – Osman Mamun
    Dec 12, 2016 at 18:48
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    $\begingroup$ There isn't a direct conversion. "ppm" is typically calculated on a weight basis. The only way to convert from moles would be if the matrix was relatively constant, such as a small amount of product in aqueous solution. $\endgroup$
    – MaxW
    Dec 12, 2016 at 21:53
  • $\begingroup$ It doesn't really make sense to do this. That unit will for example be terrible for comparison of different rates. Since dependend on the molecular weight different ppm-1s-1 could equal the same effective conversion rate in mole. $\endgroup$
    – DSVA
    Dec 13, 2016 at 20:17
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    $\begingroup$ I do agree with your concerns about comparing rate in this fashion. The thing is however that, currently I have the model build to work with PPM, as this was the unit I was able to find the kinetics in. However for 1 reaction I intend to add to that, I could only find M-1 s-1. I do intend to convert anyway (making assumptions were needed) and just see if I can get anywhere near a realistic output, at least until better data is available. $\endgroup$
    – Gladius
    Dec 14, 2016 at 14:26
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    $\begingroup$ The moral of the story is: if you don't want people to think it's homework, don't make it look like homework. When we see a new question, we have no idea who you are, why you are asking, and how many years you haven't had homework for - so the more context you provide, the better the judgments the community can make. $\endgroup$
    – orthocresol
    Dec 14, 2016 at 16:23

1 Answer 1

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We can do it in two ways:

1) For dilute solutions, ppm and mg/L is equivalent. So, for dilute solutions, the straightforward conversion scheme should look like::
$$ppm=\frac{mol}{L}\times MW\times 1000$$

2) with no assumption::

first, remember that $ppm=y_i \times 10^{-6}$

$$ppm=\frac{mol}{L} \times \frac{x gm}{mol} \times \frac{1 L}{10^{-3} m^3} \times \frac{m^3}{y~gm} \times 10^{-6}$$

here, x is the MW of solute and y is the density of the solvent (for dilute solutions) or solution in $\frac{gm}{m^3}$

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