<p>I think this is it:</p>

<p>ppm(mol)=ppm(v) x (density CO2/density total atmos) x (Molecular Weight total atmos/Molecular Weight CO2)​​​​.</p>

<p>Try some number crunching to see if that makes sense.</p>

CC BY-SA 3.0
2017-04-22T16:03:42.893Z
Well I'm looking for something more subtle, like a 1% or even smaller correction factor. 1ppmV is very close to 1umol/mol. For ideal gas they would be the same. So it's really just the deviation from the ideal gas law that I'm trying to find.
uhoh
CC BY-SA 3.0
2017-04-22T16:06:21.650Z
I think the equation you wrote is for ppm by mass, not by number (in moles).
uhoh
CC BY-SA 4.0
2022-11-03T09:42:13.127Z
You are right, uhoh... and that illustrates why the shortened abbreviation "ppm" should not be used. In contexts other than gases, ppm usually means ppmm, not ppmv. So writing "ppm" when you mean "ppmv" is inviting confusion. That quoted NOAA GML recommendation to drop the "v" in "ppmv" is very bad advice,
Dave Burton
CC BY-SA 3.0
2017-04-22T15:37:13.080Z
2017-04-22T15:37:13.080Z
user7733
<p>According to the <a href="http://cdiac.ornl.gov/oceans/ndp_067/other067.html" rel="nofollow noreferrer">US Carbon Dioxide Information Analysis Center</a> :</p>
<p>Though in their data table they use the term &quot;ppmv&quot;, they explain:</p>
<blockquote>
<p>The CO2 mixing ratios are reported as micromoles per mole (µmol/mol = ppmv) of dry air in the World Meteorological Organization (WMO) X85 mole fraction scale, traceable to primary standards at the Scripps Institution of Oceanography (SIO)</p>
</blockquote>
<p>This is further explained in <a href="https://www.esrl.noaa.gov/gmd/ccl/co2report.html" rel="nofollow noreferrer">The WMO Mole Fraction Scales for CO2 and other greenhouse gases, and uncertainty of the atmospheric measurements</a>:</p>
<blockquote>
<p>Abbreviations can be ppm, ppb, etc., whereas widely used abbreviations such as ppmv (the v is for volume) are wrong and should be abandoned. When reviewing papers, or when we are co-authors, we should convince first authors to abandon the ppmv notation. Volume has nothing to do with mole fraction.</p>
</blockquote>
<p>Supposing you know the mole fraction, if you literally wanted to calculate the parts per million by volume, first you need to define what that would mean.  Are you interested in the ratio of the volume of CO2 separately isolated relative to the whole volume? Or are you interested in the volume of CO2 separately isolated, relative to the sum of all the gases separately isolated? For either of these methods, you would need to choose a temperature and pressure, such as the actual temperature and pressure of a sample, or standard temperature and pressure.</p>
<p>Then you need an <a href="https://www.nist.gov/sites/default/files/documents/srd/jpcrd516.pdf" rel="nofollow noreferrer">equation of state</a> at least for the CO2, that is more real than the ideal gas law, such as <a href="https://en.wikipedia.org/wiki/Van_der_Waals_equation" rel="nofollow noreferrer">van der Waals</a>.</p>

CC BY-SA 3.0
2017-05-12T13:01:35.937Z
This is exactly what I was hoping for. You've resolved the quandary by explaining the ambiguity when trying to define partial volumes, and found a definitive reference to settle the matter. Thanks!
uhoh
CC BY-SA 4.0
2022-11-03T09:38:03.313Z
That quoted NOAA GML recommendation to drop the "v" in "ppmv" is ABSOLUTELY TERRIBLE advice, because it makes the units ambiguous. "ppm" can mean either "ppmm" (parts per unit by mass) or "ppmv" (parts per million by volume). If you write "ppm" when you mean "ppmv" or μmol/mol, some readers will surely mistake it for ppmm (parts per million by mass). The shortened abbreviation "ppm" should never be used, unless you also include an explicit clarifying statement to eliminate the ambiguity.
Dave Burton
CC BY-SA 4.0
2017-05-12T12:46:02.693Z
2020-08-06T19:55:19.003Z
2020-08-06T19:55:19.003Z
DavePhD
<p>For a uniform mixture of ideal gases, I think that the concentration of a gas reported in parts per million by volume (ppmV) and micro-moles per mole (μmol/mol) would be the same.</p>

<p>When I see atmospheric CO2 discussed, I have seen both units used, depending on the source. See for example, the comments under <a href="https://earthscience.stackexchange.com/a/10152/6031">this answer</a>.</p>

<p>Since multi-atomic gases like N2, O2, H2O and CO2 are not ideal gases (even monatomic gases are not absolutely ideal) I would guess that for realistic atmospheric samples at different altitudes and times, the CO2 concentrations expressed in ppmV and μmol/mol would not be numerically identical. Further, due to the variations in concentrations of the other constituents they wouldn't even be strictly proportional.</p>

<p>Is there a handy, approximate conversion constant, or function, that is more accurate than unity? Is there a  nearly-exact one?</p>

<atmosphere><atmospheric-chemistry><upper-atmosphere>
ppmV versus μmol/mol for atmospheric CO2 - how to convert?
uhoh
# ppmV versus μmol/mol for atmospheric CO2 - how to convert?

(Asked by: username_0 on 2017-04-20)

For a uniform mixture of ideal gases, I think that the concentration of a gas reported in parts per million by volume (ppmV) and micro-moles per mole (μmol/mol) would be the same.

When I see atmospheric CO2 discussed, I have seen both units used, depending on the source. See for example, the comments under [this answer](https://earthscience.stackexchange.com/a/10152/6031).

Since multi-atomic gases like N2, O2, H2O and CO2 are not ideal gases (even monatomic gases are not absolutely ideal) I would guess that for realistic atmospheric samples at different altitudes and times, the CO2 concentrations expressed in ppmV and μmol/mol would not be numerically identical. Further, due to the variations in concentrations of the other constituents they wouldn't even be strictly proportional.

Is there a handy, approximate conversion constant, or function, that is more accurate than unity? Is there a nearly-exact one?

**Tags:** atmosphere, atmospheric-chemistry, upper-atmosphere


---

## 2 answers

### Answer by username_3 on 2017-05-12. Score: 9 | Accepted answer

According to the [US Carbon Dioxide Information Analysis Center](http://cdiac.ornl.gov/oceans/ndp_067/other067.html) :

Though in their data table they use the term "ppmv", they explain:

> The CO2 mixing ratios are reported as micromoles per mole (µmol/mol = ppmv) of dry air in the World Meteorological Organization (WMO) X85 mole fraction scale, traceable to primary standards at the Scripps Institution of Oceanography (SIO)

This is further explained in [The WMO Mole Fraction Scales for CO2 and other greenhouse gases, and uncertainty of the atmospheric measurements](https://www.esrl.noaa.gov/gmd/ccl/co2report.html):

> Abbreviations can be ppm, ppb, etc., whereas widely used abbreviations such as ppmv (the v is for volume) are wrong and should be abandoned. When reviewing papers, or when we are co-authors, we should convince first authors to abandon the ppmv notation. Volume has nothing to do with mole fraction.

Supposing you know the mole fraction, if you literally wanted to calculate the parts per million by volume, first you need to define what that would mean. Are you interested in the ratio of the volume of CO2 separately isolated relative to the whole volume? Or are you interested in the volume of CO2 separately isolated, relative to the sum of all the gases separately isolated? For either of these methods, you would need to choose a temperature and pressure, such as the actual temperature and pressure of a sample, or standard temperature and pressure.

Then you need an [equation of state](https://www.nist.gov/sites/default/files/documents/srd/jpcrd516.pdf) at least for the CO2, that is more real than the ideal gas law, such as [van der Waals](https://en.wikipedia.org/wiki/Van_der_Waals_equation).

> **Comments:**
> **username_0**: This is exactly what I was hoping for. You've resolved the quandary by explaining the ambiguity when trying to define partial volumes, and found a definitive reference to settle the matter. Thanks!  
> **username_2**: That quoted NOAA GML recommendation to drop the "v" in "ppmv" is ABSOLUTELY TERRIBLE advice, because it makes the units ambiguous. "ppm" can mean either "ppmm" (parts per unit by mass) or "ppmv" (parts per million by volume). If you write "ppm" when you mean "ppmv" or μmol/mol, some readers will surely mistake it for ppmm (parts per million by mass). The shortened abbreviation "ppm" should never be used, unless you also include an explicit clarifying statement to eliminate the ambiguity.  

---

### Answer by username_1 on 2017-04-22. Score: -1

I think this is it:

ppm(mol)=ppm(v) x (density CO2/density total atmos) x (Molecular Weight total atmos/Molecular Weight CO2)​​​​.

Try some number crunching to see if that makes sense.

> **Comments:**
> **username_0**: Well I'm looking for something more subtle, like a 1% or even smaller correction factor. 1ppmV is very close to 1umol/mol. For ideal gas they would be the same. So it's really just the deviation from the ideal gas law that I'm trying to find.  
> **username_0**: I think the equation you wrote is for ppm by mass, not by number (in moles).  
> **username_2**: You are right, username_0... and that illustrates why the shortened abbreviation "ppm" should not be used. In contexts other than gases, ppm usually means ppmm, not ppmv. So writing "ppm" when you mean "ppmv" is inviting confusion. That quoted NOAA GML recommendation to drop the "v" in "ppmv" is very bad advice,  

---

