<p>@BarocliniCplusplus's answer is correct.
To convert Ozone (kg/kg) to (ppbv) you only need molar masses of dry air (28.9644 g/mol) and molar mass of Ozone (47.998 g/mol).</p>
<p>(Mass mixing ratio in ppb) = (28.9644 / 47.9982) * 1e9 * (Mass mixing ratio in kg/kg)</p>
<p>[Source: ECMWF webpage]
[1]: <a href="https://confluence.ecmwf.int/pages/viewpage.action?pageId=153391710" rel="nofollow noreferrer">https://confluence.ecmwf.int/pages/viewpage.action?pageId=153391710</a></p>

CC BY-SA 4.0
2021-09-28T08:35:43.413Z
2021-09-28T08:35:43.413Z
Vijay Kumar Sagar
<p>1 part per billion is 1x10^-9 kilograms per kilogram so to convert a kilogram per kilogram ratio into a parts per billion figure divide it by 1x10^-9.</p>

CC BY-SA 3.0
2018-02-27T18:10:17.987Z
What's the source of this information?
Eevee
CC BY-SA 3.0
2018-02-27T18:15:39.303Z
@Imtherealsanic This is a very basic mathematical relationship, one most people should be able to manage in their head, what do you mean source?
Ash
CC BY-SA 3.0
2018-02-27T18:22:58.403Z
I was going to ask you for a link to the article where you got the information provided in your answer, but instead I think I'll post an answer myself.
Eevee
CC BY-SA 3.0
2018-02-27T19:33:45.507Z
I posted a similar answer, but deleted it when I realized there's more than one way to measure a part per billion: the questioner might want a molar fraction, for example, in which case the calculation is slightly more complex. I've commented on the question to request more information.
Pont
CC BY-SA 3.0
2018-02-28T07:02:23.213Z
The asker has now clarified that they want a volume rathen than mass fraction.
Pont
CC BY-SA 3.0
2018-02-27T17:16:18.267Z
2018-02-27T17:16:18.267Z
Ash
<p>So if you have a mass-mixing ratio, you effectively $\frac{ \text{kg pollutant}}{\text{kg dry air}}$. PPBV is parts per billion volume, or number of molecules of pollutant per billion molecules of dry air. Since not all particles weigh the same, you must use a conversion factor. Consider molar mass, which is the ratio of moles (a unit describing the number of molecules/photons/atoms) to mass. Ozone has a molar mass of 48 kg mol$^{-1}$. Dry air doesn't have a molar mass per se, but an effective molar mass may be computed by a weighted sum of the molar masses of the consitituent chemicals (or you can Google it). Afterwards, you may have to multiply by a billion.$$\therefore \frac{ \text{kg pollutant}}{\text{kg dry air}} \times\frac{\frac{\text{mols of pollutant}}{\text{kg of pollutant}}}{\frac{\text{mols of dry air}}{\text{kg of dry air}}}=\frac{\text{mols of pollutant}}{\text{mols of dry air}}$$</p>

CC BY-SA 3.0
2018-03-01T11:30:56.600Z
Thanks a ton Baroclini, this definitely answers my question precisely!
HalloweenKing
CC BY-SA 3.0
2018-02-28T13:19:04.267Z
2018-02-28T13:19:04.267Z
BarocliniCplusplus
<p>I am using the CAMS model output data to figure out the ground level ozone at a particular place. It is given in mass mixing ratio, and I want to convert to parts per billion volume mixing ratio (volume/volume).</p>

<p><a href="https://i.sstatic.net/5x0Mr.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5x0Mr.jpg" alt="enter image description here"></a></p>

<p>Shown above are ozone values from a model – basically the given values on the right beside the dates are in $\mathrm{kg} \cdot \mathrm{kg}^{-1}$. How can I convert them to ppbV?</p>

CC BY-SA 3.0
2018-02-27T16:44:43.653Z
For clarification: you are looking for "ppbV" (parts per billion with respect to volume) and not for "ppbM" (... with respect to mass)? Do you have some other parameters given? Is it a homework question? What did you do to find the answer on your own?
daniel.heydebreck
CC BY-SA 3.0
2018-02-27T18:29:06.703Z
This is a VERY basic mathematical relationship unless I'm missing something, which I may be since you don't actually appear to ask a question in your question.
Ash
CC BY-SA 3.0
2018-02-27T19:30:35.210Z
As @daniel.neumann wrote, we need some more specifics here in order to give a useful answer: do you simply want the parts per billion of **mass** (in which case it's trivial, as per Ash's current answer), or a molar fraction, or a volume fraction, or something else? I'm going to vote to close this question temporarily as "unclear what you're asking"; please edit it to add the necessary information, and I will vote to re-open.
Pont
CC BY-SA 3.0
2018-02-28T02:19:48.443Z
@daniel.neumann Thank you for your response and my apologies for lacking clarity in my question! I am looking for ppbV. I shall explain what I'm trying to do. So I am using CAMS models' output data to figure out the ground level ozone at a particular place which is in mass mixing ratio and want to convert to volume mixing ratio/ volume itself.
HalloweenKing
CC BY-SA 3.0
2018-02-28T02:30:08.500Z
@Pont Good Day Pont! Apologies for the question being ambiguous. Yes, I am looking at the scenario based on the volume aspect/volume fraction, in my case ppb, since I would be looking at the pollutant concentration rather than simply jot down the mass of the pollutant component.  Thanks!
HalloweenKing
CC BY-SA 3.0
2018-02-28T07:00:51.320Z
@HalloweenKing Thanks for clarifying. I've edited your question to incorporate the information you provided in the comments. You can also edit your own question, should you want to amend my edits or add any further information.
Pont
CC BY-SA 3.0
2018-03-01T06:35:51.437Z
@Pont Thank you for the assistance :) Will amend the question if necessary!
HalloweenKing
<meteorology><atmosphere><ozone><gas><mathematics>
How do I convert kg·kg⁻¹ to ppbV (parts per billion volume)?
HalloweenKing
# How do I convert kg·kg⁻¹ to ppbV (parts per billion volume)?

(Asked by: username_0 on 2018-02-27)

I am using the CAMS model output data to figure out the ground level ozone at a particular place. It is given in mass mixing ratio, and I want to convert to parts per billion volume mixing ratio (volume/volume).

[![enter image description here](https://i.sstatic.net/5x0Mr.jpg)](https://i.sstatic.net/5x0Mr.jpg)

Shown above are ozone values from a model – basically the given values on the right beside the dates are in $\mathrm{kg} \cdot \mathrm{kg}^{-1}$. How can I convert them to ppbV?

**Tags:** meteorology, atmosphere, ozone, gas, mathematics

> **Comments:**
> **username_1**: For clarification: you are looking for "ppbV" (parts per billion with respect to volume) and not for "ppbM" (... with respect to mass)? Do you have some other parameters given? Is it a homework question? What did you do to find the answer on your own?  
> **username_2**: This is a VERY basic mathematical relationship unless I'm missing something, which I may be since you don't actually appear to ask a question in your question.  
> **username_3**: As @daniel.neumann wrote, we need some more specifics here in order to give a useful answer: do you simply want the parts per billion of **mass** (in which case it's trivial, as per Ash's current answer), or a molar fraction, or a volume fraction, or something else? I'm going to vote to close this question temporarily as "unclear what you're asking"; please edit it to add the necessary information, and I will vote to re-open.  
> **username_0**: @daniel.neumann Thank you for your response and my apologies for lacking clarity in my question! I am looking for ppbV. I shall explain what I'm trying to do. So I am using CAMS models' output data to figure out the ground level ozone at a particular place which is in mass mixing ratio and want to convert to volume mixing ratio/ volume itself.  
> **username_0**: @username_3 Good Day username_3! Apologies for the question being ambiguous. Yes, I am looking at the scenario based on the volume aspect/volume fraction, in my case ppb, since I would be looking at the pollutant concentration rather than simply jot down the mass of the pollutant component.  Thanks!  
> **username_3**: @username_0 Thanks for clarifying. I've edited your question to incorporate the information you provided in the comments. You can also edit your own question, should you want to amend my edits or add any further information.  
> **username_0**: @username_3 Thank you for the assistance :) Will amend the question if necessary!  

---

## 3 answers

### Answer by username_6 on 2018-02-28. Score: 7 | Accepted answer

So if you have a mass-mixing ratio, you effectively $\frac{ \text{kg pollutant}}{\text{kg dry air}}$. PPBV is parts per billion volume, or number of molecules of pollutant per billion molecules of dry air. Since not all particles weigh the same, you must use a conversion factor. Consider molar mass, which is the ratio of moles (a unit describing the number of molecules/photons/atoms) to mass. Ozone has a molar mass of 48 kg mol$^{-1}$. Dry air doesn't have a molar mass per se, but an effective molar mass may be computed by a weighted sum of the molar masses of the consitituent chemicals (or you can Google it). Afterwards, you may have to multiply by a billion.$$\therefore \frac{ \text{kg pollutant}}{\text{kg dry air}} \times\frac{\frac{\text{mols of pollutant}}{\text{kg of pollutant}}}{\frac{\text{mols of dry air}}{\text{kg of dry air}}}=\frac{\text{mols of pollutant}}{\text{mols of dry air}}$$

> **Comments:**
> **username_0**: Thanks a ton Baroclini, this definitely answers my question precisely!  

---

### Answer by username_4 on 2021-09-28. Score: 0

@username_6's answer is correct.
To convert Ozone (kg/kg) to (ppbv) you only need molar masses of dry air (28.9644 g/mol) and molar mass of Ozone (47.998 g/mol).

(Mass mixing ratio in ppb) = (28.9644 / 47.9982) \* 1e9 \* (Mass mixing ratio in kg/kg)

[Source: ECMWF webpage]
[1]: <https://confluence.ecmwf.int/pages/viewpage.action?pageId=153391710>


---

### Answer by username_2 on 2018-02-27. Score: 0

1 part per billion is 1x10^-9 kilograms per kilogram so to convert a kilogram per kilogram ratio into a parts per billion figure divide it by 1x10^-9.

> **Comments:**
> **username_5**: What's the source of this information?  
> **username_2**: @Imtherealsanic This is a very basic mathematical relationship, one most people should be able to manage in their head, what do you mean source?  
> **username_5**: I was going to ask you for a link to the article where you got the information provided in your answer, but instead I think I'll post an answer myself.  
> **username_3**: I posted a similar answer, but deleted it when I realized there's more than one way to measure a part per billion: the questioner might want a molar fraction, for example, in which case the calculation is slightly more complex. I've commented on the question to request more information.  
> **username_3**: The asker has now clarified that they want a volume rathen than mass fraction.  

---

