In a previous post I explained how to convert to and from units of ppm. The current post explains the units petagrams of carbon, and how to convert from ppm to petagrams of carbon.

**Petagrams**

First it is necessary to understand units of petagrams. The SI units of mass are kilograms (kg). A kilogram is 1000 grams. One can construct other units of mass by prepending a prefix to the units grams.

1 kilogram (kg) = 10

^{3}grams (g)

1 megagram (Mg) = 10

^{6}g = 10

^{3}kg

1 gigagram (Gg) = 10

^{9 }g = 10

^{6 }kg

1 tertagram (Tg) = 10

^{12 }g = 10

^{9 }kg

1 petagram (Pg) = 10

^{15 }g = 10

^{12 }kg

So one petagram is equal to one quadrillion grams, or one trillion kilograms.

**The Atmosphere**

The mean mass of the atmosphere is 5.1480 x 10

^{18}kg or 5.1480 x 10

^{21 }g. The molar mass of air is 28.966 g. So the atmosphere contains 5.1480 x 10

^{21}

**/**28.966

**=**1.7773 x 10

^{20}moles of air.

**Moles of Carbon Dioxide**

Mole fractions of carbon dioxide are expressed in ppm and directly convertible from parts-per-million by volume.

So 1 ppm carbon dioxide = 1.7773 x 10

^{20}/1,000,000 = 1.7773 x 10

^{14 }moles carbon dioxide.

In June of 2011, the Mauna Loa site measured 393.69 ppm of carbon dioxide, which equates to

393.69 x 1.7773 x 10

^{14 }

**=**6.9970 x 10

^{16}moles of carbon dioxide. It is worth noting that carbon dioxide is near its high point in the cycle for 2011, its last low point was about 386 ppm or 6.86 x 10

^{16}moles.

**Mass of Carbon Dioxide**

It is now a simple matter to convert from moles of carbon dioxide to mass of carbon dioxide. The molecular mass of carbon dioxide is

12.01 + 16.00 + 16.00 = 44.01 grams/mole.

So 1 ppm carbon dioxide =

1.7773 x 10

^{14 }moles x 44.01 grams/mole = 7.822 x 10

^{15 }grams or 7.822 petagrams of CO2.

So 393.69 ppm = (393.69 x 7.822) = 3079 Pg Pg CO2

and 386 ppm CO2 3019 Pg CO2.

**Petagrams of Carbon**

For every mole of carbon dioxide, there is one mole of carbon. The molar mass of carbon is 12.01 g.

So 1 ppm carbon dioxide =

1.7773 x 10

^{14 }moles x 12.01 grams/mole = 2.134 Pg of carbon.

So 393.69 ppm CO2

**=**840.1 Pg of carbon

and 386 ppm of

**CO2 = 823.7 Pg carbon**

**Sources**

- Trenberth, Kevin E; Smith, Lesley,
*The Mass of the Atmosphere: A Constrained Global Analysis*, J. Climate 18, 864-875 (2005) - John M. Wallace and Peter V. Hobbs,
*Atmospheric Science*, Second Edition, Elsevier, Amsterdam, 2006 - Earth System Research Laboratory Global Monitoring Division: Recent Mauna Loa CO2.

## 7 comments:

Hi,

I was just wondering if the same calculations apply for conversions of methane ppm-Pg C (being that CH4 only has one molecule of C as well)?

So for example: 4680PgC= 2193.05ppm?

Thanks

You can calculate the answer yourself by following my logic using the molecular mass of methane instead of the molecular mass of carbon dioxide and seeing if you get the same answer.

Thanks a lot you post helped me to understand the concepts very clearly

you are awesome man!

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