Petagrams of Carbon

Sometimes carbon dioxide is referenced in units of ppm, and sometimes it is referenced in petagrams of carbon.  What are the meanings of these units and how does one convert between them?

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) = 10³ grams (g)
1 megagram (Mg) = 10⁶ g = 10³ kg
1 gigagram (Gg) = 10⁹ g = 10⁶  kg
1 tertagram (Tg) = 10¹² g = 10⁹  kg
1 petagram (Pg) = 10¹⁵ g = 10¹²  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 10¹⁸ kg or 5.1480 x 10²¹ g.  The molar mass of air is 28.966 g.  So the atmosphere contains 5.1480 x 10²¹/28.966 = 1.7773 x 10²⁰ 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 10²⁰ /1,000,000 = 1.7773 x 10¹⁴ 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 10¹⁴ = 6.9970 x 10¹⁶ 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 10¹⁶ 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 10¹⁴ moles x 44.01 grams/mole = 7.822 x 10¹⁵  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 10¹⁴ 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.