## Saturday, July 9, 2011

### 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) = 10g = 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 CO3019 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

Anonymous said...

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

Rich said...

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.

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