Data And Calculations: Seeing Carbon Dioxide

The following calculations, data, and references support the article Seeing Carbon Dioxide.  In our calculations, we assume that the atmosphere behaves as an ideal gas, and all volumes are at standard temperature and pressure, defined as 77 degrees Farenheit (25 degrees Celcius) and 1.00 atmospheres (760 mm Hg).

Data

Molar Mass Of Dry Air: 28.96 g/mol
Molar Volume Of Dry Air @STP: 24.46 l/mol
Mass Of Dry Atmosphere: 5.135×10^18 kg (Source: wikipedia)
World Population: 6,820,000,000 people (Source: U.S. Census Bureau)
Carbon Dioxide Increase: 110 ppmv since pre-Industrial times (Sources: wikipedia, ESRL)

Calculations

Global number of air molecules =
dry mass of atmosphere / molar mass of dry air =
5.135×10^18 kg * 1000g/kg / 28.96 g/mol = 1.773×10^20 mol

Global number of molecules of CO2 increase =
fractional CO2 increase * global number of air molecules =
(110 parts/1000000 parts) * 1.773×10^20 mol = 1.950×10^16 mol

Global mass of CO2 increase =
global number of molecules of CO2 increase * molar mass of dry air =
1.950×10^16 mol * 28.96 g/mol = 5.647×10^17 g = 5.647×10^11 metric tons

Global volume of CO2 increase =
global number of molecules of CO2 increase * molar volume of dry air =
1.950×10^16 mol * 24.46 l/mol = 4.371×10^17 liters

Per capita volume of CO2 increase =
global volume of CO2 increase / world population =
4.371×10^17 liters / 6.82×10^9 people = 6.409×10^7 liters/person

Volume of sphere = 4/3 pi r^3
Radius of sphere = (volume of sphere / (4/3 pi)) ^ (1/3)
Radius of sphere containing per capita volume of CO2 increase =
(6.409*10^7 liters*(1 dm^3/liter) /(4/3*pi)) ^ (1/3) = 248.3 dm = 24.83 m = 81.46 feet
Diameter of sphere = 2 * Radius of sphere = 49.66 m = 162.9 feet