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
