Conversion factor from ppmv CO₂ to Gt C

I just spent half an hour on finding the references for this, so I can spend 5 minutes providing it for others on the web.

The conversion factor from ppmv CO\(_2\) to GtC is 2.14, calculated from the molar mass of roughly \(M_{\text{CO}_{2}} = 44 g/mol\) for carbon dioxide, the molar mass of \(M_{\text{C}} = 12 g/mol\) for carbon, \(M_{\text{air}} = 28.9 g/mol\) for air (Halliday et al., 2003) and \(m_{\text{air}} 5.15 \times 10^{6} Gt\) for the total mass of the air (Trenberth and Smith, 2005): \(\left ( \frac{M_{\text{air}}}{M_{\text{CO}_{2}}} · \frac{M_{\text{CO}_{2}}}{M_{C}} · \frac{1}{m_{\text{air}}} \right )^{-1}\)

(let ((Mco2 44.0) ; g / mol
      (Mair 28.9) ; g / mol
      (Mc 12.0) ; g / mol
      (mair 5.15)) ; 1,000,000 Gt
  (/ 1
     (* (/ Mair Mco2)
        (/ (/ Mco2 Mc) mair))))

Halliday et al., 2003: Halliday, D., Resnick, R., Walker, J., and Koch, S. (2003). Physik. Wiley.

Trenberth and Smith, 2005: Trenberth, K. E. and Smith, L. (2005). The mass of the atmosphere: A constraint on global analyses. Journal of Climate, 18(6):864–875.

PS: GtC Gigaton Carbon = PgC Petagram Carbon; ppmv CO₂ = parts per million (in volume) carbon dioxide in air.