Atmospheric Sink of Carbon - Rain / Cloud drops

Around 0.5 meters of rainfall per year falls annually as a global average, though this rainfall total is greatly variable. On average rainfall has a (potential of Hydrogen) pH of 5.5, compared to pure evaporated rain within cloud droplets that has a pH of exactly 7.0. By calculating the difference in H+ concentration between the rainfall and evaporated water it is possible to determine the acidity perturbation, which largely (to first order) arises from the carbonic acid contained from dissociated of atmospheric carbon-dioxide within raindrops. The acidity therefore provides an estimate of the Carbon sink of global rainfall.

a solution with a pH of 7.0 contains a concentration of 10^(-7) mol dm-3 of Hydrogen ions,
a solution with a pH of 5.5 contains 10^(-5.5) = 3.16 x 10^(-6) mol dm-3 of Hydrogen ions,

carbonic acid has a molecular mass of [1*2 + 12 + (16*3)] = 62kg mol-1

ratio of carbon to hydrogen; (1:2) - but the rate constants (which provide information about the state of equilibrium in the atmosphere to carbonic-acid dissociation reaction) suggest at a pH of 5.6 the ratio of Carbon to Hydrogen ions is 2.23 : 3.16 assuming that the atmosphere and raindrops are in equilibrium with each other [neglecting the change in rate constants from a perturbed standard state i.e. the pressure and temperatures are much lower than the standard conditions].

the density of water is approximately 1kg dm-3 = 1000kg m-3

the molar density of carbon in rain-water is ...
  0.706 x ([3.16 x 10^(-6)]   -  [10^(-7)]) = 2.16 x 10^(-6) mol dm-3

...the surface area of Earth x 0.5m depth of yearly rainfall = global volume of rainfall in m3

(4 x pi x r^2) x 0.5 = 5.1 x 10^(14) m3

1dm-3 = 10^-3 m3

the number of moles of carbon from global rainfall ....

[1.53 x 10^(-6) mol dm-3] x [(10^3)] x [5.1 x 10^(14)] =  1.103 x 10^12
(moles)

moles x 12g mol-1 = total mass of carbon over globe

...so the carbon sink due to atmospheric water droplets is 

=(1.103 x 10^12) x (12) = 1.3216 x 10^12g = 0.0132Pg / yr*

[*this is only 0.1% of the anthropogenic carbon source of 10Pg / yr currently emitted from the burning of hydrocarbons]

~ 0.01Pg per year (10^13 grams = 10^10 kilograms = 10^7 tonnes = 0.01Gt / year)