Urgent!! %CO2 solution preparation I struggle with

[Divyasri]

Hi, I have a doubt about making an equivalent %co2 solution with sodium carbonate. I have attached the reference equation quoted in the research article. If anyone knows how to derive the equation kindly help me. How 1.3g/L of Na₂CO₃ came for 5% Co₂ solution and help me to find out for 50% co2. I have doubt in this derivation.

***reference***

pH=6.30+log [ HCO₃− ] −log [ CO₂]

pH=10.09+log [ CO₃ 2- ] −log [ HCO₃-]

The values of sodium carbonate concentrations corresponding to 5%, 10%, 15%, 20% and 30% CO₂ concentrations at pH 7 are 1.3 g/L, 2.6 g/L, 3.8 g/L, 5.1 g/L, and 7.6 g/L, respectively.

****reference***

Any one kindly help me as soon as possible.... thanks in advance.

[chenbeier]

1,3 g/l Na2CO3 corresponds only to 0,05 % CO2.