A soft drink was bottled with a partial pressure bf \(CO _{2}\) of \(3\) bar over the liquid at room temperature. The partial pressure of \(CO _{2}\) over the solution approaches a value of 30 bar when \(44\, g\) of \(CO _{2}\) is dissolved in \(1\, kg\) of water at room temperature. The approximate \(pH\) of the soft drink is............... \(\times 10^{-1}\) (First dissociation constant of \(H _{2} CO _{3}=4.0 \times 10^{-7}\)\(\log 2=0.3 ;\) density of the soft \(\left.\operatorname{drink}=1\, g\, mL ^{-1}\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.