# A soft drink was bottled with a partial pressure

Question:

A soft drink was bottled with a partial pressure of $\mathrm{CO}_{2}$ of 3 bar over the liquid at room temperature. The partial pressure of $\mathrm{CO}_{2}$ over the solution approaches a value of 30 bar when $44 \mathrm{~g}$ of $\mathrm{CO}_{2}$ is dissolved in $1 \mathrm{~kg}$ of water at room temperature. The approximate $\mathrm{pH}$ of the soft drink is $\times 10^{-1}$.

(First dissociation constant of $\mathrm{H}_{2} \mathrm{CO}_{3}=4.0 \times 10^{-7}$;

$\log 2=0.3$; density of the soft drink $=1 \mathrm{~g} \mathrm{~mL}^{-1}$ )

Solution:

$\mathrm{P}_{\mathrm{CO}_{2}}=\mathrm{K}_{\mathrm{H}} \times \mathrm{CO}_{2}$

$\frac{3}{30}=\frac{\mathrm{K}_{\mathrm{H}} \cdot \mathrm{n}_{\mathrm{CO}_{2}}}{\mathrm{~K}_{\mathrm{H}} 1} \Rightarrow \mathrm{n}_{\mathrm{CO}_{2}=0.1} \mathrm{~mol}$

$\mathrm{pH}=\frac{1}{2}\left(\mathrm{pka}_{1}-\log \mathrm{c}\right)=\frac{1}{2}(6.4 \times 1)=3.7$

$\mathrm{pH}=37 \times 10^{-1}$