Henry's law constant for $\displaystyle \mathrm{CO}_{2}$ in water is $\displaystyle 1.67 \times 10^{8} \mathrm{~Pa}$ at $\displaystyle 298$ K. Calculate the number of moles of $\displaystyle \mathrm{CO}_{2}$ in $\displaystyle 500$ ml of soda water when packed under $\displaystyle 2.53 \times 10^{5} \mathrm{~Pa}$ at the same temperature.

pCO2 = KH ꭓCO2 KH = $\displaystyle 1.67$ x $\displaystyle 108$ Pa pCO2 = $\displaystyle 2.53$ x $\displaystyle 105$ Pa ꭓCO2 = pCO2 / KH =$\displaystyle 1.51$ x $\displaystyle 10$-$\displaystyle 3$ ꭓ𝐶𝑂$\displaystyle 2$= 𝑛𝐶𝑂$\displaystyle 2$ 𝑛𝐻$\displaystyle 20$ nH2O = $\displaystyle 500$/$\displaystyle 18$ = $\displaystyle 27.78$ moles nCO2 =$\displaystyle 27.78$ X $\displaystyle 1.51$ X $\displaystyle 10$-$\displaystyle 3$ moles = $\displaystyle 42.0$ X $\displaystyle 10$-$\displaystyle 3$ mol = $\displaystyle 0.042$ moles