Henry Law Constant For CO₂ In Water Is 1.67x10⁸ Pa At 298 K.Calculate The Quantity Of CO₂ In 500 ml Of Soda Water When Packed Under 2.5 atm CO₂ Pressure At 298 K ?

According to Henry's law, $p_{{\mathrm{CO}}_2}=K_{\mathrm{H}}\chi$

Here $\chi$ is the mole fraction of carbon dioxide in the carbon dioxide water mixture.

$p_{{\mathrm{CO}}_2}$ = 2.5 atm = 2.5 × 1.01325 × 10⁵ Pa = 2.533125 × 10⁵ Pa

$\chi$ = mole fraction = 2.533125 × 10⁵/ 1.67 × 10⁸ = 0.00152

$\chi$ = moles of CO₂/(moles of CO₂ + moles of H₂O)
$\chi$ ≈ moles of CO₂/moles of H₂O  (∵ Moles of CO₂ are negligible in comparison to the number of moles of water)

500 ml of water = 500 g of water = 500/18 = 27.78 moles of water

So, moles of CO₂/27.78 = 0.00152 = 0.042
Hence, the amount of CO₂ in 500 ml of soda water is 0.042 × 44 = 1.848 g