Henry’s 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, pCO2 = KHx

Here x is the mole fraction of carbon dioxide in the carbon dioxide water mixture.

pCO2 = 2.5 atm = 2.5 * 1.01325 * 105 Pa = 2.533125 * 105 Pa

x = mole fraction = 2.533125 * 105/ 1.67 * 108 = 0.00152


x = moles of CO2/(moles of CO2 + moles of H2O) ≈moles of CO2/moles of H2Oas mole of CO2are negligible in comparison to the number of moles of water

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

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

Solutiongiven thatPressure of CO2 = 2.5 atm1 atm = 1.01325 × 105 Pa So thatPressure of CO2= 2.5 × 1.01325 × 105 Pa = 2.533125 × 105 PaKH = 1.67 × 108 PaAccording to Henry’s law:p = KH × X X = p / KH = 2.533125 × 105 / 1.67 × 108 = 1.52 x 10–3ButWe have 500 mL of soda water so thatVolume of water = 500 mL[Neglecting the amount of soda present]Density of water = 1 g/ mlUse formula mass = volume × density we get500 mL of water = 500 g of waterMolar mass of water(H2O) = 18 g mol-1 Use formulaNumber of mole of water = 500 / 18 = 27.78 mol of waterNow use the formula of mole fraction Value of mole fraction is very small so it is negligible as compared to 1We get 1.52 × 10–3 = nCO2 / 27.78After calculation we getnCO2 = 0.042 molmolar mass of CO2 = 12 + 2 × 16 = 44 g mol - 1use formulamass = molar mass × number of moles = (0.042 × 44)g = 1.848g

Hello shiva,
The solution of above problem is as follow’s
According to Henry's law, pCO2 = Kh*x
where x = mole fraction of carbon dioxde
pCO2 = 2.5 atm
= 2.5 * 1.01325 * 10^5 Pa
= 2.53 * 10^5 Pa
x = mole fraction = 2.53 * 10^5/ 1.67 * 10^8
= 0.00152
= moles of CO2/(moles of CO2 + moles of H2O)
≈ moles of CO2/moles of H2O (mole of CO2 are negligible)
500 ml of water = 500g of water = 500/18 = 27.78 moles of water
So, moles of CO2/27.78 = 0.00152
moles of CO2 = 0.042 moles
Hence amount of CO2 in 500 ml of soda water is 0.042 * 44 = 1.848 g
Thanks
I hope above solution will clear your all doubts.
Please feel free to post and ask as much doubts as possible.
All the best.