Henry’s law constant for CO2 in water is 1.67 × 108 Pa at 298 K. Calculate the quantity of CO2 in 500 mL of soda water

Henry’s law constant for CO2 in water is 1.67 × 10⁸ 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.

Solution

given that

Pressure of CO₂ = 2.5 atm

1 atm = 1.01325 × 10⁵ Pa So that

Pressure of CO₂= 2.5 × 1.01325 × 10⁵ Pa = 2.533125 × 10⁵ Pa

K_H = 1.67 × 10⁸Pa

According to Henry’s law:

p = K_H × X

 X  = p / K_H  = 2.533125 × 10⁵ / 1.67 × 10⁸  = 1.52 x 10^–3

But

We have 500 mL of soda water so that

Volume of water = 500 mL

[Neglecting the amount of soda present]

Density of water = 1 g/ ml

Use formula mass = volume × density we get

500 mL of water = 500 g of water

Molar mass of water(H₂O) = 18 g mol^-1  

Use formula

Number of mole of water = 500 / 18 =  27.78 mol of water

Now use the formula of mole fraction 

 

Value of mole fraction is very small so it is negligible as compared to 1

We get  

                          

1.52 × 10^–3 = n_CO2/ 27.78

After calculation we get

n_CO2 = 0.042 mol

molar mass of CO₂ = 12 + 2 × 16 = 44 g mol _{- 1}

use formula

mass = molar mass × number of moles

       = (0.042 × 44)g

= 1.848 g