Henry's law constant for `CO_2` in water is 1.67 kbar at `25^@ C`. The quantity of `CO_2` in 1000 mL of soda water when packed under 5 bar `CO_2` pressure at `25^@ C` is

Options

A. 0.084 mol
B. 0.167 mol
C. 0.252 mol
D. 0.336 mol

Answer

B

Explanation

Given,
Pressure of ` CO_2 = 5 ` bar
`(P)= 5 xx 10^5 ` Pa
` K_H = 1.67 xx 10^8 ` Pa
From Henry's law `P= K_H = (5xx 10^5)/(1.67 xx 10^8)`
`rArr X = 2.99 xx 10^(-3)`
Volume of water (soda water) `= 1000 ml`
Density of water = 1 g/ml
Mass = Volume `xx` density.
So 1000 ml of water = 1000 g of water
Molar mass of water `(H_2 O)= 18 g //ml.`
Number of moles of water `(H_2 O) = ("Mass")/("Molar water")= (1000)/(18) = 55.55 ml ` of water
Mole fraction `= (n^(co_2))/(n_(co_2) + n_(H_2 O))`
`2.99 xx 10^(-3) = (n_(co_2) )/(55.55)`
`n_(co_2) = 0.167` mol