A 500mL Soda water is packed under 2.5 atm and CO2 pressure at 298 K. Find out the quantity of CO2 present in the bottle if Henry’s law constant for CO2 in water is 1.67x108 Pa at 298 K.
Step 1: Given Data
Pa Pressure of
Step 2: Formula used
According to Henry’s law, the amount of gas that is dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid when the temperature is kept constant.
The constant of proportionality for this relationship is called Henry’s law constant (usually denoted by ‘). The mathematical formula of Henry’s law is given by:
Where ‘P’ denotes the partial pressure of the gas in the atmosphere above the liquid., ‘C’ denotes the concentration of the dissolved gas., ‘’ is Henry’s law constant of the gas., X is a mole fraction of gas.
Step 3: Determining pressure of the gas
We know that
So Pressure of
Step 4: Applying Henry's Law
According to the relationship,
Step 5: Calculating moles of water
Given that the bottle containsof soda water
Volume of water =
Density of water =
Molar mass of water is
Number of moles of water = Mass/(Molar mass)
Step 6: Calculating mass of gas
We know that mole fraction
Value of mole fraction is negligible as compared to one
Molar mass of
Mass = molar mass x Number of moles
Hence, the quantity of Carbon dioxide present in the bottle is