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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.


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Solution

Step 1: Given Data

KH=1.67×108

Pa Pressure ofCO2=2.5atm

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 ‘kH). The mathematical formula of Henry’s law is given by:

PC(or)P=kH.COrX=kH.P

Where ‘P’ denotes the partial pressure of the gas in the atmosphere above the liquid., ‘C’ denotes the concentration of the dissolved gas., ‘kH’ 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

1atm=1.01235x105Pa

So Pressure ofCO2=2.5x1.01235x105Pa

=2.533125x105Pa

Step 4: Applying Henry's Law

According to the relationship, p=KHxX

X=p/KH=2.533125x105Pa/1.67×108PaX=1.52x10-3

Step 5: Calculating moles of water

Given that the bottle contains500mLof soda water

Volume of water = 500mL

Density of water = 1g/mL

Mass=VolumeXDensityMass=500x1=500

Molar mass of water is 18g/mol

Number of moles of water = Mass/(Molar mass)

n=500/18=27.78

Step 6: Calculating mass of gas

We know that mole fractionX=nCO2(nCO2+nH2O)

Value of mole fraction is negligible as compared to one

HenceX=nCO2(nH2O)1.52x10-3

=nCO227.78nCO2

Molar mass ofCO2=44g/mol

Mass = molar mass x Number of moles

=0.042X44=1.848g

Hence, the quantity of Carbon dioxide present in the bottle is 1.848g


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