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Question

A gaseous mixture of an equal mass of CH4 and O2 is stored over water. if the total pressure is 0.5atm then the partial pressure of dry CH4 gas is ?(aqueous tension =0.2atm)


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Solution

Step 1 : Given data:

A gaseous mixture contains an equal mass of CH4 and O2

Molecular Mass of CH4=16

Molecular Mass of O2=32

Step 2: Calculation of total moles :
Moles of CH4=x16
Moles of O2=x32

Hence the total moles =(x16)+(x32)=3x32

Step 3: Calculation of Mole fractions of CH4:

Mole fractions of CH4 can be calculated as:

=molesofCH4totalmoles=(x16)(3x32)=23

Step 4:Formula for calculation of partial pressure of any gas:

According to Dalton’s law of partial pressure, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. Dalton’s law is perfectly true for the ideal gas mixture.

Ptotal=P1+P2+P3+......Pi

Where Ptotal = total pressure of the ideal gas mixture

P1,P2,P3,Piare the partial pressures of the gases 1,2,3irespectively

In a mixture of gases, the pressure basically exerted by an individual gas is defined as its partial pressure.

The partial pressure of an individual gas of the ideal gas mixture can be given as:

Pi=xi×p

Where, Pi= Partial pressure

xi= mole fraction

p=total pressure

Step 5: Calculation of partial pressure of CH4:

The partial pressure of CH4 can be calculated as:

Pi=xi×p
=23x0.5=0.33atm

Hence, the partial pressure of dry CH4 gas is calculated to be 0.33atm.


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