Question

A rigid tank contains 2 kg of N2 and 4 kg of Co2 at temperature of 25 C and 1 MPa. Find the partial pressure of each gas respectively?

Answer 1

Answer: Partial pressures are 0.6 MPa for nitrogen gas and 0.4 MPa for carbon dioxide.

Step-by-step explanation: Dalton's Law of Partial Pressure states when there is a mixture of gases the total pressure is the sum of the pressure of each individual gas:

`P_(total) = P_(1)+P_(2)+...`

The proportion of each individual gas in the total pressure is expressed in terms of mole fraction:

`X_(i)` = moles of a gas / total number moles of gas

The rigid tank has total pressure of 1MPa.

• Nitrogen gas:

molar mass = 14g/mol

mass in the tank = 2000g

number of moles in the tank:
`n=(2000)/(14)` = 142.85mols

• Carbon Dioxide:

molar mass = 44g/mol

mass in the tank = 4000g

number of moles in the tank:
`n=(4000)/(44)` = 90.91mols

Total number of moles: 142.85 + 90.91 = 233.76 mols

To calculate partial pressure:

`P_(i)=P_(total).X_(i)`

For Nitrogen gas:

`P_{N_(2)}=1.(142.85)/(233.76)`

`P_{N_(2)}` = 0.6

For Carbon Dioxide:

`P_(total)=P_{N_(2)}+P_{CO_(2)}`

`P_{CO_(2)} = P_(total)-P_{N_(2)}`

`P_{CO_(2)}=1-0.6`

`P_{CO_(2)}=` 0.4

Partial pressures for N₂ and CO₂ in a rigid tank are 0.6MPa and 0.4MPa, respectively.