Question

A rigid tank is divided into two equal volumes. One side contains 2 kmol of nitrogen N2 at 500 kPa while the other side contains 8 kmol of CO2 at 200 kPa. The two sides are now connected and the gases are mixed and forming a homogeneous mixture at 250 kPa. Find the partial pressure of the CO2 in the final mixture.

Answer 1

The partial pressure of the
`CO_2` in the final mixture is 200 kPa.

Step-by-step explanation:

Pressure of nitrogen gas when the two tanks are disconnected = 500 kPa

Pressure of the carbon-dioxide gas when the two tanks are disconnected = 200 kPa

Moles of nitrogen gas =
`n_1= 2 kmol`

Moles of carbon dioxide gas =
`n_2=8 kmol`

After connecting both the tanks:

The total pressure of the both gasses in the tank = p = 250 kPa

According to Dalton' law of partial pressure:

Total pressure is equal to sum of partial pressures of all the gases

Partial pressure of nitrogen =
`p_(N_2)^o`

Partial pressure of carbon dioxide=
`p_(CO_2)^o`

`p_(N_2)^o=p* (n_1)/(n_1+n_2)`

`p_(N_2)^o=250 kPa* (0.2)/(0.2+0.8)=50 kPa`

`p_(CO_2)^o=p* (n_2)/(n_1+n_2)`

`p_(CO_2)^o=250 kPa* (0.8)/(0.2+0.8)=200 kPa`

The partial pressure of the
`CO_2` in the final mixture is 200 kPa.