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

Answer:

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

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=$p_{CO_2}^o$

$p_{N_2}^o=p\times \frac{n_1}{n_1+n_2}$

$p_{N_2}^o=250 kPa\times \frac{0.2}{0.2+0.8}=50 kPa$

$p_{CO_2}^o=p\times \frac{n_2}{n_1+n_2}$

$p_{CO_2}^o=250 kPa\times \frac{0.8}{0.2+0.8}=200 kPa$

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