Answer:
The partial pressure of the [tex]CO_2[/tex] 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 =[tex]n_1= 2 kmol[/tex]
Moles of carbon dioxide gas =[tex]n_2=8 kmol[/tex]
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 =[tex]p_{N_2}^o[/tex]
Partial pressure of carbon dioxide=[tex]p_{CO_2}^o[/tex]
[tex]p_{N_2}^o=p\times \frac{n_1}{n_1+n_2}[/tex]
[tex]p_{N_2}^o=250 kPa\times \frac{0.2}{0.2+0.8}=50 kPa[/tex]
[tex]p_{CO_2}^o=p\times \frac{n_2}{n_1+n_2}[/tex]
[tex]p_{CO_2}^o=250 kPa\times \frac{0.8}{0.2+0.8}=200 kPa[/tex]
The partial pressure of the [tex]CO_2[/tex] in the final mixture is 200 kPa.
