Answer:
Explanation:
Follow the steps suggested:
1. What is given:
i) Initial conditions, volume, pressure and temperature of three gases in connected, but separate containers.
a) He:
Volume: 1.5 liter
Pressure: 0.5 atm
Temperature: 298K
b) Ar:
Volume: 0.5 liter
Pressue: 2.0 atm
Temperature: 298 K
c) N₂: 1.0 liter
Pressure: 1.0 atm
Temperature: 298 K
ii) The final volume of the mixture of gases, at the same temperature of the intial gases.
a) V = 3.0liter
b) T = 298K
2. What do you want to know?
a) The partial pressure of the He gas in the mixture.
3. What else do you need to know.
a) You should calculate the number of moles of He gas.
b) You will need the ideal gas equation
c) You will need the universal constant of gases:
- R = 0.08206atm×liter / (k×mol)
d) You must know that in a mixture, the partial pressure of every gas is calculated as if each gas occupied the complete volume of the container.
You do not need to find the number of moles of the other gases.
Solution
1. Use the ideal gas equation to find the number of moles of He from the initial conditions:
[tex]pV=nRT[/tex]
[tex]n=\dfrac{pV}{RT}[/tex]
Substitute:
[tex]n=\dfrac{0.5atm\times 1.5liter}{0.08206atm\cdot liter/(K\cdot mol)298K}=0.03067mol[/tex]
2. Calculate the pressure of that amount of He gas at the final conditions
[tex]P=\dfrac{nRT}{V}\\\\\\P=\dfrac{0.03067mol\times 0.08206atm\cdot liter/(k\cdot mol)\times 298K}{3.0liter}[/tex]
[tex]P=0.25atm[/tex]
