Worksheet 12 - Partial Pressures and the Kinetic olecular Theory of Gases Dalton's Law of Partial Pressures states that the sums of the pressures of each gas in the mixture add to give the total pressure (P tot = P 1 + P 2 + P 3 +...) 1. The stopcock between a 3.00 L bulb containing oxygen at 295 torr and a 1.00 L bulb containing nitrogen at 530 torr is opened. What is the total pressure of the mixture (assume constant T = 25.0 o C)? P tot = P oxygen + P nitrogen You can treat each gas separately. After mixing, there will be the same number of moles of each gas, at the same T, just in a different volume. a) For oxygen, P 1 V 1 = P 2 V 2 V 1 = L V 2 = L P 1 = atm P 2 = atm b) For nitrogen, P 1 V 1 = P 2 V 2 V 1 = L V 2 = L P 1 = atm P 2 = atm c) P tot = P O2 + P N2 = atm Another useful concept is that of the mole fraction, X. This is defined as the number of moles of a particular gas in a mixture of gases, divided by the total number of moles of gas. d) Use the information given above to calculate the number of moles of oxygen, nitrogen and total moles of gas present.
mol O 2 = mol N 2 = mol tot = e) Calculate the mole fraction of each of the gases X O2 = X N2 = f) Given the number of moles present in the mixture, calculate the total pressure of the gas after mixing. The total pressure is equal to the sum of the partial pressure of each gas. The partial pressure of each gas is equal to its mole fraction times the total pressure. P tot = P A + P B + P C +... = X A P tot + X B P tot + X C P tot +... This also means that P A /P tot = X A g) Using this formula, calculate the partial pressure of oxygen and nitrogen in the mix. P O2 = atm P N2 = atm Compare these results to those you calculated in parts b) and c)
2. A sample of nitrogen gas is collected over water at 20. o C and a pressure of 1.00 atm. The volume of the collected gas is 250.0 L. What is the mass of N 2 collected? (At 20. o C, the vapor pressure of water is 17.5 torr). P tot = P nitrogen + P water P nitrogen = mass of N 2 = g 3. Oxygen is pumped into a tank to supply breathing air for scuba diving, until the gas pressure reaches 4.05 atm. Helium is then pumped in until the total pressure is 20.00 atm. The gases mix completely. What is the partial pressure of each gas in the tank? P tot = P oxygen + P helium P oxygen = atm P helium = atm The tank is used until the total pressure is 9.50 atm. What are the partial pressures of each gas? (Calculate X oxygen and X helium ) X oxygen = X helium = P oxygen = atm P helium = atm
The Kinetic olecular Theory of Gases explains the behavior of ideal gases. Shown below are the assumptions that this model makes: 1. The volume of the gaseous molecules is negligible compared to the total volume in which the gas is contained. Ideal gases are viewed as having mass but no volume. 2. The gaseous molecules are in constant, random motion. Their collisions with the walls of the container are the cause of the pressure exerted by the gas. 3. Attractive and repulsive forces between molecules are negligible. Ideal gases do not interact, chemically, with any other matter. 4. Energy can be transferred between molecules during collisions, but the average kinetic energy of the particles does not change with time, as long as the temperature remains constant (elastic collisions). 5. The average kinetic energy of the molecules is proportional to the absolute temperature (K) of the gas. At any given temperature the molecules of all gases have the same average kinetic energy. 4. Consider two gases, A and B, in containers of equal volume. Both are at the same V, T and P. A mass: 0.34 g 0.48 g Are the following statements true or false? Why? a) The number of molecules of A is equal to the number of molecules of B b) The molar mass of A is greater than the molar mass of B B c) Both samples have the same average kinetic energy. d) The molecules of A have the same average velocity as the molecules of B
e) The molecules of A collide with the container walls more frequently than the molecules of B Graham's Law of Effusion Graham found that the average velocity of a molecule is inversely proportional to the square root of the molar mass,. u = average velocity = constant x 1 For two gases: u1 u 2 2 1 5. You are given two balloons, one filled with helium and the other with oxygen. How much faster will the He effuse through the pores in the rubber, than the O 2?