5.6-5.7 Mixtures of Gases, Partial Pressure, Gases in Chemical Reactions & KMT

Partial Pressures of Gases in Mixtures Each gas, in a mixture of gases, exert a specific amount of pressure. This pressure can be calculated using the ideal gas law: RT RT RT Pa = na ------; Pb = nb ------; Pc = nc ------- V V V If the total name pressure of a mixture is known, as well as a few partial pressures, Daltons Law of Partial Pressures could be used: Ptotal = Pa + Pb + Pc … na Partial Pressure can also be calculated using the mole fraction: Xa = ------ ntotal Pa = XaPtotal

Let’s Try a Sample Problem A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 755 torr and the water vapor has a partial pressure of 24 torr. What amount (in moles) of hydrogen gas is contained in 1.55 L of this mixture at 298 K? Ptotal = PH2 + PH2O = 755 torr = PH2 + 24 torr PH2= 731 torr nRT PV P = ------ n = ------- V RT (731 torr)(1.55 L) n = ---------------------------------------- = 6.10X10-2 mol H2 (62.36 L torr / mol K)(298 K)

Let’s Try Another A deep sea diver breathes a heliox mixture with an oxygen mole fraction of 0.050. What must the total pressure be for the partial pressure of oxygen to be 0.21 atm? PO2 = XO2 (Ptotal) PO2 O.21 atm Ptotal = ------- = -------------- XO2 0.050 Ptotal = 4.2 atm

Gases in Chemical Reactions In the following reaction, 4.58 L of O2 was formed at P = 745 mmHg and T = 308 K. How many grams of Ag2O decomposed? 2Ag2O(s)  4 Ag(s) + O2(g) PV (745 mmHg)(4.58 L) n = ----- = ------------------------------------- = 0.178 mol O2 RT (62.36 L torr/mol K)(308 K) 2 mol Ag2O 231.74 g Ag2O 0.178 mol O2 X ---------------- X ---------------------- = 82.5 g Ag2O 1 mol O2 1 mol Ag2O

Kinetic Molecular Theory (KMT) KMT: A gas is modeled as a collection of particles in constant motion. These particles could be atoms or molecules depending on the gas. Gas particles move in straight line motions. The size of the a particle (volume) is negligibly small. The average kinetic energy (KE) of a particle is proportional to the temperature in kelvins. This means that two gases, under the same temperature conditions, will have the same kinetic energy, regardless of the size of the gas particles. This occurs because lighter particles travel faster (on average) than heavier ones. KE per molecules = ½mv2  on your reference table! Collisions between particles are completely elastic.

Walk Me Through This Depiction Draw a depiction, as described by kinetic molecular theory, of a gas sample containing equal amounts of argon and xenon. Use red dots to represent argon atoms and blue dots to represent xenon atoms (In your notebooks, you could use chemical symbols in circles rather than colors). Give each atom a “tail” to represent its velocity relative to the others in the mixture. Also, under which temperature and pressure conditions are real gases most like ideal gases? High temperature and low pressure. Ideal gases are said to have no attraction between particles, but we know that real gases are attracted to each other by intermolecular forces.

Root Mean Square If it were possible to find the velocity of each individual molecule of each gas in a gas sample, than it would be possible to calculate the average velocity of each gas. To calculate this velocity, the rms formula is used: Urms = 3𝑅𝑇 _____________ 𝑀 (where M = molar mass in kg/mol) (and R= 8.314 J / mol K) ( a joule = kg m2/s2) All this is saying is that molecules that are less massive will be moving faster, under the same temperature conditions.

Let’s Try a Practice Problem Calculate the root mean square velocity of the gaseous xenon atoms at 25oC? Urms = 3𝑅𝑇 _____________ 𝑀 K = 273 + 25 = 298 K R = 8.314 J / mol K ( a joule = kg m2/s2) M = 0.13129 kg / mol Urms = 3(8.314)(298) _____________ 1.31𝑋10−1 = 238 m/s

Another Depiction Problem Three gases, taking up the same volume of space will be drawn on the board. Gas sample one has 7 small gas particles in a given area, gas sample two, has 7 large particles in a given area, and gas sample three has 10 small gas particles in the same size area. Assume that the mass of each particle is proportional to its size and that all gases are at the same temperature. Which sample of an ideal gas has the greatest pressure, and why? Gas sample three has the greatest pressure because less massive particles will move at a greater velocity, and if there are more particles there will be more collisions with each other, as well as will the walls of the container. These collisions in the given area result in a force that we call pressure.

5.6-5.8 pg. 240-241 #’s 62, 66, 70, 72, 82, 90 Read 5.9-5.10 pgs. 229-234