Gases and the Laws That Govern Their Behavior

All gases obey a set of physical laws Describe the state of a gas by P, V, and T Pressure = force/area Measuring pressure Barometer – measures atmospheric Manometer- measures confined gas

Barometer

Manometer

Gas Laws Boyle P1V1 = P2V2 Charles V1 = V2 T1 T2 Combined P1V1 = P2V2 Avagadro’s n1 = n2 V1 V2

When all together- Ideal Ideal gas Law PV = nRT R = ideal gas law constant 0.0821 L•atm or 8.314 dm3• Kpa mol•K mol•K Most useful for finding molar mass of an unknown that is gaseous or made gaseous

A student collected a sample of gas in a 0 A student collected a sample of gas in a 0.220 L gas bulb until its pressure reached 0.757 atm at a temp of 25º C. The sample had a mass of 0.299 g. Find the molar mass of the gas. Use definition of mole and substitute PV = m RT M = m RT M PV M = (0.299)(0.0821)(298) = 43.0g/mol (0.757 atm)(0.220 L)

Find density of dry air at 15.0C and 1.15 atm if its molar mass (average) is 28.96 g/mol. Assume 1.0 L and plug in m/M for moles and solve. (1.15atm)(1.0 L) = (x/28.96)(0.0821)(288K) X = 1.41g, so density is 1.41g/L

Stoichiometry A student needs to prepare CO2 by decomposing calcium carbonate completely. If 1.25 g of calcium carbonate is decomposed, what will the volume of the gas be if the pressure is 740 mm Hg and the temperature is 25C. CaCO3  CaO + CO2 1.25 g CaCO3 x 1mole CaCO3 x 1 mole CO2 100.09g CaCO3 1 mole CaCO3 0.0125 mole CO2

V = nRT P V = (0.0125)(0.0821)(298) = 0.314 L (740/760)

Dalton’s Law of Partial pressures Pt = P1 + P2 + …Pn Total pressure is equal to sum of partial pressures of all gases in sample. Find the grams of oxygen contained in a 5.00 L tank containing only oxygen and nitrogen if the total pressure is 30 atm and the partial pressure of N2 = 15 atm

PO2 = 15 atm Ideal PVM = g RT (15.0 )(5.00)(32.00) = 98.09 g O2 (0.0821)(298)

Collecting gas over water Gases collected over water are mixtures of the gas and the water vapor pressure, Pt = Patm = PH2O + Pgas A sample of oxygen is collected over water at 20.0 C and a pressure of 738 torr. Its volume is 310 mL. (a) What is the partial pressure of the oxygen?(b) what would its volume be when dry at STP? The vapor pressure of water at 20.0 C is 17.54 torr.

Pox = 738- 17.54 = 720 torr Find volume at STP (720 torr)(310 mL) = (760torr)(V2) 293 K 273 K V2 = 274 mL

Recall Mole Fraction Xa = moles a total moles Multiply by 100 % to get mole % For gases, pressure fractions = mole fractions Find mole fractions of oxygen and nitrogen in air if their partial pressures are 160 torr and 600 torr respectively.

XO2 = 160 torr/760 torr = 0.211 XN2 = 600 torr/760 torr = 0.789 Notice that mole fractions add to = 1.00. To get mole percents, multiply by 100% Mole% O2 = 21.1 % Mole % N2 = 78.9 %

Effusion and diffusion Gas particles will naturally spread throughout any other gases. (cologne or perfume). When gases move through small openings, the movement is called effusion. Gases will move from high to low concentration. High density gases will move more slowly than low density gases

Graham’s Law Rates of effusions of two gases are inversely proportional to the square roots of their densities (or molar masses) when compared at the same pressures and temps. rate a = (db/da)1/2 = (Mb/Ma)1/2 = time b rate b time a Which effuses faster and by what factor NH3 or HCl? (36.46/17.03)1/2 = 1.463; NH3 effuses 1.463 times faster

In an effusion experiment, 45 s were required for a certain number of moles of an unknown gas X to pass through a hole into a vacuum. Under the same conditions it took 28 s for the same number of moles of Ar to effuse. Find the molar mass of the unknown. 28/45 = (39.94/x)1/2 0.387 = 39.94/x X = 39.94/.387 = 103 g/mol

Kinetic theory of Gases Gases consist of small particles in continuous, rapid, random motion which undergo frequent collisions with the containers that hold them. Collisions are elastic, no change in KE Volume of gas particles is negligible compared to distance between particles. Attractive forces between particles have negligible effect on behavior.

Two important postulates: Average translational KE of a gas particle is directly proportional to its absolute temp. Et = ½ mu2 u is average speed of a particle in a sample of gas At a given temp, all gases have same average Translational KE. Average speed is directly proportional to square root of absolute temp.

At 25 C the average speed of an O2 molecule is 482 m/s. u2/u1 = (T2/T1)1/2 ub/ua = (Ma/Mb)1/2 At 25 C the average speed of an O2 molecule is 482 m/s. what is the average speed of an H2molecule at 25C? What is the average speed of an H2 molecule at 125 C?

uH2/uO2 = (32.00/2.016)1/2 = 3.984 uH2 = 3.984 x 482 m/s = 1.92 x 103 m/s At 125 C u2/u1 = (398/298)1/2 = 1.16 = 1.16 x (1.92 x 103m/s) = 2.23x 103 m/s

Real gases As a gas gets closer to the liquid state, the molecules get closer together, and the volume of actual gas particles as well as IMF may begin to affect behavior. (High Pressure and Low temp) When the particles begin to interact, ideal behavior begins to deviate from what we expect or calculate.

Van der Waals equation (P +a/Vm)(Vm – b) = RT This equation is a derivation of the ideal gas law, but contains two constants, a and b which account for the volume of particles, b, and the attractive forces between particles, a. Much better at predicting state of gas at higher P and lower T. Vm is the molar volume of a gas

When the conditions are favorable for deviations, the IMF between molecules will cause pressure to decrease, and the calculated volume would be less than expected. If the volume becomes greater than the calculated volume it would be due to the volume of particles.