S L G. Chapter 12: The Behavior of Gases. I. First Concepts a. The 3 states of matter most important to us: solids, liquids, and gases.

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1 Chapter : he ehaior of Gases I. First Concepts a. he 3 states of atter ost iportant to us: solids, liquids, and gases. S L G b. Real Gases and Ideal Gases i. Real gases exist, ideal gases do not ii. Under conditions of high teperature and low pressure, an ideal gas approxiates the behaior of a real gas. his is because at high and low P, the particles are far apart, and therefore do not interact as strongly with one another. iii. ssuptions of the ideal gas odel. he particles are tiny point asses of zero olue. he particles do not interact with each other (do not attract or repel one another) 3. he particles collide with each other and the walls of the container with perfect elasticity. a. n elastic collision is one in which the particle loses no energy of otion. (his is ipossible). b. In reality, all collisions are inelastic. hat is, when a basketball is dropped and bounces off the ground, the ball does not bounce back up to the height fro which it was dropped. Soe of the energy is lost to friction and ibration. c. Force and Pressure i. Force is any push or pull on an object. F ass x acceleration x a. he units of force: kg kg x N (newtons) s s ii. Pressure is the force exerted on an object per unit area F force N. P Pa pascal area. he pressure of the gases of the atosphere that is pushing on each one of us and on all objects is called atospheric pressure. 3. Standard atospheric pressure the pressure that is exerted by the atosphere at sea leel on a pleasant day of cal weather. 4. Standard atospheric pressure a..3 kpa b. 76 Hg c.. at 5. baroeter is an instruent used to easure gas pressure. It is a tube of ercury that is inerted in a bath of ercury. On a nice day at sea leel, the atosphere will support a colun of ercury to a height of 76. d. Conerting units of pressure. II. Deonstrating the effects of pressure with a acuu pup and bell jar III. oyle s law a. he relationship between P and V is inerse (at constant ). b. If P increases, then V decreases and ice-ersa. c. he graph is hyperbolic (akes a hyperbola). Cured is an OK description for our purposes. Volue Pressure d. PV k e. P V P V IV. Charles s Law a. he relationship between and V is direct (at constant P). b. If increases, then V increases. If decreases, then V decreases. c. he graph is linear with a positie slope.

2 6 4 (P ) is standard pressure, and the new teperature ( ) is standard teperature. Volue Std P at Std o C 73 K 5 5 eperature d. V / k V V e. f. eperature ust always be in Kelins V. Gay-Lussac s Law a. he relationship between and P is direct (at constant V). b. If increases, then P increases. If decreases, then P decreases. c. he graph is linear with a positie slope. Pressure eperature d. P/ k P P e. f. eperature ust always be in Kelins VI. he Cobined Gas Law a. his cobines the first three gas laws b. PV/ k PV PV c. d. Major helpful tip: Cobined gas law probles often require you to find the new olue of a gas at SP. his eans that the new pressure e. eperature ust always be in Kelins VII. he Ideal Gas Law a. his suarizes all gas behaior, including the effect of adding ore oles of gas b. Sybol for oles n PV PV c. n n d. Often, this equation is used in this forat: PV nr e. R the ideal gas constant. You don t need to eorize the alue of R, but you probably will end up doing so as a result of doing the hoework. L at f. R.8 K ol VIII. Dalton s Law of Partial Pressures a. Dalton s Law of Partial Pressures: he pressure of a ixture of gases is equal to the suof the prtial pressures of each of the indiidual gases in the ixture. b. P total P + P + P P n, where n the total nuber of gases in the ixture c. Suppose that three different gases in three separate but identicallysized containers are all cobined into one container. he resulting pressure of this ixture of gases ust equal the su of the indiidual pressures.

3 P + P + P C P total exactly equal to the reerse process of condensation, waterwater apor equilibriu is achieed. iii. When this equilibriu is achieed, the water apor present, like any gas, will exert a pressure. i. his pressure of water apor by itself, the partial pressure of water apor, ust be subtracted fro the total pressure of the gas collected in order to deterine the pressure of the pure gas, also called the dry gas pressure.. Exaine the diagra of three flasks. 3 at 4 at 5 at at d. Vocabulary note: P a 3at is pronounced, the partial pressure of gas is 3 atospheres. he partial pressure of a gas is the pressure that the gas in soe ixture would exert if it were the only gas present in the container. e. his is an iportant principle. It is iportant to notice that the sizes of the particles and the identities of the gases inoled are uniportant. Dalton s Law holds true for any ixture of gases. his obseration is closely related to the work of an Italian scientist, adeo ogadro. f. ogadro s hypothesis i. Equal olues of any gases ust contain the sae nuber of particles (as long as the gases are at the sae tep and pressure). ii. his is a rearkable stateent, because it holds true een when the gas particles are not the sae size. For instance, liter of H gas (. g/ol) and liter of UF 6 gas (35 g/ol) both contain the sae nuber of particles. iii. his counterintuitie stateent akes sense if one takes into account the fact that the distances between the particles are so great that the olues of the indiidual particles are negligible. g. ogadro s nuber i. adeo ogadro didn t actually deterine ogadro s nuber (N 6. x 3 ). It was deterined 9 years after he was dead. Howeer, the nuber is naed in his honor because ogadro s ideas and work paed the way to the deterination of the size of one ole. h. Collecting gas oer water i. n iportant application of Dalton s Law is the coputation of the pressure of a pure gas when the gas is collected oer water. ii. When gas is collected oer water, the water eaporates to a sall extent. Eentually the water will reach equilibriu. his eans that the water will continue to eaporate, but the net rate of eaporation reaches zero. When the rate of eaporation is he water in flask will eaporate, and because the container is open to the air, its net eaporation will continue also. Container is closed, but the water will still eaporate. In diagra C, we see that the water is still eaporating, but the net eaporation has stopped. he net eaporation has a rate of zero because the rate of eaporation is equaled by the rate of condensation. hat is, eery tie a water olecule eaporates, another water apor olecule condense. his state of balance is called equilibriu. (In P Cheistry you will learn that this is actually a dynaic equilibriu, as opposed to a static equilibriu.) i. Exaine the diagra below of the lab set-up for generating hydrogen gas and collecting oer water.

4 ii. Once the hydrogen gas is collected oer water, there is also a certain aount of water apor collected along with the hydrogen. herefore, we ust look up the apor pressure of water at the teperature of the lab that day, and subtract that pressure away for the total pressure of the gas collected. P total P hydrogen + P water apor his inforation can be looked up in a table that is located in your book. re is a partial table below IX. Graha s Law of Effusion a. ll substances sitting in our classroo are at the sae teperature, except the huan beings and probably the electrical deices. When hot and cold objects are in contact for a long tie, they reach theral equilibriu, that is, they will reach the sae teperature. b. hus, the air in the classroo has the sae teperature as the desks and the chairs and the walls. c. eperature how hot or cold an object is is a easure of the aerage kinetic energy of the particles of a substance. (Kinetic energy is the energy of otion.) he particles of all substances at the sae teperature hae the sae aerage kinetic energy. d. he K.E. of an object is deterined by how big the object is and how fast the object is oing. (Which has ore KE: a baseball oing at 5 ph or a truck oing at 5 ph? Which has ore KE: a baseball oing at 5 ph or a baseball oing at ph?) KE ½ x x ( elocity, which for our purposes is the sae thing as speed) e. KE his is the kinetic energy of a particle of a gas f. Let us consider two different gases, Gas and gas, that hae different asses. If both gases hae the sae teperature, then the particles of both gases ust hae the sae aerage KE. What does this tell us about the speeds of the particles of the two different gases? g. KE of gas KE of gas If gas and gas are at the sae teperature, then their KEs are equal. KE of gas KE of gas

5 4.58 nswer: particles are lighter than particles, thus the heliu will effuse fro its balloon ore quickly than the krypton will effuse fro the balloon full of. he gas will effuse 4.58 ties faster than the gas will effuse. *** (we will ignore the negatie root!) *** Graha s Law of Effusion h. Graha s Law of Effusion: he ratio of the elocities of the particles of two different gases is inersely proportional to the square root of the ratio of the asses of the particles. i. Exaple Proble: wo different balloons hae been filled with two different gases: one contains heliu () and the other contains krypton (). If the balloons both deelop leaks of the sae size, which gas will effuse (leak out of the balloon) ore quickly? How any ties ore quickly will it leak? Solution: Do not try to sole for a or b. Sole for the ratio b/ a! ssign each gas to a letter. Put the lighter gas on top (Gas ). 4. g/ol, 83.8 g/ol. Gas (it s lighter), Gas (it s heaier) X. Gas Density and Deterining Molecular Mass of Gases nuber of gras a. D V nuber of liters b. Preiously, we used units of g/l (g/c 3 ) to express density. Howeer, because gases are typically thousands of ties less dense than liquids and solids, it is ore conenient to use g/l to express their densities. c. Reeber: density of a substance does not depend on the aount of the substance. (Does ass depend on the aount of the substance? Yes. Does color? No. Density is ore like color, which is an intrinsic property.) herefore, when calculating the density of gases, we can assue any aount of the gas that is conenient for us. o ake things easy on yourself, always assue one ole of gas for your calculations. (You can assue any aount that you want, and the proble will still work. It will take longer to sole, though.) d. Why assue one ole of gas? re s why: because the ass of one ole of any gas can be looked up on the periodic table. (Reeber: the olar ass of a substance is the ass of one ole. ) dditionally, the olue of a ole of any gas is.4 liters (at SP). he.4 L/ol alue is only alid for gases at SP, but I will only test you on gas densities at SP for the sake of siplicity. (It should be noted, howeer, that you could deterine the gas density at any conditions using the cobined gas law.) e. Exaple proble: Find the density of H gas at SP. Solution: ass of one ole D V olue of one ole at SP. g (froperiodic table) D.4 L D.9 g/l XI. Gas Stoichioetry.95