Substances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.

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1 Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed to as vapos. any of the popeties of gases diffe fom those of solids and liquids: Gases ae highly compessible and occupy the full volume of thei containes. When a gas is subjected to pessue, its volume deceases. Gases always fom homogeneous mixtues with othe gases. Gases only occupy a small faction of the volume of thei containes. As a esult, each molecule of gas behaves lagely as though othe molecules wee absent. Pessue Pessue is the foce acting on an object pe unit aea: F P A Lung demo Atmospheic Pessue and the Baomete The SI unit of foce is the newton (N). N kg-m/s The SI unit of pessue is the pascal (Pa). Pa N/m kg-m/s m kg/s m A elated unit is the ba, which is equal to 0 5 Pa. Gavity exets a foce on the Eath s atmosphee. A column of ai m in coss section extending to the uppe atmosphee exets a foce of 0 5 N. Thus, the pessue of a m column of ai extending to the uppe atmosphee is 00 kpa. Atmospheic pessue at sea level is about 00 kpa o ba. The actual atmospheic pessue at a specific location depends on the altitude and weathe conditions.

2 Chapte 0 Atmospheic pessue is measued with a baomete. DEO tube with wate and food coloing. Level example. Now a baomete.. If a tube is completely filled with mecuy and then inveted into a containe of mecuy open to the atmosphee, the mecuy will ise 760 mm up the tube. Standad atmospheic pessue is the pessue equied to suppot 760 mm of Hg in a column. Impotant non-si units used to expess gas pessue include: atmosphees (atm) millimete of mecuy (mm Hg) o to atm 760 mm Hg 760 to.035 x 0 5 Pa 0.35 kpa. The Gas Laws The equations that expess the elationships among T (tempeatue), P (pessue), (volume), and n (numbe of moles of gas) ae known as gas laws. Show Demo of gas immesed in liquid N Gas simulation demos P k(n) P kt P k/ Notice that gas popeties ae elated to the numbe and enegy of gas molecules. Speed is elated to tempeatue. Pessue is elated to n and. 0.4 The Ideal-Gas Equation Ideal gas equation: P n An ideal gas is a hypothetical gas whose P,, and T behavio is completely descibed by the ideal-gas equation. R gas constant L-atm/mol-K Define STP (standad tempeatue and pessue) 0 C, 73.5 K, atm. The mola volume of mol of an ideal gas at STP is.4 L. Do some example calculations using Pn What is the volume of gas poduced when 0.0 moles of NaHCO3 is eacted with 00 ml of 0. CH3COOH (aq)? a) Balance

3 Gases b) Limiting eagent compute moles of gas c) P n d) 0.0*0.0806*98/ (L) 0.45 L WHAT WOULD THE OLUE BE IF THE PRESSURE WERE 0.8 AT? In geneal, if we have a gas unde two sets of conditions, then P n T We often have a situation in which P,, and T all change fo a fixed numbe of moles of gas. Fo this set of cicumstances, P n T Which gives P T nr constant P T P T Futhe Applications of the Ideal-Gas Equation Gas Densities and ola ass Density has units of mass ove volume. Reaanging the ideal-gas equation with as mola mass we get n P n P The mola mass of a gas can be detemined as follows: P d

4 Chapte 0 d P Gas ixtues and Patial Pessues Since gas molecules ae so fa apat, we can assume they behave independently. Dalton obseved: The total pessue of a mixtue of gases equals the sum of the pessues that each would exet if pesent alone. Patial pessue is the pessue exeted by a paticula component of a gas mixtue. Dalton s law of patial pessues: In a gas mixtue the total pessue is given by the sum of patial pessues of each component: P t P + P + P 3 + Each gas obeys the ideal gas equation. Thus, P ( n + n + n3 +!) t Patial Pessues and ole Factions Let n be the numbe of moles of gas exeting a patial pessue P, then P C P t Whee C is the mole faction (n /n t ). Note that a mole faction is a dimensionless numbe. n t

5 Gases

6 Chapte olecula Effusion and Diffusion The aveage kinetic enegy of a gas is elated to its mass: e ½ mu Conside two gases at the same tempeatue: the lighte gas has a highe ms speed than the heavie gas. athematically: u The lowe the mola mass,, the highe the ms speed fo that gas at a constant tempeatue. Two consequences of the dependence of molecula speeds on mass ae: Effusion is the escape of gas molecules though a tiny hole into an evacuated space. Diffusion is the spead of one substance thoughout a space o thoughout a second substance. Gaham s Law of Effusion The ate of effusion can be quantified. Conside two gases with mola masses, and, and with effusion ates, and, espectively: The elative ate of effusion is given by Gaham s law: 3 Only those molecules which hit the small hole will escape though it. Theefoe, the highe the ms speed the moe likely that a gas molecule will hit the hole. We can show Diffusion and ean Fee Path Diffusion is faste fo light gas molecules. Diffusion is significantly slowe than the ms speed. Diffusion is slowed by collisions of gas molecules with one anothe. Conside someone opening a pefume bottle: It takes awhile to detect the odo, but the aveage speed of the molecules at 5 C is about 55 m/s (50 mi/h). The aveage distance taveled by a gas molecule between collisions is called the mean fee path. At sea level, the mean fee path fo ai molecules is about 6 x 0 6 cm. Simila mola mass elated issues (e.g., passing of paticles of solute though semipemeable membanes) fo solutions will be discussed in Ch. 3 (section 3.5). 0.9 Real Gases: Deviations fom Ideal Behavio Fom the ideal gas equation: Fo mol of an ideal gas, P/ fo all pessues. In a eal gas, P/ vaies fom significantly. The highe the pessue the moe the deviation fom ideal behavio. u u P n

7 Gases Fo mol of an ideal gas, P/ fo all tempeatues. As tempeatue inceases, the gases behave moe ideally. The assumptions in the kinetic-molecula theoy show whee ideal gas behavio beaks down: The molecules of a gas have finite volume. olecules of a gas do attact each othe. As the pessue on a gas inceases, the molecules ae foced close togethe. As the molecules get close togethe, the fee space in which the molecules can move gets smalle. The smalle the containe, the moe of the total space the gas molecules occupy. Theefoe, the highe the pessue, the less the gas esembles an ideal gas. As the gas molecules get close togethe, the intemolecula distances decease. The smalle the distance between gas molecules, the moe likely that attactive foces will develop between the molecules. Theefoe, the less the gas esembles an ideal gas. As tempeatue inceases, the gas molecules move faste and futhe apat. Also, highe tempeatues mean moe enegy available to beak intemolecula foces. As tempeatue inceases, the negative depatue fom ideal-gas behavio disappeas. The van de Waals Equation We add two tems to the ideal gas equation to coect fo The volume of molecules: nb Fo molecula attactions: ( ) & n a # $! % " The coection tems geneate the van de Waals equation: ' n a $ % P " + ( nb) n & # whee a and b ae empiical constants that diffe fo each gas. van de Waals constants fo some common gases can be found in Table 0.3. To undestand the effect of intemolecula foces on pessue, conside a molecule that is about to stike the wall of the containe. The stiking molecule is attacted by neighboing molecules. Theefoe, the impact on the wall is lessened.