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Chapter 12 BEHAVIOR OF GASES Dr. S. M. Condren

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BEHAVIOR OF GASES Dr. S. M. Condren

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**Importance of Gases Airbags fill with N2 gas in an accident.**

Gas is generated by the decomposition of sodium azide, NaN3. 2 NaN3 2 Na N2 if bag ruptures 2 Na H2O 2 NaOH + H2 Dr. S. M. Condren

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THREE STATES OF MATTER Dr. S. M. Condren

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THREE STATES OF MATTER Dr. S. M. Condren

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**General Properties of Gases**

There is a lot of “free” space in a gas. Gases can be expanded infinitely. Gases occupy containers uniformly and completely. Gases diffuse and mix rapidly. Dr. S. M. Condren

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**Properties of Gases V = volume of the gas (L) T = temperature (K)**

Gas properties can be modeled using math. Model depends on— V = volume of the gas (L) T = temperature (K) n = amount (moles) P = pressure (atmospheres) Dr. S. M. Condren

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Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Dr. S. M. Condren

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Pressure Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). P of Hg pushing down related to Hg density column height Dr. S. M. Condren

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**Pressure Column height measures P of atmosphere**

1 standard atm = 760 mm Hg = 29.9 inches Hg = about 34 feet of water SI unit is PASCAL, Pa, where 1 atm = kPa Dr. S. M. Condren

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**Effect of Pressure Differential**

Dr. S. M. Condren

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**P V = n R T IDEAL GAS LAW Brings together gas properties.**

Can be derived from experiment and theory. Dr. S. M. Condren

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**Boyle’s Law If n and T are constant, then PV = (nRT) = k**

This means, for example, that P goes up as V goes down. Robert Boyle ( ). Son of Earl of Cork, Ireland. Dr. S. M. Condren

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**Boyle’s Law A bicycle pump is a good example of Boyle’s law.**

As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. Dr. S. M. Condren

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Boyle’s Law Dr. S. M. Condren

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**Charles’s Law If n and P are constant, then V = (nR/P)T = kT**

V and T are directly related. Jacques Charles ( ). Isolated boron and studied gases. Balloonist. Dr. S. M. Condren

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**Charles’s original balloon**

Modern long-distance balloon Dr. S. M. Condren

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Charles’s Law Balloons immersed in liquid N2 (at -196 ˚C) will shrink as the air cools (and is liquefied). Dr. S. M. Condren

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Charles’s Law Dr. S. M. Condren

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**Avogadro’s Hypothesis**

Equal volumes of gases at the same T and P have the same number of molecules. V = n (RT/P) = kn V and n are directly related. twice as many molecules Dr. S. M. Condren

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**Avogadro’s Hypothesis**

The gases in this experiment are all measured at the same T and P. 2 H2(g) O2(g) 2 H2O(g) Dr. S. M. Condren

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**Combining the Gas Laws V proportional to 1/P V prop. to T V prop. to n**

Therefore, V prop. to nT/P V = 22.4 L for 1.00 mol when Standard pressure and temperature (STP) ST = 273 K SP = 1.00 atm Dr. S. M. Condren

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Using PV = nRT How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC? R = L•atm/K•mol memorize Solution 1. Get all data into proper units V = 27,000 L T = 25 oC = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm Dr. S. M. Condren

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Using PV = nRT How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC? R = L•atm/K•mol Solution 2. Now calc. n = PV / RT n = 1.1 x 103 mol (or about 22 kg of gas) Dr. S. M. Condren

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**R has other values for other sets of units.**

Ideal Gas Constant R = L*atm/mol*K R has other values for other sets of units. R = mL*atm/mol*K = J/mol*K = cal/mol*K Dr. S. M. Condren

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**Gases and Stoichiometry**

2 H2O2(liq) ---> 2 H2O(g) + O2(g) Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Solution Strategy: Calculate moles of H2O2 and then moles of O2 and H2O. Finally, calc. P from n, R, T, and V. Dr. S. M. Condren

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**Gases and Stoichiometry**

2 H2O2(liq) ---> 2 H2O(g) + O2(g) Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Solution #mol H2O2 = 1.1g H2O2 (1mol/ 34.0g H2O2) = mol H2O2 #mol O2 = (0.032mol H2O2)(1mol O2/2mol H2O2) = 0.016mol O2 P of O2 = nRT/V = (0.016mol)(0.0821L*atm/K*mol)(298K) 2.50L = 0.16 atm Dr. S. M. Condren

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**Gases and Stoichiometry**

2 H2O2(liq) ---> 2 H2O(g) + O2(g) What is P of H2O? Could calculate as above. But recall Avogadro’s hypothesis. V n at same T and P P n at same T and V There are 2 times as many moles of H2O as moles of O2. P is proportional to n. Therefore, P of H2O is twice that of O2. P of H2O = 0.32 atm Dr. S. M. Condren

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Dalton’s Law John Dalton Dr. S. M. Condren

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**Dalton’s Law of Partial Pressures**

2 H2O2(liq) ---> 2 H2O(g) + O2(g) 0.32 atm atm What is the total pressure in the flask? Ptotal in gas mixture = PA + PB + ... Therefore, Ptotal = P(H2O) + P(O2) = atm Dalton’s Law: total P is sum of PARTIAL pressures. Dr. S. M. Condren

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**Collecting Gases over Water**

Dr. S. M. Condren

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**Example A student generates oxygen gas and collects it over water**

Example A student generates oxygen gas and collects it over water. If the volume of the gas is 245 mL and the barometric pressure is 758 torr at 25oC, what is the volume of the “dry” oxygen gas at STP? Pwater = 23.8 torr at 25oC PO2 = Pbar - Pwater = ( ) torr = 734 torr P1= PO2 = 734 torr; P2= SP = 760. torr V1= 245mL; T1= 298K; T2= 273K; V2= ? (V1P1/T1) = (V2P2/T2) V2= (V1P1T2)/(T1P2) = (245mL)(734torr)(273K) (298K)(760.torr) = 217mL Dr. S. M. Condren

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**GAS DENSITY Low density helium PV = nRT n = P V RT m = P MV RT**

Where m => mass M => molar mass and density (d) = m/V Higher Density air d = m/V = PM/RT d and M are proportional Dr. S. M. Condren

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USING GAS DENSITY The density of air at 15 oC and 1.00 atm is 1.23 g/L. What is the molar mass of air? What is air? 79% N2; M a 28g/mol 20% O2; M a 32g/mol 1. Calc. moles of air. V = 1.00 L P = 1.00 atm T = 288 K n = PV/RT = mol 2. Calc. molar mass mass/mol = g/ mol = 29.1 g/mol Reasonable? Dr. S. M. Condren

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**KINETIC MOLECULAR THEORY (KMT)**

Theory used to explain gas laws KMT assumptions are Gases consist of atoms or molecules in constant, random motion. P arises from collisions with container walls. No attractive or repulsive forces between molecules. Collisions elastic. Volume of molecules is negligible. Dr. S. M. Condren

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**Kinetic Molecular Theory**

Because we assume molecules are in motion, they have a kinetic energy. KE = (1/2)(mass)(speed)2 At the same T, all gases have the same average KE. As T goes up for a gas, KE also increases – and so does the speed. Dr. S. M. Condren

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**Kinetic Molecular Theory**

Maxwell’s equation where u is the speed and M is the molar mass. speed INCREASES with T speed DECREASES with M Dr. S. M. Condren

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**Velocity of Gas Molecules**

Molecules of a given gas have a range of speeds. Dr. S. M. Condren

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**Velocity of Gas Molecules**

Average velocity decreases with increasing mass. All gases at the same temperature Dr. S. M. Condren

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**GAS DIFFUSION AND EFFUSION**

DIFFUSION is the gradual mixing of molecules of different gases. Dr. S. M. Condren

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GAS EFFUSION EFFUSION is the movement of molecules through a small hole into an empty container. Dr. S. M. Condren

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**GAS DIFFUSION AND EFFUSION**

Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is proportional to T inversely proportional to M. Therefore, He effuses more rapidly than O2 at same T. He Dr. S. M. Condren

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**GAS DIFFUSION AND EFFUSION**

Graham’s law governs effusion and diffusion of gas molecules. Rate of effusion is inversely proportional to its molar mass. Thomas Graham, Professor in Glasgow and London. Dr. S. M. Condren

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**Gas Diffusion relation of mass to rate of diffusion**

HCl and NH3 diffuse from opposite ends of tube. Gases meet to form NH4Cl HCl heavier than NH3 Therefore, NH4Cl forms closer to HCl end of tube. Dr. S. M. Condren

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**Deviations from Ideal Gas Law**

Real molecules have volume. There are intermolecular forces. Otherwise a gas could not become a liquid. Dr. S. M. Condren

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**Deviations from Ideal Gas Law**

Account for volume of molecules and intermolecular forces with VAN DER WAALS’s EQUATION. J. van der Waals, , Professor of Physics, Amsterdam. Nobel Prize 1910. Measured V = V(ideal) Measured P nRT V nb V 2 n a P ) ( vol. correction intermol. forces Dr. S. M. Condren

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**Deviations from Ideal Gas Law**

Cl2 gas has a = 6.49, b = For 8.0 mol Cl2 in a 4.0 L tank at 27 oC. P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm Dr. S. M. Condren

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Dr. S. M. Condren

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Dr. S. M. Condren

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**Carbon Dioxide and Greenhouse Effect**

Dr. S. M. Condren

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**Composition of Air at Sea Level**

Dr. S. M. Condren

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**Some Oxides of Nitrogen**

N2O NO NO2 N2O4 2 NO2 = N2O4 brown colorless NOx Dr. S. M. Condren

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**Air Pollution in Los Angles**

Dr. S. M. Condren

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