B. Characteristics of Gases assume volume and shape of container very compressible mix evenly and completely lower density than liquids and solids

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1 Chapter 5: Gases Laws for gases are simpler than for liquids and solids. The behavior of gases is predictable. 5.1 Substances that exist as gases Air - 78 % N2; 21 % O2; 1 % other (including CO2 which is associated with global warming) A. Elements and Molecules O2, H 2, N 2, F 2, O 3, all Group VIII (Noble gases) Ionic compounds are never gases at room temperature (24 C at 1 atmosphere); electrostatic forces are too strong to allow ions to separate molecular compounds that are small can be gases or have low boiling points: CO, CO 2, HCl, CH 4, NH 3, SO 2, etc. B. Characteristics of Gases assume volume and shape of container very compressible mix evenly and completely lower density than liquids and solids 5.2 Pressure of a Gas Molecules of a gas are in rapid and constant motion. A. Units of Pressure SI Units force = mass x acceleration Newton (N) = Kg x m/s 2 Pressure = force/area = 1 N/ m2 = Pascal (Pa)

2 B. Atmospheric Pressure pressure exerted by Earth's atmosphere gas molecules have mass, thus gravity affects them 50 % of the atmosphere's molecules are within 4 miles of surface measured by barometer (Figure 5.3) 760 mm Hg at sea level standard is 1 atm at 0 C 1 atm = x 10 5 Pa 2 1 mm Hg = 1 Torr 1 atm = 760 Torr = 760 mm Hg

3 5.3 Gas Laws 3 simple laws : Boyle's, Charles', Avogadro's 3 A. Boyle's Law (at constant T and n) volume decreases as pressure increases V 1/P or PV = constant P1V1 = P2V2 See Figure 5.6

4 B. Charles' Law (Gay-Lussac's) (at constant P and n) 4 volume increases as temperature increases V T or V / T = constant V 1 /V 2 = T 1 /T 2 always use the Kelvin Scale for T Figure 5.9 note all lines converge at absolute 0 or C 0 K = C

5 5 Gay-Lussac's Law C. Combined Gas Law (for constant n) PV / T = constant P 1 V 1 P 2 V 2 = T 1 T 2

6 D. Avogadro's Law (constant temperature and pressure) 6 equal volumes of gas have the same number of molecules (atoms) V n where n = moles See practice problems in book. Fig Volume relationships of gases. Volume relationship is the same as the mole relationship.

7 5.4 Ideal Gas Equation 7 Ideal gas - volume of molecules is negligible; applies in most temperature and pressure ranges. combination of gas laws and Avogadro's Principle Standard Molar Volume (STP) Standard Temperature (0 C or 273 K) Standard Pressure (1 atm) 1 mole of any gas occupies 22.4 L or 22.4 L = 1 mole but ONLY at STP PV = nrt where R = "universal gas constant" = L atm / mole K memorize Where does R come from? R = PV/nT (Ideal gas law rearranged) R = (1 atm)( L) / (1 mol)(273.15k) = L atm / mole K { Useful in many different kinds of calculations involving gases!!! }

8 Example: 8 At STP, the density of a certain gas is 4.29 g/l. molecular mass of the gas? What is the 4.29 g L x 22.4 L mole = 96.0 g / mole Example: What is the density (g/l) of UF 6 at 779 mm Hg and 62 C? PV = nrt and d = m/v n/v = P/RT i.e., n V = P RT and n = m / ` where ` = molar mass m/ ` V = P/RT i.e., m M V = RT P m/v = d = P ` / RT i.e., d = m V P M = RT m V = 1 atm 779 mm Hg x x 760 mm Hg L atm x 335 K mole K 352 g mol = 13.1 g / L Note: alternate way will be done in class

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10 5.5 Gas Stoichiometry 10 Example: Acetylene (welding gas), C2H2, is produced by hydrolysis of calcium carbide. CaC 2 (s) + 2 H 2 O Ca(OH) 2 (s) + C 2 H 2 (g) Starting with 50.0 g of CaC 2, what is the theoretical yield of acetylene in liters, collected at 24 C and a pressure of 745 Torr? CaC2 (s) + 2 H2O Ca(OH)2 (s) + C2H2 (g) 1st find yield in moles: 1 mole CaC 50.0 g CaC 2 x 2 1 mole C x 2 H 2 = mole C 2 H g CaC 1 mole CaC now use ideal gas law to find volume of C2H2: PV = nrt V = V = nrt P (0.780 mole) x ( L atm / mole K) x (297 K) (745 torr) x (1 atm / 760 torr) = 19.4 L

11 11 3 A + 2 B 4 C + D

12 5.6 Dalton's Law of Partial Pressures 12 A. For a mixture of gases: PT = Pa + Pb + Pc PT = Pa + Pb = nart / V + nbrt / V P T = (n a + n b ) (RT / V) Pa n a RT / V n a = = P t (n a + n b )RT / V n a + n b = Xa X a = mole fraction ( dimensionless quantity) X a = moles of one component / total moles present Pi = Xi. PT

13 Example: A sample of natural gas contains 8.24 moles of CH4, moles of ethane, moles of C3 H 8. If the total pressure of the gas is 1.37 atm., what is the partial pressure of each gas? 13 PCH 4 = XCH 4.PT X CH 4 = 8.24 moles / ( ) moles = X C 2 H 6 = moles / moles = X C 3 H 8 = moles / moles = PCH 4 = x 1.37 atm = 1.29 atm PC 2 H 6 = x 1.37 atm = atm PC 3 H 8 = x 1.37 atm = atm

14 B. Gases are often prepared and collected over water: 14 Ptotal = Pgas + Pwater where Pwater = vapor pressure of water (depends on temperature) e.g., at 25 C, at 50 C, Pwater = 23.8 Torr Pwater = 92.5 Torr

15 15 Pressure of water vs temperature

16 Example: A sample of N2 gas was prepared and collected over water at 15 C. The total pressure of the gas was 745 Torr in a volume of 310 ml. Calculate the mass of N2 in grams. 16 P total = P gas + P water 745 Torr = Pgas Torr Pgas = Torr PV = nrt n = PV RT n = (732.2 torr) x (1 atm / 760 torr) x (0.310 L) ( L atm / mole K) x (288 K) = mole N 2 mass N 2 = ( mole N 2 ) x (28.0 g N 2 / mole N 2 ) = g N 2

17 5.7 Kinetic Molecular Theory 17 Kinetic Theory of Gases -- Basic Postulates: A gas consists of a very large number of very small particles separated by large distance in constant random motion undergo perfectly elastic collisions with each other and the container walls with no attraction or repulsion between the particles Temp average KE KE = ½ m u 2 = C T where u = average velocity of all molecules, T is temperature in Kelvin The kinetic theory "explains" the gas laws, pressure, etc. based on motion and kinetic energy of gas molecules. e.g., Boyle's Law (P 1 / V) -- at constant Temp (same average KE) If volume of container is reduced, there are more gas particles per unit volume, thus, more collisions with the container walls per unit area. higher pressure

18 Root Mean Square 18 average speed of molecule inversely proportional to square root of molar mass of molecule directly proportional to square roof of the temperature u rms = 3 R T molar mass

19 Graham's Law of Diffusion 19 gradual mixing of molecules of one gas with molecules of another results from motion of molecule lighter gases move faster (urms) Graham's law states that under the same conditions of temperature and pressure, rates of diffusion for gases are inversely proportionhal to the sqaure roots fo their molar masses. r 1 r 2 = M 2 M 1 Gas Effusion

20 5.8 Deviations from Ideal Gas Laws (Real Gases) 20 For real gases, small corrections can be made to account for: Actual volume of the gas particles themselves, and Intermolecular attractive forces Due to molecules getting closer together and slowing down: circumstances where intermolecular forces become important (e.g., at high pressure and low temperatures) One common approach is to use the Van der Waals' Equation: P + na 2 V 2 (V - nb) = nrt Where, a and b are empirical parameters that are dependent on the specific gas. These are experimentally determined. (see Table 5.4). a intermolecular attractive forces b molecular size

21 5.68 A sample of zinc reacts with HCl according to the equations 21 Zn + 2 HCl ZnCl2 + H2 The H2 is collected over water and has a volume of 7.80 L and pressure is atm. Calculate the amount of Zn consumed. Vapor pressure of H2O at 25 C is 23.8 mm Hg.

22 A sample of NH3 is completely decomposed to N2 and H2 over heated iron wool. If the total pressure is 866 mm Hg, calculate the partial pressure of N2 and H2.

23 Air entering the lungs ends up in tiny sacs called alveoli. It is from these alveoli that O2 diffuses into the blood. The average radius of alveoli is about cm and the air inside contains 14 % O2. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is 37 C, calculate the number of O2 molecules in one of the alveoli. (Hint: The volume of a sphere is V = 4/3 πr3.)

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25 Periodic Table of the Elements 25 IA Periodic Table of the Elements VIIIA (1) (18) H IIA IIIA IVA VA VIA VIIA He (2) (13) (14) (15) (16) (17) Li Be B C N O F Ne Na Mg IIIB IVB VB VIB VIIB VIIIB IB IIB Al Si P S Cl Ar (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Uuu Uub Uug (261) (262) (266) (264) (270) (268) (281) Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr