Characteristics of Gases

1. Characteristics of Gases • Vapor = term for gases of substances that are often liquids/solids under ordinary conditions • Unique gas properties • Highly compressible • Inverse pressure-volume relationship • Form homogeneous mixtures with other gases Mullis

2. Pressures of Enclosed Gases and Manometers • Barometer: Used to measure atmospheric pressure* • Manometer: Used to measure pressures of gases not open to the atmosphere • Manometer is a bulb of gas attached to a U-tube containing Hg. • If U-tube is closed, pressure of gas is the difference in height of the liquid. • If U-tube is open, add correction term: • If Pgas < Patm then Pgas + Ph = Patm • If Pgas > Patm then Pgas = Ph + Patm * Alternative unit for atmospheric pressure is 1 bar = 105 Pa Mullis

3. Kinetic Molecular Theory • Number of molecules • Temp • Volume • Pressure • Number of dancers • Beat of music • Size of room • Number and force of collisions Mullis

4. Kinetic Molecular Theory • Accounts for behavior of atoms and molecules • Based on idea that particles are always moving • Provides model for an ideal gas • Ideal Gas = Imaginary: Fits all assumptions of the K.M theory • Real gas = Does not fit all these assumptions Mullis

5. 5 assumptions of Kinetic-molecular Theory • Gases = large numbers of tiny particles that are far apart. • Collisions between gas particles and container walls are elastic collisions (no net loss in kinetic energy). • Gas particles are always moving rapidly and randomly. • There are no forces of repulsion or attraction between gas particles. • The average kinetic energy of gas particles depends on temperature. Mullis

6. Physical Properties of Gasses • Gases have no definite shape or volume – they take shape of container. • Gas particles glide rapidly past each other (fluid). • Gases have low density. • Gases are easily compressed. • Gas molecules spread out and mix easily Mullis

7. Diffusion = mixing of 2 substances due to random motion. • Effusion = Gas particles pass through a tiny opening……..… Mullis

8. Real Gases • Real gases occupy space and exert attractive forces on each other. • The K-M theory is more likely to hold true for particles which have little attraction for each other. • Particles of N2 and H2 are nonpolar diatomic molecules and closely approximate ideal gas behavior. • More polar molecules = less likely to behave like an ideal gas. Examples of polar gas molecules are HCl, ammonia and water. Mullis

9. Gas Behavior • Particles in a gas are very far apart. • Each gas particle is largely unaffected by its neighbors. • Gases behave similarly at different pressures and temperatures according to gas laws. • To identify a gas that is “most” ideal, choose one that is light, nonpolar and a noble gas if possible. • Ex: Which gas is most likely to DEVIATE from the kinetic molecular theory, or is the “least” ideal: N2, O2, He, Kr, or SO2? Answer: sulfur dioxide due to relative polarity and mass. Mullis

10. Boyle’s Law • Pressure goes up if volume goes down. • Volume goes down if pressure goes up. • The more pressure increases, the smaller the change in volume. Mullis

11. Boyle’s law • Pressure is the force created by particles striking the walls of a container. • At constant temperature, molecules strike the sides of container more often if space is smaller. V1P1 = V2P2 • Squeeze a balloon: If reduce volume enough, balloon will pop because pressure inside is higher than the walls of balloon can tolerate. Mullis

12. Charles’ Law • As temperature goes up, volume goes up. • Assumes constant pressure. V1 = V2 T1 T2 T , V Mullis

13. Charles’ law • As temperature goes up volume goes up. • Adding heat energy causes particles to move faster. • Faster-moving molecules strike walls of container more often. The container expands if walls are flexible. • If you cool gas in a container, it will shrink. • Air-filled, sealed bag placed in freezer will shrink. Mullis

14. Gay-Lussac’s Law • As temperature increases, pressure increases. • Assumes volume is held constant. P1 = P2 T1 T2 • A can of spray paint will explode near a heat source. • Example is a pressure cooker. Mullis

15. Combined Gas Law • In real life, more than one variable may change. If have more than one condition changing, use the combined formula. • In solving problems, use the combined gas law if you know more than 3 variables. V1P1 = V2P2 T1 T2 Mullis

16. Using Gas Laws • Convert temperatures to Kelvin! • Ensure volumes and/or pressures are in the same units on both sides of equation. • STP = 0° C and 1 atm. • Use proper equation to solve for desired value using given information. V1P1 = V2P2 V1 = V2 P1 = P2 V1P1 = V2P2 T1 T2 T1 T2 T1 T2 Mullis

17. Gay Lussac’s law of combining volumes of gases • When gases combine, they combine in simple whole number ratios. • These simple numbers are the coefficients of the balanced equation. N2 + 3H2 2NH3 • 3 volumes of hydrogen will produce 2 volumes of ammonia Mullis

18. Avogadro’s Law and Molar Volume of Gases • Equal volumes of gases (at the same temp and pressure) contain an equal number of molecules. In the equation for ammonia formation, 1 volume N2 = 1 molecule N2 = 1 mole N2 • One mole of any gas will occupy the same volume as one mole of any other gas • Standard molar volume of a gas is the volume occupied by one mole of a gas at STP. Standard molar volume of a gas is 22.4 L. Mullis

19. Sample molar volume problem • A chemical reaction produces 98.0 mL of sulfur dioxide gas at STP. What was the mass, in grams, of the gas produced? ***Turn mL to L first! (This way, you can can use 22.4 L) 98 mL 1 L 1 mol SO2 64.07g SO2 = 0.280g SO2 1000 mL 22.4 L 1 mol SO2 Mullis

20. Sample molar volume problem 2 What is the volume of 77.0 g of nitrogen dioxide gas at STP? 77.0 g NO2 1 mol NO2 22.4 L = 37.5 L NO2 46.01g NO2 1 mol NO2 Mullis

21. Ideal Gas Law • Mathematical relationship for PVT and number of moles of gas PV = nRT n = number of moles R = ideal gas constant P = pressure V = volume in L T = Temperature in K R = 0.0821 if pressure is in atm R = 8.314 if pressure is in kPa R = 62.4 if pressure is in mm Hg Mullis

22. Sample Ideal Gas Law Problem • What pressure in atm will 1.36 kg of N2O gas exert when it is compressed in a 25.0 L cylinder and is stored in an outdoor shed where the temperature can reach 59°C in summer? V = 25.0 L T = 59+273 = 332 K P = ? R = 0.0821L-atm n = 1.36 kg converted to moles mol-K • 1.36 kg N2O 1000 g 1 mol N2O = 30.90 mol N2O 1 kg 44.02 g N2O • PV = nRT • P = 30.90 mol x 0.0821 L-atm x 332 K = 33.7 atm 25.0 L mol-K Mullis

23. Volume-Volume Calculations • Volume ratios for gases are expressed the same way as mole ratios we used in other stoichiometry problems. N2 + 3H2 2NH3 Volume ratios are: 2 volumes NH33 volumes H2 2 volumes NH3 3 volumes H2 1 volume N2 1 volume N2 Mullis

24. Sample Volume-Volume Problem • How many liters of oxygen are needed to burn 100 L of carbon monoxide? 2CO + O2 2CO2 100 L CO 1 volume O2 = 50 L O2 2 volume CO Mullis

25. Sample Volume-Volume Problem 2 Ethanol burns according to the equation below. At 2.26 atm and 40° C, 55.8 mL of oxygen are used. What volume of CO2 is produced when measured at STP? C2H5OH + 3O2 2CO2 + 3H2O Number moles oxygen under these conditions is? PV = nRT: 2.26 atm(.0558L) = n = 0.0049 mol O2 (0.0821 L-atm)(313K) mol-K 0.0049 mol O2 2 mol CO2 22.4 L =0.073 L CO 2 3 mol O2 1 mol CO2 Mullis

26. Gas Densities and Molar Mass • Need units of mass over volume for density (d) • Let M = molar mass (g/mol, or mass/mol) PV = nRT MPV = MnRT MP/RT = nM/V MP/RT = mol(mass/mol)/V MP/RT = density M = dRT P Mullis

27. Sample Problem: Density 1.00 mole of gas occupies 27.0 L with a density of 1.41 g/L at a particular temperature and pressure. What is its molecular weight and what is its density at STP? M.W. = 1.41 g |27.0 L = 38.1 g___ L |1.0 mol mol M = dRT d= M P = 38.1 g (1 atm)______________ = 1.70 g/L P RT mol (0.0821 L-atm )(273K) ( mol-K ) OR…AT STP: 38.1 g | 1 mol = 1.70 g/L mol | 22.4 L Mullis

28. Example: Molecular Weight A 0.371 g sample of a pure gaseous compound occupies 310. mL at 100. º C and 750. torr. What is this compound’s molecular weight? n=PV = (750 torr)(.360L) = 0.0116 mole RT 62.4 L-torr(373 K) mole-K MW = x g_= 0.371 g = 32.0 g/mol mol 0.0116 mol Mullis

29. Partial Pressures • Gas molecules are far apart, so assume they behave independently. • Dalton: Total pressure of a mixture of gases is sum of the pressures that each exerts if it is present alone. Pt = P1 + P2 + P3 + …. + Pn Pt = (n1 + n2 + n3 +…)RT/V = ni RT/V • Let ni = number of moles of gas 1 exerting partial pressure P1: P1 = X1P1 where X1 is the mole fraction (n1/nt) Mullis

30. Collecting Gases Over Water • It is common to synthesize gases and collect them by displacing a volume of water. • To calculate the amount of a gas produced, correct for the partial pressure of water: • Ptotal = Pgas + Pwater • The vapor pressure of water varies with temperature. Use a reference table to find. Mullis

31. Kinetic energy • The absolute temperature of a gas is a measure of the average* kinetic energy. • As temperature increases, the average kinetic energy of the gas molecules increases. • As kinetic energy increases, the velocity of the gas molecules increases. • Root-mean square (rms) speed of a gas molecule is u. • Average kinetic energy, ε ,is related to rms speed: ε = ½ mu 2 where m = mass of molecule *Average is of the energies of individual gas molecules. Mullis

32. Maxwell-Boltzmann Distribution • Shows molecular speed vs. fraction of molecules at a given speed • No molecules at zero energy • Few molecules at high energy • No maximum energy value (graph is slightly misleading: curves approach zero as velocity increases) • At higher temperatures, many more molecules are moving at higher speeds than at lower temperatures (but you already guessed that) Just for fun: Link to mathematical details: http://user.mc.net/~buckeroo/MXDF.html Source: http://www.tannerm.com/maxwell_boltzmann.htm Mullis

33. Molecular Effusion and Diffusion • Kinetic energy ε = ½ mu 2 • u = 3RT Lower molar mass M, higher rms speed u M Lighter gases have higher speeds than heavier ones, so diffusion and effusion are faster for lighter gases. Mullis

34. Graham’s Law of Effusion • To quantify effusion rate for two gases with molar masses M1 and M2: r1 = M2 r2M1 • Only those molecules that hit the small hole will escape thru it. • Higher speed, more likely to hit hole, so r1/r2 = u1/u2 Mullis

35. Sample Problem: Molecular Speed Find the root-mean square speed of hydrogen molecules in m/s at 20º C. 1 J = 1 kg-m2/s2 R = 8.314 J/mol-K R = 8.314 kg-m2/mol-K-s2 u2= 3RT = 3(8.314 kg-m2/mol-K-s2)293K M2.016 g |1 kg___ mol |1000g u2= 3.62 x 106 m2/s2 u = 1.90 x 103 m/s Mullis

36. Example: Using Graham’s Law An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of O2 at the same temperature. What is the unknown gas? rx = MO2 0.355 = 32.0 g/mol rO2Mx 1 Mx Square both sides: 0.3552 = 32.0 g/mol Mx Mx = 32.0 g/mol = 254 g/mol  Each atom is 127 g, 0.3552 so gas is I2 Mullis

37. The van der Waals equation • Add 2 terms to the ideal-gas equation to correct for • The volume of molecules (V-nb) • Molecular attractions (n2a/V2) Where a and b are empirical constants. P + n2a (V – nb) = nRT V2 • The effect of these forces—If a striking gas molecule is attracted to its neighbors, its impact on the wall of its container is lessened. Mullis