Chapter 10 Gases & the Atmosphere

1. Chapter 10 Gases & the Atmosphere General Chemistry I T.Ara

2. A. Properties of Gases • The earth is surrounded by a sea of gases (the atmosphere). • Scientists have been studying the properties of gases for hundreds of years.

3. A. Properties of Gases • On the macroscale, gases have a number of properties in common: • Gases can be compressed. • Gases exert pressure on whatever surrounds them. • Gases expand into whatever volume is available. • Gases mix completely with one another. • A sample of a gas can be described in terms of its temperature & pressure, the volume it occupies & the number of molecules or atoms present.

4. 1. Pressure • The pressure of a gas is equal to the force it exerts on a surface per unit area. Pressure = Force/Area • The SI unit for force is: 1 Newton (N) = 1 kg m/s2 • The SI unit for pressure is: 1 Pascal (Pa) = 1 N/m2 = 1 kg/ms2

5. Other Common Units of Pressure

6. Convert a pressure reading of 682 mm Hg to a) torr & b) kPa.

7. 2. Kinetic-Molecular Theory • All gases behave similarly on the macroscale. • The similar macroscopic properties of gases are a result of the general nanoscopic behavior of gas molecules. • The nanoscopic behavior of gas molecules is described by the Kinetic-Molecular Theory. We will focus on five main points.

8. 2. Kinetic-Molecular Theory 1. Gases are composed of molecules (or atoms) whose size is much smaller than the distances between them – molecular size is negligible. - Because there is a great deal of unoccupied space, gases are easily compressed, and two gases can quickly mix completely with each other.

9. 2. Kinetic-Molecular Theory 2. Gas molecules move randomly at various speeds & in every possible direction. - Because of this constant random motion, gas particles quickly & completely fill any container in which they are placed.

10. 2. Kinetic-Molecular Theory 3. Except when gas molecules collide, forces of attraction & repulsion between them are negligible. There are no noncovalent interactions. - The behavior of a gas does not depend on its polarity or polarizability. - All gases behave the same way, regardless of the possible noncovalent interactions between the particles.

11. 2. Kinetic-Molecular Theory 4. Collisions between molecules in the gas phase are elastic. - The total kinetic energy of two colliding molecules is the same after the collision as it is before the collision. - The kinetic energy in a gas sample never “runs down”, with all molecules falling to the bottom of the container.

12. 2. Kinetic-Molecular Theory 5. The average kinetic energy of a gas molecule is proportional to the absolute temperature (Kelvin). - This concept is not technically part of the Kinetic-Molecular Theory, but it does help to explain the behavior of gases. - Gas molecules can escape a container through a tiny hole faster as the temperature of the gas increases.

13. Kinetic Energy = Ek = (mv2)/2 • AverageEk increases with absolute temperature.

14. Kinetic Energy = Ek = (mv2)/2 • At a given temperature, the average kinetic energy is the same for all gases. • Gases with larger masses have smaller average velocities…Why?

15. Arrange these gaseous substances in order of increasing average molecular speed (v) at 25 °C.Cl2, H2, NH3, SF6

16. a) Effusion & Diffusion • The dependence of molecular speed on molar mass affects the behavior of gases. Effusion: escape of gas molecules from a container through a tiny hole into a vacuum Diffusion: the spread of gas molecules of one type through those of another type

17. a) Effusion & Diffusion • Gases with smaller molar masses undergo effusion & diffusion at faster rates. He N2 • Helium atoms are smaller & faster than nitrogen molecules – more frequent collisions with balloon wall.

18. B. The Behavior of Ideal Gases • For hundreds of years, scientist have been investigating the relationships between the pressure, volume, temperature & amount of a gas. • These empirically determined relationships have been summarized by several gas laws. • Gases that obey these laws are said to be ideal gases. • Most gases are “ideal” at room temperature and pressures close to atmospheric pressure. At very high pressures & low temperatures, gases deviate from ideal behavior.

19. 1. Boyle’s Law: Relating P & V • The volume (V) of an ideal gas varies inversely with the applied pressure (P) when temperature (T) and amount (n, moles) are constant. V  1/P (at constant T & n) V = constant × (1/P) VP = constant

20. 1. Boyle’s Law: Relating P & V • Boyle used J-tubes to measure the relationship between pressure and volume. • When the pressure on a gas is increased, the volume decreases. • V1P1 = V2P2

21. 1. Boyle’s Law: Relating P & V • On the nanoscale: • A decrease in the volume of a gas means that there is less room for the gas molecules to move around before colliding with the walls of the container. • There are more collisions between the gas molecules & the walls, and more collisions means a higher pressure.

22. A sample of gas is placed in a 256-mL flask, where it exerts a pressure of 75.0 mm Hg. What is the pressure of the gas if it is transferred to a 125-mL flask at constant temperature?

23. 2. Charles’s Law: Relating T & V • The volume (V) of an ideal gas varies directly with absolute temperature (T) when pressure (P) and amount (n, moles) are constant. • Charles plotted V versus T for different gases and found that they all reach zero volume at the same temperature – absolute zero. V  T (at constant P & n) V = constant × T V/T = constant V1/T1 = V2/T2

24. a) Absolute Temperature • When using gas laws, temperature must be expressed using the absolute temperature scale (Kelvin). • One Kelvin is the same size as one degree Celsius – values for ∆T will be the same on either scale. • T (K) = T (°C) + 273.15

25. 2. Charles’s Law: Relating T & V • On the nanoscale: • As the temperature of a gas increases, the gas molecules have higher kinetic energy & higher average molecular speed. • The more rapidly moving molecules strike the walls of the container more often & with more force. • In order for the pressure to remain constant, the volume of the container must expand.

26. A balloon is inflated with helium to a volume of 4.5 L at 23 °C. The balloon is then taken outside on a cold day (-10 °C). What is the final volume of the balloon?

27. 3. Avogadro’s Law: Relating n & V • The volume (V) of an ideal gas varies directly with amount of gas (n, moles) when temperature (T) & pressure (P) are constant. • In other words, an equal volume of any gas under the same conditions (T & P) will contain the same number of particles (atoms or molecules). V  n (at constant T & P) V = constant × n V/n = constant V1/n1 = V2/n2

28. 3. Avogadro’s Law: Relating n & V • On the nanoscale: • Increasing the number of molecules at constant temperature means that the added molecules have the same average kinetic energy as the original molecules. • The number of collisions with the container walls increases in proportion to the number of molecules. • If the volume were held constant, the pressure would increase. • To maintain constant pressure, the volume must increase.

29. a) The Law of Combining Volumes • Avogadro’s Law explained an experimentally derived law proposed by French scientist Gay-Lussac – The Law of Combining Values. • Gay-Lussac observed that at constant temperature and pressure, the volumes of reacting gases are always in the ratios of small whole numbers.

30. a) The Law of Combining Volumes • Avogadro’s law explained this observation on a molecular scale. • Because volume is • directly proportional to • n (moles of gas), this • law results from the fact • that atoms and molecules • react with each other in • whole-number ratios – • the observed volumes are • related to the stoichiometry of the reaction.

31. C. The Ideal Gas Law • The three individual gas laws can be combined to give the Ideal Gas Law.

32. C. The Ideal Gas Law • The ideal gas constant, R, can be calculated by measuring the pressure and volume of a known quantity of gas at a given temperature. • One mole of a gas at 0 °C and a pressure of 1 atm has a volume of 22.4 L. • These conditions are called standard temperature and pressure (STP), and the volume (22.4 L) is called the standard molar volume.

33. C. The Ideal Gas Law Plugging the measured values for P, V, n and T into the ideal gas law gives: R = PV/nT R = (22.414 L)(1.00 atm)/(1.00 mol)(273.15 K) R = 0.0821 L atm/mol K

34. What is the pressure exerted by 0.508 mol O2 in a 15.0-L container at 303 K?

35. What is the volume occupied by 16.0 g ethane gas (MW = 30.07 g/mol) at 720. torr and 18 C?

36. 3. Combined Gas Law • The ideal gas constant can be used to quantitatively relate a sample of gas under two sets of conditions: R = P1V1 and R = P2V2 n1T1 n2T2 • Setting these two equal gives: P1V1 = P2V2 n1T1 n2T2

37. 3. Combined Gas Law • When the amount of gas, n, is a constant: P1V1 = P2V2 T1 T2 • This simplified equation is known as the combined gas law. • How do you know when to use the ideal gas law and when to use the combined gas law?

38. 4. Using the Ideal Gas Law • When three of the variables (P, V, n, T) are given, and the value of the fourth variable is needed, use the ideal gas law and solve for the appropriate variable. PV = nRT P = nRT/V V = nRT/P n = PV/RT T = PV/nR

39. How many moles of nitrogen gas are there in a sample that occupies 35.0 L at a pressure of 3.15 atm and a temperature of 852 K?

40. 4. Using the Ideal Gas Law • When one complete set of conditions (P, V, T) is given for a sample of a gas and one of the variables under a new set of conditions is needed for the same sample of gas (n is constant), use the combined gas law and cancel out any of the three variables that do not change. P1V1 = P2V2 T1 T2

41. A sample of gas occupies 754 mL at 295 K and a pressure of 0.217 atm. What is the volume if the temperature is raised to 315 K and the pressure is raised to 0.349 atm?

42. Some butane is placed in a 3.50-L container at 298 K; its pressure is 0.967 atm. If the gas is transferred to a 15.0-L container at the same temperature, what is the pressure of the gas in the larger container?

43. D. Stoichiometry: Gases in Chemical Reactions • The law of combining volumes & the ideal gas law make it possible to use the volume of a gas (instead of its mass or molar amount) in calculations based on reaction stoichiometry. • This is because the volume of a gas at constant temperature and pressure is directly proportional to the mass & the molar amount of the gas.

44. D. Stoichiometry: Gases in Chemical Reactions • H2 (g) + Cl2 (g)  2 HCl (g) • How many moles of HCl are produced from the reaction of 1.0 mol of hydrogen gas with excess chlorine?

45. D. Stoichiometry: Gases in Chemical Reactions • H2 (g) + Cl2 (g)  2 HCl (g) • How many liters of HCl gas are produced from the reaction of 1.0 L of hydrogen gas with excess chlorine?

46. D. Stoichiometry: Gases in Chemical Reactions • H2 (g) + Cl2 (g)  2 HCl (g) • How many liters of Cl2 gas, at standard temperature and pressure, are required to react with 4.00 g H2? (Hint: At STP, the standard molar volume is 22.4 L.)

47. D. Stoichiometry: Gases in Chemical Reactions • H2 (g) + Cl2 (g)  2 HCl (g) • How many liters of Cl2 gas (at 0.937 atm & 22.00 °C) are required to react with 1.00 g H2? (Hint: You have to use the Ideal Gas Law.)

48. E. Gas Density & Molar Masses • The ideal gas law can be used to relate the density of a gas (g/L) to its molar mass (g/mol). • The number of moles (n) of a compound is equal to its mass (m) divided by its molar mass (M): n = m/M

49. E. Gas Density & Molar Masses • Substituting m/M for n gives: PV = mRT/M • Solving for density (m/V) gives: Density (d) = m/V = PM/RT • The density of a gas (d) is directly proportional to its molar mass (M).

50. Forty miles above the earth’s surface, the temperature is 250 K, and the pressure is only 2.63x10-4 atm. What is the density of air (average molar mass = 29.0 g/mol) at this altitude?