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Gases

Gases. Measurements on Gases. Volume- amount of space the gas occupies: 1 L = 1000 mL = 1000 cm 3 = 1 x10 -3 m 3 Amount – most commonly expressed in terms of moles (n): m = MM x n Temperature – measured in degrees Celsius but commonly must convert to Kelvin:

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Gases

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  1. Gases

  2. Measurements on Gases • Volume- amount of space the gas occupies: 1 L = 1000 mL = 1000 cm3 = 1 x10-3 m3 • Amount – most commonly expressed in terms of moles (n): m = MM x n • Temperature – measured in degrees Celsius but commonly must convert to Kelvin: TK = t*C + 273.15 • Pressure – gas molecules are constantly colliding & because of this they exert a force over an area: 1.013 bar = 1 atm = 760 mmHg (or torr) = 1 x 105 Pa = 14.7 psi

  3. Barometer

  4. Manometer

  5. Example 1 • A balloon with a volume of 2.06 L contains 0.368 g of helium at 22 degrees Celsius and 1.08 atm. Express the volume of the balloon in m3, the temperature in K, and the pressure in mmHg. • V = 2.06 x 10-3 m3 • nHe = 0.0919 mole • T = 22 + 273.15 = 295 K • P = 821 mmHg

  6. Gas Laws • Boyle’s Law: P1V1 = P2V2 • Charles’ Law: V1 = V2 T1 T2 • Gay-Lusaac’s Law: P1 = P2 T1 T2 • Combined Gas Law: P1V1 = P2V2 T1 T2

  7. Example 2 • A tank is filled with a gas to a pressure of 977 mmHg at 25*C. When the tank is heated, the pressure increases to 1.50 atm. To what temperature was the gas heated? • 75oC

  8. The Ideal Gas Law • The Ideal Gas Law Constant (R): 0.0821 L atm/mol K - ideal gas law problems 8.31 J/ mol K - equations involving energy 8.31 Kg m2/s2 mol k - molecular speed problems

  9. Molar Volume

  10. Gas Law Calculations Initial & Final State Problems: • Starting with a sample of gas at 25*C and 1.00 atm you might be asked to calculate the pressure developed when the sample is heated to 95*C at a constant volume. Determine a two-point equation and solve for the final pressure. • Initial State: P1V = nRT1 • Final State: P2V = nRT2 • Divide the 2 equations to derive a “two-point” equation: • P1 = T1 P2 = T2 • Rearrange to solve for the variable you want: P2 = P1 T2 T1 Ans: 1.23 atm

  11. Example 3 • A 250.0 mL flask, open to the atmosphere, contains 0.0110 mol of air at 0 *C. On heating, part of the air escapes: how much remains in the flask at 100 *C? • 0.00805 mol of air

  12. Example 4 • If 2.50 g of sulfur hexafluoride is introduced into an evacuated 500.0 mL container at 83*C, what pressure (atm) is developed? • Ans: 1.00 atm

  13. Density & The Ideal Gas LawThe ideal gas law offers a simple approach to the experimental determination of the molar mass of a gas. Remember that m = MM x n and n = PV and d = m RT V So you can substitute these equations into the ideal gas law to solve fro density (d) or molar mass (M)

  14. Gas Density and Human Disasters: Many gases that are denser than air have been involved in natural and human-caused disasters. The dense gases in smog that blanket urban centers, such as Mexico City (see photo), contribute greatly to respiratory illness. In World War I, poisonous phosgene gas (COCl2) was used against ground troops as they lay in trenches. In 1984, the unintentional release of methylisocyanate from a Union Carbide India Ltd. chemical plant in Bhopal, India, killed thousands of people as vapors spread from the outskirts into the city. In 1986 in Cameroon, CO2 released naturally from Lake Nyos suffocated thousands as it flowed down valleys into villages. Some paleontologists suggest that a similar process in volcanic lakes may have contributed to dinosaur kills.

  15. Example 5 Acetone is widely used in nail polish remover. A sample of liquid acetone is placed in a 3.00 L flask and vaporized by heating to 95*C at 1.02 atm. The vapor filling the flask at this temperature and pressure weighs 5.87 g: (a) What is the density of acetone vapor under these conditions? Ans: 1.96 g/L (b) Calculate the molar mass of acetone. Ans: 58.1 g/mol (c) Acetone contains three elements C, H, and O. When 1.00 g of acetone is burned 2.27 g of CO2 and 0.932 g of H2O are formed. What is the molecular formula of acetone? Ans: C3H6O

  16. Stoichiometry of Gaseous Reactions • A molar ratio from a balanced chemical reaction is also used in reactions involving gases however, the ideal gas law can now be applied. • Example 6: A nickel smelter in Sudbury, Ontario produces 1% of the world’s supply of sulfur dioxide by the reaction of nickel II sulfide with oxygen another product of the reaction is nickel II oxide: What volume of sulfur dioxide at 25oC and a pressure of one bar is produced from a metric ton of nickel II sulfide? Ans: 2.73 x 105 L

  17. Gas A to Gas B

  18. Example 7 • Octane, C8H18, is one of the hydrocarbons in gasoline. On combustion octane produces carbon dioxide and water. How many liters of oxygen, measured at 0.974 atm and 24*C, are required to burn 1.00 g of octane? • Ans: 2.73 L

  19. Law of Combining Volumes • The volume of any 2 gases in a reaction at constant temperature and pressure is the same as the reacting molar ratio: 2 H2O (l) 2H2(g) + O2(g) 4 L H2 x 1 L O2 = 2 L O2 2 L H2

  20. Example 8 • Consider the reaction for the formation of water from its elemental units. • (a) What volume of hydrogen gas at room temperature and 1.00 atm is required to react with 1.00 L of oxygen at the same temperature and pressure? • Ans: 2.00 L hydrogen gas • (b) What volume of water at 25*C and 1.00 atm (d=0.997 /mL) is formed from the reaction in (a)? • Ans: 1.48 mL of water • (c) What mass of water is formed from the reaction assuming a yield of 85.2%? • Ans: 1.26 g of water

  21. Example 9 The alkali metals react with the halogens to form ionic metal halides. What mass of potassium chloride forms when 5.25 L of chlorine gas at 0.950 atm and 293 K reacts with 17.0 g of potassium? Ans: 30.9 g KCl

  22. Dalton’s Law of Partial Pressures • The total pressure of a gas mixture is the sum of the partial pressures of the components of the mixture. Ptot = PA + PB +….. PH2 = 2.46 atm PHe = 3.69 atm then Ptot = 6.15 atm

  23. Wet Gases • When a gas is collected by bubbling through water then it picks up water vapor. Then the total pressure is the sum of the pressure of the water vapor and the gas collected. So Dalton’s Law can be applied by: Ptot = PH2O + PA *The partial pressure of water is equal to the vapor pressure of water. This has a fixed value at a given temperature (PH2O @ 25*C = 23.76 mmHg)

  24. Gas collection by water displacement.

  25. Example 10 • A student prepares a sample of hydrogen gas by electrolyzing water at 25oC. She collects 152 mL of hydrogen gas at a total pressure of 758 mmHg. Calculate: • (a) the partial pressure of hydrogen gas. • Ans: 734 mmHg • (b) the number of moles of hydrogen gas collected. • Ans: 0.00600 mol of hydrogen gas

  26. Partial Pressures & Mole Fraction • The partial pressure of a gas (PA) divided by the total pressure (Ptot) is equal to the number of moles of that gas divided by the total moles of gases: • PA = nA Ptot ntot • Mole fraction: XA = nA ntot • Partial Pressures: PA = XA Ptot

  27. Example 11 • Methane burns in air. When one mole of methane and four moles of oxygen are heated: (a) What are the mole fractions of oxygen, carbon dioxide, and water vapor in the resulting mixture (assume all the methane is converted)? XCH4 = 0, XCO2 = 0.200, XH2O =0.400, XO2 = 0.400 (b) If the total pressure of the mixture is 1.26 atm, what are the partial pressures of each gas? PCO2 = 0.252 atm, PH2O =0.504 atm, PO2 = 0.504 atm

  28. Kinetic Theory of Gases The Molecular Model of Gases: • Gases are mostly empty space (assumes that gases do not have their own volume). • Gas molecules are in constant and chaotic motion. Their velocities are constantly changing because of this. • Collisions of gases are elastic (assumes no attractive forces). • Gas pressure is caused by collisions of molecules with the walls of the container. As a result, pressure increases with the energy and frequency of these collisions. Also, average kinetic energy of a collection of gases is assumed to be directly proportional to the Kelvin temperature of the gas sample.

  29. Average Speed (Root Mean Square Velocity) • The equation below is derived from the average translational kinetic energy of a gas molecule: • It follows that at a given temperature, molecules of different gases have the same average kinetic energy of translational motion and • the average translational kinetic energy of a gas molecule is directly proportional to the Kelvin temperature so that: u = _(3RT) ½ (M) * An R value of 8.31 x 103 g m2/(s2 mol K) is used for average speed calculations.

  30. Example 12 • Calculate the average velocity for the atoms in a one mole sample of helium gas at 25oC. • urms = 1.36 x 103 m/s

  31. Graham’s Law of Effusion • The average speed is inversely proportional to the square root of the molar mass (MM). So for two different gases A and B at the same temperature then we can write: rate of effusion B = (MMA)1/2 rate of effusion A (MMB)

  32. Example: Using Graham’s Law A mixture of helium (He) and methane (CH4) is placed in an effusion apparatus. Calculate the ratio of their effusion rates: Ans: He effuses 2.002 times faster than methane

  33. Example 13 In an effusion experiment, argon gas is allowed to expand through a tiny opening into an evacuated flask of volume 120.0 mL for 32.0 s, at which point the pressure in the flask is found to be 12.5 mmHg. This experiment is repeated with a gas X of unknown molar mass at the same T and P. It is found that the pressure in the flask builds up to 12.5 mmHg after 48.0 s. Calculate the molar mass of X. Ans: 89.9 g/mol

  34. Real Gases • The ideal gas law has been used with the assumption that it applies exactly. However, all real gases deviate at least slightly from the ideal gas law. • These deviations arise because the ideal gas law neglects two factors: • 1. attractive forces between gas particles • 2. the finite volume of gas particles *In general, the closer a gas is to the liquid state, the more it will deviate from the ideal gas law.

  35. Correction for Real Gas Behavior

  36. Chemistry in the Atmosphere • Principal components of the Earth’s atmosphere are nitrogen and oxygen. The lowest layer of the atmosphere is called the troposphere. • Other gases in smaller amounts are water vapor, carbon dioxide, argon, neon, helium, methane, krypton, hydrogen, nitrogen monoxide and xenon. • Chemistry in higher levels of the atmosphere is mostly determined by the effects of high energy radiation (coming from the sun and other sources in space).

  37. Air Pollution • The combustion of petroleum in vehicles produces CO, CO2, NO, and NO2. • In the troposphere, the NO2 formed assist in the formation of ozone. The ozone formed then leads to the formation of OH (the hydroxyl radical) and other pollutants. This process is often referred to as photochemical smog.

  38. Acid Rain • Another major source of pollution results from the burning of coal to produce electricity. • Some coal (especially in the Midwest) contains significant amounts of sulfur, which when burns produces SO2. • The SO2 then becomes oxidized by oxygen in the air to produce SO3. • The SO3 then reacts with water to produce H2SO4. This acid results in acid rain that is harmful to the environment and living organisms.

  39. MC #1 • When a sample of oxygen gas in a closed container of constant volume is heated until its absolute temperature is doubled, which of the following is also doubled? (A) The density of the gas(B) The pressure of the gas(C) The average velocity of the gas molecules(D) The number of molecules per cm3(E) The potential energy of the molecules

  40. MC #2 • At 25 °C, a sample of NH3 (molar mass 17 grams) effuses at the rate of 0.050 mole per minute. Under the same conditions, which of the following Gas effuses at approximately one-half that rate? (A) O2 (B) He (C) CO2(D) Cl2(E) CH4

  41. MC #3 • Equal masses of three different ideal Gas, X, Y, and Z, are mixed in a sealed rigid container. If the temperature of the system remains constant, which of the following statements about the partial pressure of gas X is correct? (A) It is equal to 1/3 the total pressure(B) It depends on the intermolecular forces of attraction between molecules of X, Y, and Z.(C) It depends on the relative molecular masses of X, Y, and Z.(D) It depends on the average distance traveled between molecular collisions.(E) It can be calculated with knowledge only of the volume of the container.

  42. MC #4 • When the actual gas volume is greater then the volume predicted by the ideal gas law, the explanation lies in the fact that the ideal gas law does NOT include a factor for molecular. (A) volume(B) mass(C) velocity(D) attractions(E) shape

  43. MC #5 • A sample of 9.00 grams of aluminum metal is added to an excess of hydrochloric acid. The volume of hydrogen gas produced at standard temperature and pressure is (A) 22.4 liters(B) 11.2 liters(C) 7.46 liters(D) 5.60 liters(E) 3.74 liters

  44. MC #6 • A gaseous mixture containing 7.0 moles of nitrogen, 2.5 moles of oxygen, and 0.50 mole of helium exerts a total pressure of 0.90 atmosphere. What is the partial pressure of the nitrogen? (A) 0.13 atm(B) 0.27 atm(C) 0.63 atm(D) 0.90 atm(E) 6.3 atm

  45. MC #7 • A sample of an ideal gas is cooled from 50.0 °C to 25.0 °C in a sealed container of constant volume. Which of the following values for the gas will decrease? I. The average molecular mass of the gasII. The average distance between the moleculesIII. The average speed of the molecules (A) I only(B) II only(C) III only(D) I and III(E) II and III

  46. MC #8 NH4NO3(s) --> N2O(g) + 2H2O(g) A 0.03 mol sample of NH4NO3(s) decomposes completely according to the balanced equation above. The total pressure in the flask measured at 400 K is closest to which of the following? (A) 3 atm(B) 1 atm(C) 0.5 atm(D) 0.1 atm(E) 0.03 atm

  47. MC #9 • As the temperature is raised from 20 ° C to 40 ° C, the average kinetic energy of neon atoms changes by a factor of (A) 1/2(B) [square root of](313/293)(C) 313/293(D) 2(E) 4

  48. MC #10 • A hydrocarbon gas with an empirical formula CH2 has a density of 1.88 grams per liter at 0 °C and 1.00 atmosphere. A possible formula for the hydrocarbon is (A) CH2(B) C2H4(C) C3H6(D) C4H8(E) C5H10

  49. FRQ #1 2 H2O2(aq) → 2 H2O(l) + O2(g) • The mass of an aqueous solution of H2O2 is 6.951 g. The H2O2 in the solution decomposes completely according to the reaction represented above. The O2(g) produced is collected in an inverted graduated tube over water at 23.4°C and has a volume of 182.4 mL when the water levels inside and outside of the tube are the same. The atmospheric pressure in the lab is 762.6 torr, and the equilibrium vapor pressure of water at 23.4°C is 21.6 torr. (a) Calculate the partial pressure, in torr, of O2(g) in the gas-collection tube. (b) Calculate the number of moles of O2(g) produced in the reaction. (c) Calculate the mass, in grams, of H2O2 that decomposed. (d) Calculate the percent of H2O2 , by mass, in the original 6.951 g aqueous sample. (e) What is the oxidation number of the oxygen atoms in H2O2 and the oxidation number of the oxygen atoms in O2. (f) Write the balanced oxidation half-reaction for the reaction.

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