by Steven S. Zumdahl & Donald J. DeCoste University of Illinois Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed.

Chapter 13 Gases

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 3 Properties of Gases Expand to completely fill their container Take the shape of their container Low density –Much less than solid or liquid state Compressible Mixtures of gases are always homogeneous Fluid

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 4 Gas Pressure Pressure = total force applied to a certain area –Larger force = larger pressure –Smaller area = larger pressure Gas pressure caused by gas molecules colliding with container or surface More forceful or more frequent collisions mean higher gas pressure

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 5 Air Pressure Constantly present when air present Decreases with altitude –Less air = less pressure Varies with weather conditions

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 6 Air Pressure (cont.) Measured using a barometer –Column of mercury supported by air pressure –Longer mercury column supported = higher pressure –Force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 7 Measuring Pressure of a Trapped Gas A device (called a manometer) for measuring the pressure of a gas in a container.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 8 Measuring Pressure of a Trapped Gas (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 9 Units of Gas Pressure Atmosphere (atm) Height of a column of mercury ( mm Hg, in Hg ) Torr Pascal (Pa) Pounds per square inch (psi, lbs/in 2 ) atm = mm Hg = in Hg = torr = 101,325 Pa = kPa = psi

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 10 Boyle’s Law Pressure is inversely proportional to volume –Constant T and amount of gas As P increases, V decreases by the same factor. P x V = constant P 1 x V 1 = P 2 x V 2

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 11 Boyle’s Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 12 Boyle’s Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 13 What is the new volume if a 1.5 L sample of Freon-12 at 56 torr is compressed to 150 torr? Example using Boyle’s Law:

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 14 Example (cont.) Choose the correct gas law: Since we are looking at the relationship between pressure and volume we use Boyle’s Law. P 1 x V 1 = P 2 x V 2 Solve equation for the unknown variable:

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 15 Plug in the known values and calculate the unknown: P 1 = 56 torrP 2 = 150 torr V 1 = 1.5 LV 2 = ? L Example (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 16 Practice Problem 13.2 A A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. What is the volume of the new container? Assume constant temperature. Answer: V 2 = 43.7 L

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 17 Practice Problem 13.2 B A steel tank of argon gas has a pressure of 34.6 atm. If all of the argon is transferred to a new tank with a volume of 456 L, the pressure is measured to be 2.94 atm. What is the volume of the original container? Assume constant temperature. Answer: V 1 = 38.7 L

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 18 Absolute Zero Theoretical temperature at which a gas would have zero volume and no pressure –Calculated by extrapolation 0 K = °C = -459 °F Kelvin T = Celsius T Never attainable (though we’ve gotten really close) All gas law problems use Kelvin temperature scale.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 19 Charles’ Law Volume is directly proportional to temperature –Constant P and amount of gas V = constant x T (T must be measured in Kelvin) V 1 = V 2 T 1 T 2

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 20 Charles’ Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 21 Charles’ Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 22 Practice Problem 13.4 A A sample of oxygen gas has a volume of 4.55 L at 25°C. Calculate the volume of the oxygen gas when the temperature is raised to 45°C. Assume constant pressure V 1 = V 2 T 1 T 2 Answer: V 2 = 4.86 L

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 23 Avogadro’s Law Volume directly proportional to the number of gas molecules –V = constant x n (moles) –Constant P and T –More gas molecules = larger volume

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 24 Avogadro’s Law (cont.) Count number of gas molecules by moles One mole of any ideal gas occupies L at standard conditions = molar volume Equal volumes of gases contain equal numbers of molecules. –It doesn’t matter what the gas is!

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 25 Practice Problem 13.7 A If 2.55 mol of helium gas occupies a volume of 59.5 L at a particular temperature and pressure, what volume does 7.83 mol of helium occupy under the same conditions? Answer: 183 L

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 26 Practice Problem 13.7 B If 4.35 g of neon gas occupies a volume of 15.0 L at a particular temperature and pressure, what volume does 2.00 g of neon gas occupy under the same conditions? Answer: 6.88 L

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 27 Ideal Gas Law By combining the proportionality constants from the gas laws we can write a general equation. R is called the gas constant. The value of R depends on the units of P and V. –Generally use R = when P in atm and V in L PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 28 Ideal Gas Law (cont.) Use the ideal gas law when you have gas at one set of conditions Most gases obey this law when pressure is low (at or below 1 atm) and temperature is high (above 0°C).

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 29 Practice Problem 13.8 A sample of hydrogen gas, H 2, has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the number of moles of H 2 present in this gas sample. (Assume that the gas behaves ideally). Answer: 0.57 mol PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 30 Ideal Gas Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 31 Practice Problem 13.8 A A 2.50 mol sample of nitrogen gas has a volume of 5.50 L at a temperature of 27°C. Calculate the pressure of the nitrogen gas Answer: 11.2 atm PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 32 Practice Problem 13.8 B A 5.00 mol sample of oxygen gas has a pressure of 1.25 atm at 22°C. What volume does this gas occupy? Answer: 96.8 L PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 33 Practice Problem 13.9 A A sample of neon gas has a volume of 3.45 L at 25°C and a pressure of 565 torr. Calculate the number of moles of neon present in this gas sample? Answer: mol PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 34 Practice Problem 13.9 B A mol sample of argon gas has a volume of 9.00 L at a pressure of 875 mm Hg. What is the temperature (in °C) of the gas? Answer: 232 °C PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 35 Combined Gas Law

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 36 Practice Problem A Consider a sample of helium gas at 23°C with a volume of 5.60 L at a pressure of 2.45 atm. The pressure is changed to 8.75 atm and the gas is cooled to 15°C? Calculate the new volume of the gas using the ideal gas law equation Answer: 1.53 L PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 37 Practice Problem A Consider a sample of hydrogen gas at 63°C with a volume of 3.65 L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35°C. Calculate the new volume of the gas. Answer: 4.28 L PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 38 Practice Problem B Consider a sample of oxygen gas at 27°C with a volume of 9.55 L at a pressure of 2.97 atm. The pressure is changed to 8.25 atm and the gas is heated to 125°C? Calculate the new volume of the gas using the ideal gas law equation Answer: 4.56 L PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 39 Scuba divers going deeper than 150ft use a helium and oxygen mixture Divers experience high pressure under several hundred feet of pressure Nitrogen gas dissolves in blood under these conditions Returning to the surface too quickly results in “the bends”

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 40 Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures each gas would exert independently. Partial pressure: the pressure a gas in a mixture would exert if it were alone in the container P total = P gas A + P gas B + …

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 41 Dalton’s Law (cont.) Particularly useful for determining the pressure a dry gas would have after it is collected over water P air = P wet gas = P dry gas + P water vapor P water vapor depends on the temperature, look up in table

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 42 Partial Pressures The partial pressure of each gas in a mixture can be calculated using the Ideal Gas Law:

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 43 Practice Problem Mixtures of helium and oxygen are used in the “air” tanks of underwater divers for deep dives. For a particular dive, 12 L of O 2 at 25°C and 1.0 atm and 46 L of He at 25°C at 1 atm were both pumped into a 5.0 L tank. Calculate the partial pressure of each gas in the tank at 25°C Answer: 2.4 atm O 2 ; 9.3 atm He; 11.7 atm total n= RT PV

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 44 When two gases are present, the total pressure is the sum of the partial pressures of the gases. Partial Pressures

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 45 The total pressure of a mixture of gases depends on the number of moles of gas particles (atoms or molecules) present, not on the identities of the particles. Note that these three samples show the same total pressure because each contains 1.75 mol of gas. The detailed nature of the mixture is unimportant. Partial Pressures

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 46 Practice Problem A A 5.00 g sample of helium gas is added to a 5.00 g sample of neon gas in a 2.50 L container at 27°C. Calculate the partial pressure of each gas and the total pressure Answer: 12.3 atm He; 2.44 atm Ne; 14.7 atm total PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 47 Practice Problem B Equal masses of oxygen and nitrogen gas are present in a container. Which gas exerts the larger partial pressure? By what factor? Answer: N 2 exerts a partial pressure that is 1.14 times as great as the partial pressure of O 2 PV = nRT

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 48 Water Vapor Pressure A mixture of gases occurs whenever a gas is collected by displacement of water. The production of oxygen by thermal decomposition of KClO 3 2KClO 3 (s)  2KCl(s) + 3O 2 (s)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 49 Practice Problem KClO 3 (s)  2KCl(s) + 3O 2 (s) The oxygen produced was collected by displacement of water at 22°C. The resulting mixture of O 2 and H 2 O vapor had a total pressure of 754 torr and a volume of 0.650L. Calculate the partial pressure of O 2 in the gas collected and the number of moles of O 2 present. The vapor pressure of water at 22°C is 21 torr.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 50 Practice Problem KClO 3 (s)  2KCl(s) + 3O 2 (s) The oxygen produced was collected by displacement of water at 22°C. The resulting mixture of O 2 and H 2 O vapor had a total pressure of 754 torr and a volume of 0.650L. Calculate the partial pressure of O 2 in the gas collected and the number of moles of O 2 present. The vapor pressure of water at 22°C is 21 torr. P total = P O 2 + P H 2 O Answer: P O 2 = atm n O 2 = 2.59 x mol

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 51 Practice Problem A A sample of oxygen gas is saturated with water vapor at 30.0°C. The total pressure is 753 torr, and the vapor pressure of water at 30.0°C is torr. What is the partial pressure of oxygen gas in atm? Answer: atm

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 52 Practice Problem B A sample of oxygen gas is saturated with water vapor at 27°C. The total pressure is torr, and the partial pressure of oxygen is torr. What is the vapor pressure of water at 27°C? Answer: 26.7 torr ( atm)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 53 Kinetic-Molecular Theory The properties of solids, liquids, and gases can be explained based on the speed of the molecules and the attractive forces between molecules. In solids, the molecules have no translational freedom. They are held in place by strong attractive forces. –May only vibrate

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 54 Kinetic-Molecular Theory (cont.) In liquids, the molecules have some translational freedom, but not enough to escape their attraction to neighboring molecules. –They can slide past one another and rotate, as well as vibrate.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 55 Kinetic-Molecular Theory (cont.) In gases, the molecules have “complete” freedom from each other. They have enough energy to overcome “all” attractive forces. Kinetic energy depends only on the temperature.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 56 Describing a Gas Gases are composed of tiny particles. The particles are small compared to the average space between them. –Assume the molecules do not have volume

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 57 Describing a Gas (cont.) Molecules constantly and rapidly move in a straight line until they bump into each other or the wall. –Average kinetic energy proportional to the temperature –Results in gas pressure Assume that the gas molecules attraction for each other is negligible.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 58 Visual

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 59 Postulates of the Kinetic-Molecular Theory of Gases 1.Gases consist of tiny particles (atoms and molecules) 2.These particles are so small, compared with the distances between them, that the volume (size) of the individuals particles can be assumed to be negligible (zero). 3.The particles are in constant random motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas. 4.The particles are assumed not to attract or repel each other. 5.The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 60 The Meaning of Temperature Temperature is a measure of the average kinetic energy of the molecules in a sample. –Not all molecules have same kinetic energy Kinetic energy is directly proportional to the Kelvin temperature. –Average speed of molecules increases as the temperature increases

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 61 Gas Properties Explained Gases have indefinite shape and volume because the freedom of the molecules allows them to move and fill the container they’re in. Gases are compressible and have low density because of the large spaces between the molecules.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 62 Pressure and Temperature As the temperature of a gas increases, the average speed of the molecules increases. The molecules hit the sides of the container with more force (on average) and more frequently, resulting in an increase in pressure.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 63 Pressure and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 64 Volume and Temperature In a rigid container, raising the temperature increases the pressure. For a cylinder with a piston, the pressure outside and inside stays the same.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 65 Volume and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 66 Gas Stoichiometry Use the general algorithms discussed previously to convert masses or solution amounts to moles. Use gas laws to convert amounts of gas to moles.