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

Pressure Section 13-1

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 4 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 | 5 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 | 6 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 | 7 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 | 8 Measuring Pressure of a Trapped Gas

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 9 Measuring Pressure of a Trapped Gas (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 10 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 | 11 Pressure and Volume: Boyle’s Law Section 13-2

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

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 14 Boyle’s Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 15 What is the new volume if a 1.5 L sample of Freon-12 at 56 torr is compressed to 150 torr? Example:

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 16 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 | 17 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 | 18 Volume & Temperature: Charles Law Section 13-3

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 19 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 | 20 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 | 21 Charles’ Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 22 Charles’ Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 23 Gay-Lussac’s Law Named after Joseph Gay-Lussac ( ) Shows the relationship between Temperature and Pressure at a constant volume Shows that temperature and pressure are directly proportional

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 24 Gay-Lussac’s Law Formula P 1 P 2 T 1 T 2 Shows that Pressure (P) and Temperature (T) are directly proportional ___ =

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 25 Aerosol Can Why does the aerosol can get cold when you spray air from it?

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 26 Think About It! Why does the aerosol can get cold when you spray air from it?

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 27 The Power of Gay-Lussac’s Law Let’s see a Demo

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 28 Real Life Example of Gay-Lussac’s Law What happens to the air pressure in a Nascar tire (assuming that the volume of the tire remains constant) after the race car speeds around the track for hours?

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 29 The Power of Gay-Lussac’s Law Let’s see a Demo

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 30 Volume & Moles: Avogadro’s Law Section 13-4

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 31 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 | 32 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 | 33 The Ideal Gas Law Section 13-5

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 34 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 | 35 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 | 36 Ideal Gas Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 37 Combined Gas Law

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 38 Dalton’s Law of Partial Pressure Section 13-6

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 39 Dalton’s Law 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 | 40 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 | 41 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 | 42 The Kinetic Molecular Theory of Gases Section 13.8

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 43 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 | 44 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 | 45 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 | 46 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 | 47 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 | 48 Visual

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 49 The Implications of the Kinetic Molecular Theory Section 13-9

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 50 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 | 51 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 | 52 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 | 53 Pressure and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 54 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 | 55 Volume and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 56 Gas Stoichiometry Section 13-10

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 57 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.