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

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 Self check p 390 On a summer day in Colorado, the atmospheric pressure is 525 mm Hg. What is this air pressure in atmospheres? P418- Q7. Convert the following into atmospheres kPa, 781 torr, 781 mm Hg, 15.2 psi Q9. Convert the following into mm Hg 822 torr, kPa, 1.14 atm, 9.75psi

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 11 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 | 12 Boyle’s Law (cont.)

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

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 14 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 | 15 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 | 16 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 | 17 Self check p 394 A sample of neon to be used in a sign has a volume of 1.51 L at a pressure of 635 torr. Calculate the volume of a gas after it is pumped into the glass tubes of the signs where it shows a pressure of 785 torr. P 418 q 17. Calculate new volume of the gas V=249 mmHg; 654mmHg, V=?L V=1.04 atm; 0.671atm, V=?L V= mmHg, V=?

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 Self check p 398 A child blows a bubble that contains air at 8°C and has a volume of 23 cm 3 a atm. As the bubble rises, it encounters a pocket of cold air (temp 18 ° C). If there is no change in pressure, will the bubble get larger or smaller as the air inside cools to 18 ° C? Calculate the new volume of the gas. P 419 q31

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 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 | 26 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 | 27 Ideal Gas Law (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 28 Combined Gas Law

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 29

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 30 Self check p 405 A sample of argon gas with a volume of 11 L at a temp of atm is heated to 56°C and a pressure of 1.18 atm. Calculate the final volume. Avogadro’s law- p 420 q 41. If mol of helium gas occupies a vol of 2.35 L at a certain temp and pressure, what volume would mol of helium occupy under the same conditions? Q43- If 3.25 mol of Ar gas occupies a vol of 100L at a particular temp and pressure, what vol does mol of Ar occupy under the same conditions?

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 31 Self check p 403, 404 A weather balloon contains 1.1X10 5 mol of He and has a vol of 2.7 X 10 6 L at 1 atm pressure. Calculate the temp of the helium in the balloon in kelvins and in °C. Ra can pose a hazard to humans by seeping into houses, and there is a concern about this problem in many areas. A 1.5 mol sample of this gas has a vol of 21 L at 33°C. What is the pressure of this gas? A sample of methane gas has a vol of 3.8L at 5 °C and is heated to 86C at constant pressure. Calculate its new volume.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 32 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 | 33 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 | 34 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 | 35

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 36 Self check p 409, 410 A 2 L flask contains a mixture of nitrogen gas and oxygen gas at 25°C. The total pressure of the gaseous mixture is 0.91 atm, and the mixture is known to contain mol of N 2. Calculate the partial pressure of oxygen and the moles of oxygen present. Consider a sample of hydrogen gas collected over water is 24 torr. The volume occupied by the gaseous mixture is 0.5 L and the total pressure is 0.95 atm. Calculate the partial pressure of H 2 and the number of moles of H 2 present.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 37 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 | 38 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 | 39 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 | 40 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 | 41 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 | 42 Visual

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 43 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 | 44 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 | 45 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 | 46 Pressure and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 47 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 | 48 Volume and Temperature (cont.)

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 49 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.

Copyright © Houghton Mifflin Company. All rights reserved. 13 | 50 Self check p 415 Calculate the volume of hydrogen produced at 1.5 atm and 19C by the reaction of 26.5 g of zinc with excess HCl according to the balanced equation Zn (s)+ 2HCl (aq)--> ZnCl 2 (aq)+H 2 (g) Ammonia is commonly used as a fertilizer to provide a source of nitrogen for plants. A sample of NH 3 (g) occupies a volume of 5L at 25°C and 15atm. What volume will this sample occupy at STP? Book Assignment- p 420 q 49, 51, 55, 57, 67, 73, 85, 87, 89, 95. Turn in on April 5th. Late work will result in lowered credit.