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Honors Chemistry Julien Name _________________________ Period _____ Date _______________ Gases Chapter 11 Gases and Their Properties 4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept: a. Students know the random motion of molecules and their collisions with a surface create the observable pressure on that surface. b. Students know the random motion of molecules explains the diffusion of gases. c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases. d. Students know the values and meanings of standard temperature and pressure (STP). e. Students know how to convert between the Celsius and Kelvin temperature scales. f. Students know there is no temperature lower than 0 Kelvin. g.* Students know the kinetic theory of gases relates the absolute temperature of a gas to the average kinetic energy of its molecules or atoms. h.* Students know how to solve problems by using the ideal gas law in the form PV = nRT. i.* Students know how to apply Dalton’s law of partial pressures to describe the composition of gases and Graham’s law to predict diffusion of gases. I. Properties of gases. Read Section 11.1 in your eText! I will be able to use the kinetic molecular theory of gases to describe the properties of gases. Do the Properties of Gases Tutorial! Do the Properties of Gases Self Study Activity! A. Kinetic Molecular Theory of Gases. 1. A gas consists of small particles (atoms or molecules) that move randomly with high velocities. a. Gas molecules moving in random directions at high speeds cause a gas to fill the entire volume. 2. The attractive forces between the particles of a gas are usually very small. a. Gas particles are far apart and fill a container of any size and shape. 3. The actual volume occupied by gas molecules is extremely small compared to the volume that the gas occupies. a. The volume of the gas is considered equal to the volume of the container. b. Most of the volume of a gas is empty space, which allows gases to be easily compressed. 4. Gas particles are in constant motion, moving rapidly in straight paths. Honors Chemistry Page 1 Chapter 11 Notes from Basic Chemistry a. When gas particles collide, they rebound and travel in new directions. b. Every time they hit the walls of the container, they exert pressure. c. An increase in the number or force of collisions against the walls of the container causes an increase in the pressure of the gas. 5. The average kinetic energy of gas molecules is proportional to the Kelvin temperature. a. Gas particles move faster as the temperature increases. b. At higher temperatures, gas particles hit the walls of the container more often and with more force, producing higher pressures. 6. Kinetic Molecular Theory of Gases— a. Molecules from a perfume bottle move at about 1000 miles per hour when escaping from the bottle at room temperature. B. Pressure (P). 1. Gas particles collide with the walls of the chamber or surface that contains the gas, creating pressure. 2. Atmospheric pressure— C. D. E. 1. 2. 3. Gas pressure is measured atmospheres (atm), millimeters of mercury (mmHg), torr, Pascals (Pa), kiloPascals (kPa), and inches of mercury. Volume (V). 1. The volume of a gas is dependent on the size of the container or the collisions of the gas with the walls of a flexible container. 2. The most common units of volume are liters (L) and milliliters (mL). Temperature (T). 1. The temperature of a gas is related to the kinetic energy of its particles and based on temperature that starts at absolute zero. 2. Temperature has only one unit and that is Kelvin (K). Amount of gas (n). Air can be measured by the number of particles and this is measured in the lab in terms of grams. The grams must be converted to moles (mol) to relate it to the number of particles. Honors Chemistry Page 2 Chapter 11 Notes from Basic Chemistry Problem 1: When helium is added to a balloon, the mass of the gas, in grams, increases. What property of gas is described? II. Gas Pressure. Read Section 11.2 in your eText! I will describe the units of measurement used for pressure, and change from one unit to another. Do the Converting Between Units of Pressure Tutorial! A. Pressure. 1. Pressure— Pressure = force area 2. Atmosphere (atm)— 3. If 760 mmHg equals 760 torr, then 1 mmHg equals 1 torr. 4. Using the SI system, pressure is measured in pascals (Pa), so 1 atm equals 1.01325 x 105 Pa or 101.325 kPa or 14.7 pounds per square inch (psi). B. Barometer. 1. Early barometers were based on a column of mercury that is 29.9 inches high under standard conditions and taller under higher pressure and shorter under lower pressure. 2. Altimeters are based on barometric readings as are pressure gauges used by scuba divers Do the Scuba Diving and Blood Gases Case Study! Honors Chemistry Page 3 Chapter 11 Notes from Basic Chemistry You are now able to do problems Converting Between Units of Pressure Tutorial in your first homework assignment. III. Pressure and volume (Boyle’s Law). Read Section 11.3 in your eText! I will use the pressure-volume relationship (Boyle’s Law) to determine the new pressure or volume of a certain amount of gas at a constant temperature. A. Boyle’s Law. 1. Boyle’s Law— P1V1 = P2V2 Do the Pressure and Volume Tutorial! Guide to Using the Gas Laws STEP 1: Organize the data in a table of initial and final conditions. STEP 2: Rearrange the gas law for the unknown. STEP 3: Substitute values into the gas law and solve for the unknown. Problem 2: A sample of helium gas has a volume of 312 mL at 648 torr. If the volume expands to 825 mL at constant temperature, what is the new pressure in torr. Honors Chemistry Page 4 Chapter 11 Notes from Basic Chemistry Problem 3: A sample of methane gas, CH4, has a volume of 125 mL at 0.600 atm pressure and 25 °C. How many milliliters will it occupy at a pressure of 1.50 atm and 25 °C? You are now able to do problems 11.19 and 11.20 in your first homework assignment. IV. Temperature and volume (Charles’ Law). Read Section 11.4 in your eText! I will use the temperature-volume relationship (Charles’ Law) to determine the new temperature or volume of a certain amount of gas at a constant temperature. Do the Temperature and Volume Tutorial! A. Charles’ Law. 1. Charles’ Law— 2. All temperatures used in gas law calculations must be converted to their corresponding Kelvin (K) temperatures. V1 V2 = T1 T2 Problem 4: A mountain climber inhales 486 mL of air at a temperature of –8 C. What volume, in mL, will the air occupy in the lungs if the climber’s body temperature is 37 °C? You are now able to do problems 11.25 and 11.28 in your first homework assignment. V. Temperature and pressure (Gay-Lussac’s Law). Read Section 11.5 in your eText! I will use the temperature-pressure relationship (GayLussac’s Law) to determine the new temperature or pressure of a certain amount of gas at a constant volume. Do the Temperature and Pressure Tutorial! A. Gay-Lussac’s Law. Honors Chemistry Page 5 Chapter 11 Notes from Basic Chemistry 1. Gay-Lussac’s Law— 2. All temperatures used in gas law calculations must be converted to their corresponding Kelvin (K) temperatures. P1 P = 2 T1 T2 Problem 5: In a storage area where the temperature has reached 55 °C, the pressure of oxygen gas in a 15.0-L steel cylinder is 965 torr. To what Celsius temperature would the gas have to be cooled to reduce the pressure to 850. torr? B. Vapor pressure and boiling point. 1. Vapor pressure— 2. As temperature increases, more vapor forms, and vapor pressure increases. 3. A liquid reaches its boiling point when its vapor pressure becomes equal to the external pressure. 4. At higher altitudes, atmospheric pressures are lower and the boiling point of water is lower than 100 °C. 5. Pressure cookers and autoclaves are sealed and increase the pressure, which increases the boiling point of the liquid. You are now able to do problems 11.30, 11.31 and 11.36 in your first homework assignment. VI. The combined gas law. Read Section 11.6 in your eText! I will use the combined gas law to find the new pressure, volume, or temperature of a gas when changes in two of these properties are given. Do the Combined Gas Law Tutorial! A. The Combined Gas Law. 1. The Combined Gas Law— P1V1 PV = 2 2 T1 T2 Honors Chemistry Page 6 Chapter 11 Notes from Basic Chemistry Problem 6: A weather balloon is filled with 15.0 L of helium at a temperature of 25 °C and a pressure of 685 mmHg. What is the pressure, in mmHg, of the helium in the balloon in the upper atmosphere when the temperature is –35 °C and the volume becomes 34.0 L? You are now able to do problems 11.38 and 11.41 in your first homework assignment. VII. Volume and moles (Avogadro’s Law). Read Section 11.7 in your eText! I will use Avogadro’s law to describe the relationship between the amount of a gas and its volume, and use this relationship in calculations. Do the Volume and Moles Tutorial! A. Avogadro’s Law. 1. Avogadro’s Law— V1 V2 = n1 n2 Problem 7: A sample containing 8.00 g of oxygen has a volume of 5.00 L. What is the volume (L) after 4.00 g of oxygen is added to the 8.00 g of oxygen in the balloon, if the temperature and pressure do not change? B. STP and molar volume. 1. STP— a. Standard temperature is exactly 0 °C (273 K). b. Standard pressure is exactly 1 atm (760 mmHg). 2. Molar volume— Honors Chemistry Page 7 Chapter 11 Notes from Basic Chemistry 1 mol gas (STP) = 22.4 L 22.4 L 1 mol gas (STP) 1 mol gas (STP) 22.4 L Problem 8: What is the volume (L) of 5.10 g He at STP? C. Density of a gas at STP. 1. Because of Avogadro’s Law, the volume of one mole of gas at STP is known to be 22.4 L. 2. The formula for the density of any gas at STP can be calculated using the mass of a mole (mass found in the Blue Sheet) divided by the volume of a mole (22.4 L). 3. Calculating the density of carbon dioxide (44.00 g/22.4 L or 1.96 g/L) explains why balloons filled with this gas settle on the floor and balloons of oxygen (32.00 g/22.4 L or 1.43 g/L) will float just above them and helium balloons (4.00 g/22.4 L or 0.179 g/L) will rise rapidly because the density of air is 1.29 g/L. Problem 9: What is the density of hydrogen gas (H2) at STP? You are now able to do problems 11.50 and Avogadro’s Law Simulation in your second homework assignment. VIII. The Ideal Gas Law. Read Section 11.8 in your eText! I will use the ideal gas law to solve for P, V, T, or n of a gas when given three of the four values in the ideal gas law. Calculate density, molar mass, or volume of a gas in a chemical reaction. Do the Introduction to the Ideal Gas Law Tutorial! A. The Ideal Gas Law. 1. The Ideal Gas Law— Honors Chemistry PV = nRT Page 8 Chapter 11 Notes from Basic Chemistry PV nT (1 atm)(22.4 L) 0.0821 atm iL For one mole at STP: R = = (1.00 mol)(273 K) mol iK If we rearrange the equation: R = 2. Universal gas constant, R,— Problem 10: Chlorine gas, Cl2, is used to purify the water in swimming pools. How many moles of chlorine gas are in a 7.00-L tank if the gas has a pressure of 865 mmHg and a temperature of 24 K? Problem 11: What is the volume of 1.20 g of carbon monoxide at 8 °C if it has a pressure of 724 mmHg? B. Molar mass of a gas. 1. The molar mass of a gas can be determined by determining the number of moles of a gas and then dividing the mass of the gas by the number of moles. Do the Introduction to the Ideal Gas Law Self Study! Problem 12: What is the molar mass of an unknown gas in a 1.50-L container if 0.488 g of the gas has a pressure of 0.0750 atm at 19.0 °C? Honors Chemistry Page 9 Chapter 11 Notes from Basic Chemistry You are now able to do problems 11.58 and 11.86 in your second homework assignment. IX. Gas laws and chemical reactions. Read Section 11.9 in your eText! I will determine the mass or volume of a gas that reacts or forms in a chemical reaction. Do the Ideal Gas Law and Stoichiometry Tutorial! A. Gas laws and chemical reactions. 1. The Ideal Gas Law can be incorporated into a stoichiometry reaction. a. Convert the given mass into moles. b. Finding the moles of the wanted gas will set you up to use the Ideal Gas Law. c. The moles of the wanted gas will become the “n” factor in the equation and volume can be determined. Guide to Reactions Involving Gases STEP 1: Calculate the moles of given using molar mass or ideal gas law. STEP 2: Determine the moles of needed using a mole-mole factor. STEP 3: Convert the moles of needed to mass or volume using molar mass or ideal gas law. Problem 13: If 12.8 g of aluminum reacts with HCl, how many liters of H2 would be formed at 715 mmHg and 19 °C? 2Al(s) + 6HCl(aq) 2AlCl3(aq) + 3H2(g) You are now able to do problems 11.60, 11.62, 11.64, and 11.104 in your second homework assignment. X. Partial Pressures (Dalton’s Law). Honors Chemistry Page 10 Chapter 11 Notes from Basic Chemistry Read Section 11.10 in your eText! I will use partial pressures to calculate the total pressure of a mixture of gases. Do the Mixtures of Gases Tutorial! A. Partial Pressures (Dalton’s Law). 1. Partial pressure— 2. Dalton’s law— Ptotal = P1 + P2 + P3 + … B. Air is a gas mixture. 1. The air you breathe is approximately 78.2% nitrogen and 21.0% oxygen. 2. Carbon dioxide, argon, and water make up about 0.8%. Guide to Solving for Partial Pressure STEP 1: Write the equation for sum of partial pressures. STEP 2: Solve for the unknown pressure. STEP 3: Substitute known pressures and calculate the unknown. Honors Chemistry Page 11 Chapter 11 Notes from Basic Chemistry Problem 14: An anesthetic consists of a mixture of cyclopropane gas, C3H6, and oxygen gas, O2. If the mixture has a total pressure of 1.09 atm, and the partial pressure of the cyclopropane is 73 mmHg, what is the partial pressure of the oxygen in the anesthetic? C. Gases collected over water. 1. Collecting gas is hard to do because it can easily escape. 2. Bubbling a gas into an inverted container, filled with water can capture the gas the gas without letting it escape. 3. The water vapor that occurs because of evaporation must be subtracted from the pressure reading of the collected gas. Guide to Gases Collected over Water STEP 1: Obtain the vapor pressure of water. STEP 2: Subtract vapor pressure from total P of gas mixture to give partial pressure of needed gas. STEP 3: Use ideal gas law to convert Pgas to moles or grams of gas collected. Honors Chemistry Page 12 Chapter 11 Notes from Basic Chemistry Problem 15: A 456-mL sample of oxygen gas (O2) was collected over water at a pressure of 744 mmHg and a temperature of 20. °C. How many grams of dry O2 were collected? You are now able to do problems 11.66 in your second homework assignment. Honors Chemistry Page 13 Chapter 11 Notes from Basic Chemistry