Name Chemistry Pre-AP Notes: Gas Laws and Gas Stoichiometry Period Part 1: The Nature of Gases and The Gas Laws I. Nature of Gases A. Kinetic-Molecular Theory The - theory was developed to account for the behavior of atoms and molecules that make up and is based on the idea that particles of matter are always in. An gas is an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory below. Assumptions of the Kinetic-Molecular Theory of Gases: 1. Gases consist of large numbers of tiny particles. Particle size is relative to the overall volume. - gas particles occupy volumes 800-1000 times compared to liquid or solid state - most of the volume of a gas is 2. Collisions between gas particles and between particles and container walls are collisions, meaning that there is net loss of energy. - total kinetic energy remains as long as remains constant 3. Gas particles are in, rapid, motion. 4. There are no or forces between gas particles. 5. The energy of a gas particle depends on its and KE = B. Nature of Gases 1. Expansion gases do not have definite or gases completely any closed container explained by fact that gas particles move rapidly in directions 2. Fluidity gas particles easily past one another explained by high energy and lack of forces between gas particles a substance whose particles flow is called a (both gases and liquids) 3. Low Density density of a gas is MUCH than the density of the same substance in the liquid or solid state (800-1000 times lower) 1
explained by the fact that gas particles are very apart 4. Compressibility the of a gas can be greatly decreased or increased explained by the fact that most of the volume of a gas is C. Deviations from Ideal Gas Behavior most gases do not exhibit gas behavior a gas is a gas that does not behave totally according to the - theory in reality, gas particles do occupy and exert forces on one another the deviation from ideal gas behavior is greatest at pressures and temperatures. gases get closer to exhibiting ideal behavior when there is attraction between gas particles (i.e. low pressures and high temperatures) Correction for nonideal behavior is beyond the scope of this course; in other words, we will assume ideal behavior in our calculations. II. Measuring Gases A. Temperature is a measure of the kinetic energy of the particles in a material. There will be a of kinetic energies in the particles within a sample of material. The average kinetic energy of any gas is directly proportional to its temperature in. C = K 273 K = C + 273 Important Temperatures C K Absolute Zero* Freezing point of water Standard Temperature Boiling point of water *Absolute Zero is the point at which all of particles completely stops (KE = 0 because velocity = 0). B. Pressure 1. Definition is defined as the amount of exerted by the particles in a gas as they hit the sides of the. P = 2
2. Units Units for pressure: o atmospheres (atm): 1 is defined as the average atmospheric pressure at o millimeters of mercury (mm Hg) 1 atm = mm Hg o Torr: named after Evangelista Torricelli 1 atm = Torr o kilopascals (kpa): metric unit for pressure 1 atm = kpa o pounds per square inch (psi): 1 atm = psi 3. Measuring Pressure A mercury was an early device used to measure atmospheric pressure. It was invented by Evangelista Torricelli in the 1600s. It consisted of a straight glass tube filled with and closed at one end. It was placed with the open end down in a dish of mercury and the height of mercury that rose in the column was measured. 4. Factors Affecting Gas Pressure At sea level the height of mercury in a mercury barometer is typically or. We live at the bottom of an ocean of air. --Torricelli http://www.mhhe.com/physsci/chemistry/animations/chang_2e/properties_of_gases.swf Three main factors affect the pressure (P) of a gas:,, and. 1) Amount of a Gas (or moles, n) As the amount of gas in a container increases, pressure. 3
2) Volume (V) As the volume of a container increases, the pressure. 3) Temperature (T) As the temperature of a gas increases, the pressure. C. Standard Values STP stands for and is defined as and. III. Gas Laws A. Boyle s Law 22.4 L = 1 mole for any ideal gas at STP Boyle s Law states that the pressure of a fixed amount of gas is proportional to its. (at constant ) Formula: Sketch of Graph: 4
B. Charles Law Charles Law states that the of a fixed amount of gas is proportional to its in. (at constant ) Formula: Sketch of Graph: What does a constant pressure situation look like? The container must be able to expand and/or contract (change volume) so that the pressure stays constant even with changes in temperature. C. Gay-Lussac s Law Gay-Lussac s Law states that the of a fixed amount of gas is proportional to its in. (at constant ) Formula: Sketch of Graph: 5
Conceptual Practice: Do not use a calculator! 1. If the volume of a gas is increased from 100. ml to 200. ml at constant T, does the pressure increase or decrease? By what factor? What law did you use? 2. If the Kelvin temperature of a gas is cut in half at constant V, does the pressure increase or decrease? By what factor? What law did you use? 3. If the temperature of a gas increases from 300 K to 900 K at constant P, does the volume increase or decrease? By what factor? What law did you use? 4. If the volume of a gas is decreased from 10.0 L to 2.0 L at constant T, does the pressure increase or decrease? By what factor? What law did you use? D. Combined Gas Law All 3 gas laws can be obtained from the Combined Gas Law: Just block out any variable that is constant to obtain the simpler Boyle s, Charles, or Gay- Lussac s Law. Gas Law Calculations: **To minimize unit conversion errors, rearrange the formula first before plug-in** Ex 1: A high-altitude balloon contains 30.0 L of helium at 103 kpa. What is the volume when the balloon rises to an altitude where the pressure is 0.750 atm? (Assume constant T) Ex 2: The gas left in an aerosol can is at a pressure of 1.5 atm at 25 C. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches the fire temperature of 928 C? Ex 3: The volume of a gas-filled balloon is 30.0 L at 40 o C and 153 kpa. What volume will the balloon have at STP? 6
Practice 1. The pressure on a 2.50 L cylinder of anesthetic gas changes from 105 kpa to 40.5 kpa. What will the new volume be if the temperature of the gas remains constant? 2. A gas at 155 kpa and 25 o C occupies a container with an initial volume of 1.00 L. By changing the volume, the pressure of the gas increases to 605 kpa as the temperature is also increased to 125 o C. What is the new volume? 3. A gas with a volume of 3.00 x 10 2 ml at 150.0 o C is heated until its volume is 6.00 x 10 2 ml (at constant pressure). To what temperature was this gas heated? E. Dalton s Law of Partial Pressures (for mixtures of gases) The contribution each gas in a mixture makes to the total pressure is called the pressure exerted by that gas. In a mixture of gases, the pressure is the of the partial pressures. Ex: A gas mixture containing oxygen, nitrogen, and carbon dioxide has a total pressure of 257 mm Hg. If P O2 = 52 mm Hg and P N2 = 171 mm Hg, what is P CO2? Part 2: The Ideal Gas Law and Gas Stoichiometry I. Avogadro s Law Avogadro s Law states that volumes of gases at the temperature and pressure contain equal numbers of particles (moles). - Remember, at STP, particles will have a volume of Using Avogadro s Law at STP: 7
Ex 1: Determine the volume (in L) occupied by 212 g of oxygen at STP. Ex 2: Determine the density of nitrogen at STP. (hint: assume 1 mole of nitrogen) Practice 1. Suppose you need 4.22 ml of chlorine gas. What mass would you need to use at STP? 2. The density of an unknown gas at STP is 2.09 g/l. What is its molar mass? II. Ideal Gas Law Until now, we have always kept the of gas constant. Recognize that as the amount of gas changes, its corresponding changes. (Avogadro s Law; assumes constant T and P) the number of moles of gas is proportional to its volume. V α n If we want to relate all 4 variables to each other, it looks like this: V α nt P If we call the proportionality constant R, the relationship can be written as follows: Ideal Gas Law: V = R x nt P This constant R, called the ideal gas constant, can be determined using the volume of 1 mole of gas at STP: 8
Other commonly used values for R (different units) can be found in your homework packet or online. Using the Ideal Gas Law: Ex 1: You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen to a final pressure of 2.00 x 10 4 kpa at 28 C. How many moles of nitrogen does the cylinder contain? Another form of the ideal gas law can be used to solve for density (D) or molar mass (M) of a gas: (density has the units g/l for this equation; recall that molar mass is in units of g/mol) M = DRT P EX 2: 1.67 g of an unknown liquid are vaporized at a temperature of 125 C. The gas volume is measured as 0.421 L at 749 mm Hg. Calculate the molar mass. Practice 1. When the temperature of a rigid hollow sphere containing 685 L of helium is held at 621 K, the pressure of the gas is 1.89 x 10 3 kpa. What mass of helium does the sphere contain? 2. A tank of hydrogen has a volume of 22.9 L and hold 14.0 mol of gas at 12 C. What is the reading on the pressure gauge in atm? 3. Hydrogen is the least dense of all substances at a given temperature and pressure. Calculate its density in g/l at typical reaction conditions of 22 C and 751 mm Hg. III. Stoichiometry of Gases RECALL: For reactions with gaseous reactants and products, the in a balanced equation can be used to determine volume ratios. (assuming all substances are at the same temperature and pressure) Ex 1: What volume of oxygen is needed for the complete combustion of 4.00 L of propane (C 3 H 8 )? (assume all gases at same conditions) 9
Of course, typical stoichiometry can be combined with the ideal gas law as well: Ex 2: If 5.00 L of nitrogen reacts with excess hydrogen at 3.00 atm and 298 K, what volume of ammonia is produced at STP? Ex 3: What volume of oxygen gas (in L) can be collected at 0.925 atm and 25.0 C when 123.4 g of potassium chlorate (solid) decompose? Practice 1. What mass of sodium is needed to produce 61.2 L of hydrogen at STP via the given reaction: 2 Na + 2 H 2 O 2 NaOH + H 2 2. Determine the volume of hydrogen gas that forms at 25.0 C and 98.3 kpa when 9.00 g of aluminum reacts with 9.00 g of hydrochloric acid. IV. Measuring Gases in the Lab Gases that do not dissolve well in water can be collected by in the lab. In most cases, the gas is collected in a long, graduated tube called a, that is filled with water and inverted over a pan or glass dish also filled with water. The gas is collected by inserting an inlet tube into the bottom of the eudiometer. The height of the eudiometer is then adjusted so the level of water in the eudiometer is equal to the level of water in the pan. The pressure of the gas inside the eudiometer is then equal to pressure. 10
Once you have collected a gas, you now have TWO gases in the tube: the collected gas and. To determine the partial pressure of the dry collected gas, subtract the of water from the atmospheric pressure. Vapor pressure is the pressure exerted by a vapor over its liquid. Atmospheric pressure = pressure of gas + vapor pressure of water (this is Dalton s Law) So. Pressure of gas = Atmospheric pressure vapor pressure of water The vapor pressure of water is dependent on temperature and must be determined from a vapor pressure table. Examples: Temperature ( C) Vapor Pressure (mm Hg) 20 17.5 21 18.7 22 19.8 23 21.1 24 22.4 25 23.8 Ex 1: 500.0 ml of hydrogen is collected over water when the atmospheric pressure is 757 mm Hg. If the temperature of the collected gas is 25 C, what is the volume of hydrogen at STP? (Assume levels of water inside and outside the collecting tube are the same.) Practice 1. Methane gas is collected in an eudiometer at 25 C. When the water level is equalized inside and outside the tube, the volume of gas inside the tube is 78.0 ml. If the atmospheric pressure is 764 mm Hg, determine the volume of methane collected at STP. 11