Gases Learning Guide 5.1 & 5.2 PDF

Gases Learning Guide 5.1 & 5.2  Desired Learning Competencies: Interpret the gas laws in terms of relationships between pressure, volume, temperature, and amount of gases. Solve mathematical problems applying the gas laws. Explain practical applications of the gas laws.  Gas Laws (Boy...

Gases Learning Guide 5.1 & 5.2  Desired Learning Competencies: Interpret the gas laws in terms of relationships between pressure, volume, temperature, and amount of gases. Solve mathematical problems applying the gas laws. Explain practical applications of the gas laws.  Gas Laws (Boyle’s,Charles’, Avogadro’s Law, Combined Gas Law) Learning Guide 521 1.What happens to a balloon left under the heat of the sun? 2.What happens to a balloon brought to a higher elevation? 3.What happens when a balloon is pumped with more gas? Variables we need to know: T, P, V, and n  TEMPERATURE (T) Temperature (T) – how fast gas particles are moving The kelvin scale does not have negative temperatures, and zero kelvin (0 K) is considered absolute zero. TKELVIN = TCELCIUS + 273.15 For example 0 C̊ = 273.15 K 25 C̊ = 298.15 K 100 C ̊ = 373.15 K  PRESSURE (P) Pressure – how frequent particles collide on walls of its container At sea level, the air pressure is 1 atm. STANDARD TEMPERATURE AND PRESSURE: Temperature = 273.15 K or 0 C ̊ Pressure = 1 atm NORMAL TEMPERATURE AND PRESSURE: Temperature = 293.15 K or 20 C ̊ Pressure = 1 atm  AMOUNT OF GAS (n): Expressed in moles At standard temperature and pressure (STP), 1 mole of gas occupying a volume of 22.4 L at 1 atm pressure.  Boyle’s Law Boyle’s Law states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to the volume of the gas. P1V1 = P2V2 at constant temperature P V  Sample Problems: 1. Calculate the volume of a sample of gas at 5.75 atm if it occupies 5.14 L at 2.49 atm. (Assume constant temperature.) Solution: Use the relationship below to solve for V2: P1V1 = P2V2 2.23 L 2. If a skin diver takes a breath at the surface, filling his lungs with 5.82 L of air, what volume will the air in his lungs occupy when he dives to a depth where the pressure of 1.92 atm? (Assume constant temperature and that the pressure at the surface is exactly 1 atm.) Strategy Use P1V1 = P2V2 to solve for V2. Solution P1 = 1.00 atm, V1 = 5.82 L, and P2 = 1.92 atm. Think About It At higher pressure, the volume should be smaller. Therefore, the answer makes sense.  APPLICATIONS of BOYLE’S LAW Breathing While inhaling, the lungs are filled with air; therefore, they expand. The volume increases, hence the pressure level goes down. Similarly, when the lungs are evacuated of air, they shrink; therefore, the volume reduces and the pressure increases.  APPLICATIONS of BOYLE’S LAW Inflating Tires When air is pressed into flat tires with the help of an air pump, the air molecules get tightly packed. The more the air molecules present in the tire, the more will be the pressure exerted on the walls of the tire.  APPLICATIONS of BOYLE’S LAW Soda Bottle A soda bottle, filled with a mixture of carbon dioxide and water. When the soda can or bottle is sealed, it is difficult to compress. This is because the air molecules present inside the container are tightly packed and do not have space to move. When the can or the bottle is opened, some of the air molecules escape, thereby making space for the movement of air molecules and allowing the bottle to get compressed.  APPLICATIONS of BOYLE’S LAW Syringe It consists of a cylinder to contain the fluid and a plunger to vary the pressure. When the plunger is pushed down, the volume of the fluid reduces, thereby increasing the pressure. Similarly, on pulling up the plunger, the volume is increased, and the pressure is reduced.  APPLICATIONS of BOYLE’S LAW Scuba Diving When a diver enters or approaches the depth of the water body, he/she experiences high pressure. The high pressure increases the solubility of gases in the human blood. When he/she tends to ascend or move upwards, the pressure begins to reduce, and the gases present in the blood begin to expand. Hence, the diver must ascend at a slow rate to avoid any sort of injury.  Charles’ Law states that the volume of a gas maintained at constant pressure is directly proportional to the absolute temperature of the gas. at constant pressure  Sample Problems: 1. A sample of argon gas that originally occupied 14.6 L at 25.0°C was heated to 50.0°C at constant pressure. What is its new volume? Strategy Use V1/T1 = V2/T2 to solve for V2. Remember that temperatures must be expressed in kelvin. Solution T1 = 298.15 K, V1 = 14.6 L, and T2 = 323.15 K. Think About It When temperature increases at constant pressure, the volume of a gas sample increases. 2. A container holds 50.0 mL of nitrogen at 25oC and a pressure of 726 mmHg. What will be its volume if the temperature increases by 35oC? Strategy Use V1/T1 = V2/T2 to solve for V2. Remember that temperatures must be expressed in kelvin. Solution T1 = 298 K, V1 = 50 mL, and T2 = 333 K V1 × T2 50.0 mL × 333 K V2 = = 298 K = 55.9 mL T1 APPLICATION OF CHARLES’ LAW Learning Check: 1. A sample of gas has an initial pressure of 2.44 atm and an initial volume of 4.01 L. Its pressure changes to 1.93 atm. What is the new volume if temperature and amount are kept constant? 2. A sample of gas has an initial pressure of 722 torr and an initial volume of 88.8 mL. Its volume changes to 0.663 L. What is the new pressure? 3. A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 liters. If the balloon is filled with 2.0 liters of helium at sea level (101.3 kPa), and rises to an altitude of 88.144 kPa, will the balloon burst? 4. When the volume of a gas is changed from ___ mL to 852 mL, the temperature will change from 315 °C to 452 °C. What is the starting volume? Learning Check: A sample of gas has an initial pressure of 2.44 atm and an initial volume of 4.01 L. Its pressure changes to 1.93 atm. What is the new volume if temperature and amount are kept constant?  A sample of gas has an initial pressure of 722 torr and an initial volume of 88.8 mL. Its volume changes to 0.663 L. What is the new pressure?  A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 liters. If the balloon is filled with 2.0 liters of helium at sea level (101.3 kPa), and rises to an altitude of 88.144 kPa, will the balloon burst? = 2.3 L  When the volume of a gas is changed from ___ mL to 852 mL, the temperature will change from 315 °C to 452 °C. What is the starting volume?  Avogadro’s Law Avogadro’s law states that the volume of a sample of gas is directly proportional to the number of moles in the sample at constant temperature and pressure. at constant temperature and pressure Avogadro’s Law: V1/n1=V2/n2  Sample Problem: 1. 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? Solution: V1n2 = V2n1 (5.00 L) (1.80 mol) = (x) (0.965 mol) x = 9.33 L  Learning Check: 1. A balloon has been filled to a volume of 1.90L with 0.0920mol of helium gas. If 0.0210 mol of additional helium is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?  A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.)  Combined Gas Law States that, for a given amount of gas, the volume is inversely proportional to the pressure and directly proportional to its absolute temperature If n1=n2 Cooling at constant volume: Heating at constant pressure decreases volume: pressure increases  Sample Problems: 1. The volume of a bubble starting at the bottom of a lake at 4.55°C increases by a factor of 10 as it rises to the surface where the temperature is 18.45°C and the air pressure is 0.965 atm. What is the initial pressure of air inside the bubble Solution: 2. If a child releases a 6.25-L helium balloon in the parking lot of an amusement park where the temperature is 28.50°C and the air pressure is 757.2 mmHg, what will the volume of the balloon be when it has risen to an altitude where the temperature is -34.35°C and the air pressure is 366.4 mmHg? Solution T1 = 301.65 K, T2 = 238.80 K. V2 = P1T2V1 = 757.2 mmHg × 238.80 K × 6.25 L = 10.2 L P2T1 366.4 mmHg × 301.65 K  Learning Check: Find the volume of a gas at STP when 2.00 liters is collected at 745.0 mm Hg and 25.0 degrees Celsius.  A balloon of air now occupies 10.0 L at 25.0 °C and 1.00 atm. What temperature was it initially, if it occupied 9.40 L and was in a freezer with a pressure of 0.939 atm?  A gas occupies an 8.00 mL flexible-walled container. The pressure is doubled, the absolute temperature is quadrupled, and 15% of the gas leaks out. What is the new volume? Assume values: 1.00 atm and 1.00 K Learning Check A flexible container at an initial volume of 5.120 L contains 8.500 mol of gas. More gas is then added to the container until it reaches a final volume of 18.10 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container. If 0.00810 mol neon gas at a particular temperature and pressure occupies a volume of 214 mL, what volume would 0.00684 mol neon gas occupy under the same conditions? Learning Check A gas has a volume of 800.0 mL at −23.0 °C and 300.0 torr. What would the volume of the gas be at 227.0 °C and 600.0 torr of pressure? Applications of Gas Laws: https://www.youtube.com/watch?v=lSHpqUYv 9-M  REFERENCES Brown, T.L., LeMay, H.E., Bursten, B.E., Murphy, C.J., and Woodward, P.M. (2012) Chemistry: The Central Science, (12th Edition). Pearson Publishing Inc. Petrucci, Ralph H., Herring, F. Geoffrey., Madura, Jeffrey D., Bissonnette, Carey, (2011) General Chemistry: Principles and Modern Applications (10th Edition) Pearson Canada Inc. Silverberg, Martin S., (2006) Chemistry: The Molecular Nature of Matter and Change (4th Edition) Mc Graw Hill Higher Education. Silverberg, Martin S., (2013) Principles of General Chemistry (3rd Edition) McGrawHill Companies, Inc., New York. Wilbraham, Anthony C., Staley, Dennis D., Matta, Michael S., Waterman, Edward L. (2005) Chemistry (4th Edition) Prentice-Hall Inc.