Gas Laws - Chemistry 1 - Unit 4

GENERAL _ CHEMISTRY 1 - Unit 4 — The Gas Phase Chapter 9: The Gas Law Chapter 10: Kinetic Molecular Theory DESCRIBING GASES 7 Learning Outcomes = We should be able to: ¢ Describe gases, and explain the postu...

GENERAL _ CHEMISTRY 1 - Unit 4 — The Gas Phase Chapter 9: The Gas Law Chapter 10: Kinetic Molecular Theory DESCRIBING GASES 7 Learning Outcomes = We should be able to: ¢ Describe gases, and explain the postulates if the kinetic theory as applied to gases ¢ Relate how these postulates account for the properties of gases  GAS | It is a matter in a state in | which it will expand freely to fill the whole of a container, having no fixed shape (unlike a solid) and no fixed volume (unlike a liquid). = —_| = WHY ARE GASES 14 IMPORTANT? FUNDAMENTALS OF GASES * VOLUME PRESSURE ° TEMPERATURE ° MOLE VOLUME * quantity of 3-dimensional space occupied by matter. * common units used to express volume : Liters (1), cubic meters (m°*), milliliters (ml) PRESSURE °* a force’ exerted by the substance per unit area on another substance * common units used: atm, torr, Pa and kPA (a) Low pressure (b) High pressure PRESSURE ¢ other units used: |bs per square foot, Ibs per square inch, kg per Square centimeter a quliy My) / = QP sone (a) Low pressure (b) High pressure TEMPERATURE ¢ measures the kinetic energy of the gas molecules * common units used: Celsius, Fahrenheit, kelvin [| Cotee Temperature (T2) FOR THESE LESSON, WE WILL BE USING TEMPERATURE MEASUREMENTS IN KELVIN (KX) The Kelvin scale starts at Absolute 0, which is -273.15°C. To convert Celsius to Kelvin, add 273.15 EXAMPLE: 20 °C TO K 20+ (273.15) = 293.15 K MOLE ‘amount of substance which contains the same number of particles Since we cant count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular weight of the gas. 23 6.022 x 10 How do they all relate? GAS LAWS as properties can be modeled using math. Model depends on ¢ V=volume of the gas (L) ¢ T= temperature (IK) ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! * n= amount (moles) ¢ P= pressure (atmospheres)  FACTORS AFFECTING PRESSURE - David Bowie AMOUNT OF GAS: Increasing the number of particles increases _ collisions which increases pressure. Removing particles reduces pressure. VOLUME: Increasing the volume will decreases the pressure of a gas since collisions are less likely. Decreasing the volume has the opposite effect. TEMPERATURE: Increasing the temperature increases the speed of the molecules, w/c leads to more collisions and greater pressure. GAS LAWS If the temperature is constant, as pressure of a gas increases the volume decreases. How is the pressure applied to a gas related to its volume? Gas molecules Gas molecules Piston Volume is inversely proportional to applied pressure. Boyle’s Law: P1V1 = P2V2 Problem #1: A gas occupies 14.3 liters at a pressure of 42.0 mmHg. What is the volume when the pressure is increased to 69.0 mmHg? Vi=14.3L P1i= 42.0 mmHg V2 = 42.0 mmNg x 14.3 L V2= ? P2= 69.0 mmHg 69.0 NmHg R A V2=8.70L V2= 7? Problem #2: lf the pressure of helium gas in a balloon has a volume of 4.0 L at 210 kPa, what will the pressure be at2.5L? Vi= 4.0 L P1=210 kPa V2 = 210 kPa Kye V2= 2.5L P2=? 2.5 A V2 = 336 kPa P2V/2 If the pressure is constant, as temperature of a gas increases the volume increases. Temperature must be in Kelvin for all gas laws How is the volume of a gas related to its temperature? volume of a gas is moveable mass ree (constant pressure) directly proportional to san molecule its absolute temperature Why did the volume change? What happens to the average speed of the gas molecules?  How is the volume of a gas related to its temperature? moveable mass (constant pressure) gas molecules The volume of a gas is directly proportional to its Temperature (temperature must be in Kelvin) CHARLES’S LAW: ee Problem #1. A gas sample is observed to occupy 12.0L under a pressure of 101.325kPa (also 1 atm) at 27 °C. What will be the volume of the gas if it is heated to 5/7 °C under the same pressure? Problem #1: A gas sample is observed to occupy 12.0L under a pressure of 101.325kPa (also 1 atm) at 2/7 °C. What will be the volume of the gas if it is heated to 5/7 °C under the same pressure? Vi=12.0L P1= 101.325 kPa V2= 12.0 L x 330 V2= ? P2= 101.325 kPa 300 T1= 27+273= 300K T2= 57+ 273= 330k A V2=13.2L V2=? Vi = V2 Problem #2: A sample of gas occupies a volume of 275 ml at 20 °C at 1 atm pressure. Calculate the volume of the gas at 0 °C and 1 atm pressure ? Problem #2: A sample of gas occupies a volume of 275 mi at 20 °C at 1 atm pressure. Calculate the volume of the gas at O °C and 1 atm pressure? Vi= 275 mL T1= 20+273= 293K V2 =275 mL x _ 273 V2= ? T2= 0+273= 273 K 293 A V2 = 256.23 mL V2= ? Vi =NV2 Problem #3: Calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L. Problem #3: Calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L. Vi= 6.00 L T1= 20+273= 293K s T2 =4.00 Ax 293 K V2= 4.00 L T2=? 6.00 A T2=195 K T2= ? V1 = V2 ¢ Problem #2: A container containing 5.00 L of a gas is collected at 100 K and then allowed to expand to 20.0 L. What must the new temperature be in order to maintain the same pressure (as required by Charles’ Law)? Temperature & Pressure: Gay- Lussae’s Law As the temperature of an enclosed gas increases the pressure increases at constant volume. GAY- LUSSAC’S LAW: P, P, T, T, ¢Problem #1: The pressure of a gas in a tank is 3.2 atm at 22 °C. If the temperature rises to 60 °C, what will be the pressure in the tank? ¢Problem #2: If a gas is cooled from 323.0 K to 273 K and the volume is kept constant. What final pressure would result if the original pressure was 750.0 mmHg? What is the primary factor that determines the pressure of a gas? TEMPERATURE VOLUME NUMBER OF MOLES What is the primary factor that determines the pressure of a gas? TEMPERATURE VOLUME NUMBER OF MOLES eee A sealed container of gas has a pressure of 2.0 atm at a temperature of at a temperature of 3U0 K. It the temperature of the gas is increased to gas is increased to BUU K, what will be the new pressure of the gas? IDEAL GAS LAWS  IDEAL GAS LAWS 1. Contains ALL variables Standard Pressure 2 PV=nRT 1atm= 760 torr 760 mmHg. Witere 101.3 kPa P =pressure (depends on R) 14.7 psi V = volume (liters) n = amount of gas (moles) R = ideal gas constant (depends on pressure) (8.3 J/(mol-K)) or (0.0821 L-atm/(K-mal) T = temperature (Kelvin)  IDEAL GAS LAWS 1. Contains ALL variables Standard Pressure 2. PV=nRT 1atm= 760 torr 3. Where 760 mmHg P = pressure (depends on R) 101.3 kPa V = volume (liters) 44 7. n = amount of gas (moles) PS R = ideal gas constant (depends on R=(8.314 J/ (mol-K)) pressure).. T = temperature (Kelvin) (0.0821 L-atm/ (K mal) 8.314J mol K = 8.314 kPa.L/ mol K since lJ =lkPaL P= 1 kPa = 1000 Pa Problem #1 A sample of carbon dioxide (CO) gas is collected at a pressure of 95 kPa and a temperature of 25.0 °C. If there are 0.150 moles of CO,, what is the volume of the gas in liters? Problem #2 A sample of an ideal gas is contained in a 5.0-liter vessel at a pressure of 2.0 atm and a temperature of 300 K. How many moles of the gas are present in the vessel? Problem #3 Oxygen gas is collected at a pressure of 123 kPa in a container w/c has a volume of 10.0L. What temperature must be maintained on 0.500 moles of this gas in order to maintain this pressure. Express the temperature in degree Celsius. Problem # 4 What volume of He is occupied by 2.35 mol of He at 25 Cand a pressure of 0.980 atm.  DALTON’S LAW OF PARTIAL PRESSURE DALTON’S LAW OF PARTIAL PRESSURE states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases 1. Contains only pressure 2. Where pressure must be in the same units S Pig total Py Pt Pet wax Problem #1: A container has 3 gases in it, C, CO, NH3. The partial pressures of the gases are 3.0 atm, 2.5 atm, and 1.5 atm respectively. What is the total pressure inside the container. Problem #2: lf the total pressure of a mixture of oxygen & nitrogen gases was 820 mmHg, how much pressure would nitrogen exert if oxygen had 580 mmHg? Problem #3: A container holds three gases: nitrogen (N2), oxygen (O2), and argon (Ar). The partial pressures of nitrogen and oxygen are 600 torr and 150 torr, respectively. What is the partial pressure of argon, and what is the total pressure in the container? Problem #3: A laboratory experiment involves a gas mixture containing nitrogen (Nz) and argon (Ar). The partial pressures of nitrogen and argon are measured to be 450 mmHg and 200 mmbdg, respectively. What is the total pressure of the gas mixture? VOR TRC AR THEORY  KINETIC MOLECULAR THEORY ¢ defines pressure as the force exerted per unit area in container walls ¢ [ft the temperature remains constant, the rate of molecular collisions does not change the total force exerted by the molecules does not change. However, if the volume of the gas is decreased, the total surface area is decreased and this results to an increase in force per unit area. This means that at constant temperature, a decrease in volume causes the increase in pressure. [his supports the inverse relationship between pressure and volume in constant temperature described by Boyle's Law.  The Kinetic Theory of Matter A theory of. the thermodynamic behavior of matter where particles (atoms> mall molecules, GF ions) in all forms of matter (solid, liquid, gas, and plastia) are in constant motion: either vibrate, slide, or fly around. - Kinetic Energy of Particles of Matter Increasing —— > Distance between Particles of Matter Increasing ——a> Speed between Particles of Matter Increasing —— > Solid Liquid Gas Plasma Molecules have strong Molecules have moderate Molecules fly in random Mixture of electrons and attractive forces between attractive forces between directions at high speed nuclei when atoms lose them and = arranged in them which prevent them when attractive forces their electros at extreme regular frequent pattern, from flying away and let between them are minor. high temperatures. but can vibrate’ within them take on the shape an insignificant area. of the containers. oN aw. am. 1 2 3 4 | | | The Four State of Matter Example: Temperature & Kinetic Energy In which of the following gas samples do molecules process higher average kinetic energy? He(g) at 10°C or Ne(g) at 20 °C Example: Temperature & Kinetic Energy In which of the following gas samples do molecules process higher average kinetic energy? He(g) at 10°C or Ne(g) at 20 °C Example: Temperature & Kinetic Energy In which of the following gas samples do molecules process higher average kinetic energy? O2zg) at 20°C or CO(g) at 20°C Example: Temperature & Kinetic Energy In which of the following gas samples do molecules process higher average kinetic energy? O2zg) at 20°C or CO(g) at 20°C