University:
High School
Course:
High School Physics
Academic year:

2024
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311

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77
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SpaceCadet101

Unit- 5 Gases & Kinetic Molecular Theory Assumptions of Kinetic Molecular Theory 4 variables determine gas behavior: • Pressure – force exerted by molecules on an object • Volume – the amount of space they have to move in • Temperature- the amount of kinetic energy the molecules have • Amount of gas present (grams, moles, atoms) Variables that Influence Gases (check it out online) Can Crush Demo When you heat the can the water turns to steam, displacing the air. While there is steam in the can its pressure is equal to the air pressure outside, so there is no overall force on the can. When it cools, the steam condenses very rapidly, leaving nothing to support the can from the inside so the air pressure crushes it! Real Life “Can” Crush Marshmallow Man Normal Low Pressure States of Matter Phase Change Names 3 States of Matter Compared Solid Liquid Gas •Particles vibrate (low kinetic energy) • tightly packed •Strong intermolecular (attractive) forces • High density** • Not compressible • definite volume & shape •slide past each other (med. Kinetic energy) • not tightly packed • Medium Intermolecular forces (hydrogen bonds) • medium density • compressible •definite volume & takes shape of container •in rapid motion (High kinetic energy) • far apart • Weak intermolecular forces • low density •Highly compressible • diffuses- no set volume & takes volume of container Misconception: Density of Gases Not all gases “rise” • Helium =0.1613 g/L Helium is less dense than air and rises. • CO2 gas density= 1.98 g/L Dry ice ( carbon dioxide gas) is more dense than air & sinks Hot air moves faster and is less dense than cold air allowing for “hot air balloons” Misconception- Some solids are less dense than liquid form • Water is a unique example • Solid is less dense than liquid form Pressure The pushing force of an object Pressure & Gases • molecules exert pressure on an object when they collide with it • Pressure = force area Barometers • Measure the atmospheric pressure Weather forecasters use barometers Units of Pressure • • • • mmHg = millimeters of mercury torr – (named after Torricelli) pascal – (named after Pascal) atm - atmosphere 1 atm = 760 torr = 760 mmHg = 101 kPa Practice: Convert the following units of pressure: – USE DIMENSIONAL ANALYSIS – 2.5 atm  torr 2.5 atm x 760 torr 1 atm = 1900 torr – 789 mmHg  atm 789 mmHg x 1 atm 760 mmHg = 1.04 atm – 0.347 kPa  atm 0.347 kPa x 1 atm 101 kPa = 0.00344 atm Standard Temperature & Pressure (STP) • Most experiments with gases are done at STP • Known by everyone in science to be: – Standard temperature = 0 ºC (273 K) – Standard pressure = 1 atm - Standard volume for 1 mole of gas= 22.4 L (kind of like normal body temp. is known by everyone without having to say 98.6°F) Divers experience pressure of air above them and the water around them The atmosphere has pressure! Earth's atmosphere is pressing against each square inch of you with a force of 1 kilogram per square centimeter (14.7 pounds per square inch). -Why don’t you get crushed by all this pressure? Pressure of the Atmosphere • Higher density of air molecules = more pressure at sea level than at higher altitudes. Pressure & the Balloon Molecules create pressure inside the balloon Molecules create pressure outside the balloon What happens to the balloon? Balloon gets bigger (more pressure inside than outside) Balloon gets smaller (less pressure inside than outside) Real Life Examples • Ears popping on airplanes • Helicopter rescues on Mt. Everest • Body adaptations to altitude (produce more red blood cells) Temperature Temperature • measure of the average kinetic energy of the particles of a substance. Principles:  When molecules are moving, there is kinetic energy.  Hot molecules move faster than cold molecules.  Since it’s an average, it doesn’t depend on quantity of particles. 40° C 100° C Beaker A Beaker B Molecules in Beaker A, on avg. are moving slower than Beaker B Heat Vs. Temperature (briefly) Heat= total energy in a substance (kinetic & potential) -need to consider # of molecules Temperature= an aspect of heat… average kinetic energy 40° C 40° C Beaker A Ex: Temperatures are the same in the beaker & bathtub -Bathtub contains more heat because it has more molecules moving Temperature- average kinetic energy in molecules Measured in : • Farenheit (ºF) • Celsius (ºC) • Kelvin (K)! “KFC” ***All Temps must be converted to Kelvin for gas problems K = 273 + ºC °F = 1.8 (°C) + 32 Air moves at about 1,100 mph at room temp. Practice with Temperature • Convert the following units of temperature: • 0 ºC  K K = 273 + 0ºC = 273 K • 25 ºC (room temperature) K K = 273 + 25ºC = 298 K • 298 K  ºC 298 K – 273 = ºC = 25ºC • 252 k  ºC 252 K – 273 = ºC = -21ºC Absolute Temperature: Kelvin Scale • Absolute Zero = O Kelvin • Kelvin scale based on molecular motion. • O Kelvin = no molecular motion (not possible…molecules always move) • Unlike ºF & ºC, 0 Kelvin can’t be achieved. More on Absolute Zero • The lowest natural temperature recorded on Earth was in Antarctica -89.2 °C (-128.56 °F). • Low Temperature Lab, Finland 0.000 000 000 1 K above the absolute zero Volume • 3 dimensional space an object occupies Volume: 5 x 5 x 5 = 125 cm3 1 cm3 = 1 mL Contents cube would fill 125 mL in graduated cylinder. Volume Balloon A has a larger volume B A If both balloons have the same number of gas particles inside, how can they be different sizes? -Different temperature -Different pressure What would happen to the balloon? Think about why this is true: Increase in temp. causes molecules to move faster Faster molecules = more collisions More collisions = more pressure inside container More pressure = bigger volume What may happen to the can? • Think about why this is true: – Increase in temp. causes molecules to move faster – Faster molecules = more collisions – More collisions = more pressure inside container Gases are easily compressed Liquid The Gas Laws Mathematical relationships between volume, temperature, pressure and amount of gas Combined Gas Law: Pressure, Volume &Temperature P1V1 P2V2 = T1 T2 All temperatures must be in Kelvin!!! Sample Problem #1 • A sample of oxygen gas has a volume of 150 mL At standard pressure. What will the volume of the gas be at a pressure of 2 atm if temperature is held constant? Given V1 = 150 mL : P1 = 1 atm P2 = 2 atm Find: V2 Solution to sample #1 Given V1 = 150 mL P1 = 1 atm P2 = 2 atm Find: V2 Plan: P1 V1 = P2 V2 T1 T2 *Remove the T’s since temp is not part of this problem (…constant) *Solve Using algebra Solution: (1 atm) (150 mL) = (2 atm) V2 V2 = 75 mL Practice Problem #2 • A sample of neon gas occupies a volume of 752 mL at 25 ºC. What volume will the gas occupy at 50 ºC? Given: V1 = 752 mL T1 = 25 ºC + 273 = 298 K T2 = 50 ºC + 273 = 323 K All temperatures must be in Kelvin!!! Find: V2 Solution to sample # 2 Given: V1 = 752 mL T1 = 25 ºC + 273 = 298 K T2 = 50 ºC + 273 = 323 K Find: Plan: P1 V1 = P2 V2 T1 T2 *Remove the P’s since pressure is not part of this problem *Solve using algebra Solution: V 1 = V2 T1 T2 752 mL 298 K V2 = 815 mL = V2 323 K V2 Sample Problem #3 • Gas in an aerosol can is at a pressure of 3.00 atm 25 ºC. What would the pressure be in the can at 52 ºC? Given: P1 = 3.00 atm T1 = 25 ºC + 273 = 298 K T2 = 52 ºC + 273 = 325 K All temperatures must be in Kelvin!!! Find: P2 Practice Problem # 3 Given: P1 = 3.00 atm T1 = 25 ºC + 273 = 298 K T2 = 52 ºC + 273 = 325 K Find: P2 Plan: P1 V1 = P2 V2 T1 T2 *Remove the V’s since volume is not part of this problem *Solve using algebra Solve: P2 P2 (3.00 atm)(325 K) = 298 K = 3.27 atm Practice Problem #4 • A helium filled balloon has a volume of 50.0 L at 25 ºC and 1.08 atm. What volume will it have at 0.855 atm and 10 ºC? Given V1 = 50.0 L P1 = 1.08 atm : T1 = 25 ºC + 273 = 298 K P2 = 0.855 atm T2 = 10 ºC + 273 = 283 K Find: V2 Practice Problem #4 Given V1 = 50.0 L Find: V2 P1 = 1.08 atm T1 = 25 ºC + 273 = 298 K P2 = 0.855 atm T2 = 10 ºC + 273 = 283 K Plan: P1 V1 = P2 V2 T1 T2 *Solve using algebra Solve: V2 = V2 (1.08 atm)(50.0 L)(283 K) (0.855 atm)(298 K) = 60.0 L How Gases Behave Kinetic Molecular Theory Diffusion • The random mixing of different gas particles Osmosis= diffusion of water Assumptions of Kinetic Molecular Theory Ideal Gases Vs. Real Gas Ideal Gas- describes behavior of most gases @ normal temp. & press.: Fit assumptions of kinetic molecular theory: • Molecules far apart • Collisions are elastic • Continuous, rapid, random motion • No forces of attraction between molecules. Real Gas- a gas that does not behave ideally because of extreme conditions: • high pressures • low temperatures Why : • They get too close & move too slow and start to be attracted to each other. Ideal Gases Vs. Real Gases • We assume gases are “ideal” to simplify our calculations • Limitations: – Most accurate for monoatomic gases @ high temperatures and low pressures Ideal Gas Law Mathematical relationship between pressure, volume, temperature & number of moles of a gas Avogadro’s Law (Molar Volume of Ideal Gases) •1 mole of any gas at STP occupies a volume of 22.4 L •Same amount of gas = same volume 1 mol O2 gas Volume = 22.4 L Mass = 32.00 g # = 6.02 X 1023 1 mole 22.4 L 1 mol H2 gas Volume = 22.4 L Mass = 2.02 g # = 6.02 X 1023 Molar Volume Examples • What volume will 0.068 mol of O2(g) occupy at STP? 0.068 mol O2 22.4 L O2 1 mol O2 = 1.5 L O2 • How many moles of H2 (g) are in 40.6 L of gas? 40.6 L H2 1 mol H2 22.4 L H2 = 1.81 mol H2 Molar Volume Examples • How much does 0.098 L of SO2 (g) weigh at STP? 0.098 L SO2 1 mol SO2 22.4 L SO2 64.07 g SO2 = .28 g SO2 1 mol SO2 (molar mass) Ideal Gas Law Ideal gas constant (.0821) Pressure (atm) PV = nRT Volume (liters) # moles temperature (Kelvin) Ideal Gas Constant, “R” L·atm R = 0.0821 • mol·K How did we find the value of R? 1. Solve ideal gas law for R PV R= nT 2. Substitute variables with values from conditions of STP (1 atm)(22.4 L) R= (1 mol)(273 K) L·atm = 0.0821 mol·K Ideal Gas Law Example 1 • What is the pressure in atm exerted by a 0.5 mol sample of nitrogen gas in a 10 L container at 298 K? – Given: V = 10 L Find: P n = 0.5 mol R = 0.0821 (L·atm)/(mol·K) T = 298 K Ideal Gas Law Example 1 – Given: V = 10 L Find: P n = 0.5 mol R = 0.0821 (L·atm)/(mol·K) T = 298 K – Plan: PV = nRT P = nRT V – Solve: P = (0.5 mol)(0.0821 (L·atm)/(mol·K))(298 K) 10 L P = 1 atm Ideal Gas Law Example 2 • What is the volume, in liters, of 0.250 mol of oxygen gas at 20 C and 0.947 atm? – Given: P = 0.947 atm Find:V n = 0.250 mol R = 0.0821 (L·atm)/(mol·K) T = 20 C + 273 = 293 K Ideal Gas Law Example 2 • Given: P = 0.947 atm n = 0.250 mol R = 0.0821 (L·atm)/(mol·K) T = 20 C + 273 = 293 K • Plan: PV = nRT V = nRT P Find: V • Solve: V = (0.250 mol)(0.0821 (L·atm)/(mol·K))(293 K) 0.947 atm V = 6.35 L Ideal Gas Law example 3 • What volume will 56 g of nitrogen (N2) gas occupy at 720 Torr and 20 C ? Answer • PV = nRT (formula to use) P= 720 Torr x 1 Atm =.947 Atm 760 Torr V=? n = 56 g x 1 mole = 2 moles 28 g T= 20 + 273 = 293 K R= .0821 Plug in values into PV = nRT V= 51 L Phase Changes Generic Phase Diagram • tells you what temperature & pressure a substance must be in at each phase. 1 Atm = Sea Level 293 K = 68 F Room Temp. Phase Change Diagram for water- shows relationship between physical state of H2O and its temperature and pressure. critical point = temperature & pressure that substance cannot exist in liquid state. Triple point = where temperature & pressure conditions allow all 3 states of matter to exist. Sample questions At 1 atm of pressure, what temperature does water become a liquid? ( 0 C) At 0.5 atm of pressure, what temperature does water become a gas? ( 80 “ish” C… can’t tell exactly, but can estimate) Liquid Nitrogen Liquid Nitrogen Info. • Temp = - 320 F “Burn” off skin growths Cryogenics Liquid Nitrogen No amount of pressure will get nitrogen to be a liquid at room temperature Room Temperature 68 F = 293 K SNUBA Boyle’s Law: Pressure & Volume • As pressure increases, volume decreases : ↑P ↓V • As pressure decreases, volume increases: ↓P ↑V Pressure and Volume • Think about why this is true: – Pressure is caused by gas molecules hitting the container – If the volume of the container is decreased, the same number of gas molecules are moving in a much smaller area & will hit the container more often Charles’s Law: Volume & Temperature • When temperature increases, volume increases : ↑T ↑V • When temperature decreases, volume decreases: ↓T ↓ V Relationship between Volume and Temperature • Think about why this is true: – – – – Increase in temp. causes molecules to move faster Faster molecules  more collisions More collisions  more pressure inside container More pressure  bigger volume Gay-Lussac’s Law: Pressure & Temperature • When temperature increases, pressure increases : ↑T ↑P • When temperature decreases, pressure decreases: ↓T ↓P Relationship between Temperature and Pressure • Think about why this is true: – Increase in temp. causes molecules to move faster – Faster molecules  more collisions – More collisions  more pressure inside container