Gases Kinetic Molecular Theory and Gas Laws Learning Objectives Be able to explain behavior of Gases using Kinetic Molecular Theory Explain relationship of volume temperature and pressure Use absolute temperature scale ID: 762063
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Gases Kinetic Molecular Theory and Gas Laws
Learning Objectives Be able to explain behavior of Gases using Kinetic Molecular Theory Explain relationship of volume, temperature, and pressure Use absolute temperature scale Explain partial pressure, diffusion.
What is air? Air is a homogeneous mixture of gases: N 2 (78%), O 2 (~ 20%), Ar , CO 2 , Ne, He, CH 4 , Kr.
Composition of Air
States of Matter
Gas Gas is a state of matter in which particles (atoms or molecules) are moving randomly throughout a volume that is primarily empty space.
Gas Pressure Gas pressure results from the collisions of gas particles with the walls of the container . Gas pressure depends on Force of collisions of gas particles with an object Number of collisions
Gas Pressure Gas pressure is the force exerted by the gas particles per unit surface area of an object. Force exerted on object s urface area of an object
Factors Affecting Gas Pressure The amount of gas Volume Temperature
Pressure Units of Measurement The SI (International System of Units) unit of pressure is the Pascal (Pa). Other common units of pressure: atm (atmosphere) mmHg (millimeters of mercury). 1 atm = 760 mmHg = 101325 Pa = 101.325 kPa
Atmospheric Pressure Atmospheric pressure results from the collision of air particles with an object . More collisions per unit area – higher pressure. Object
A column of air 1.00 m 2 in cross-sectional area extending from the earth’s surface through the upper atmosphere has a mass of about 10,300 kg, producing an atmospheric pressure of approximately 101,000 Pa.
Atmospheric Pressure Atmospheric pressure results from the collision of air particles with an object. More collisions per unit area – higher pressure.
Where atmospheric pressure is lower, on the top of the mountain or at sea level? Why? Atmospheric pressure is higher at the sea level and lower at the top of the mountain.
Barometer Atmospheric pressure: is measured by barometer . depends on weather and altitude. at sea level can support a column of mercury that is 760 mm high. 1 atm = 760 mmHg
A mercury barometer is measures atmospheric pressure by determining the height of a mercury column supported in a sealed glass tube. The downward pressure of the mercury in the column is exactly balanced by the outside atmospheric pressure that presses down on the mercury in the dish and pushes it up the column.
Convert units of pressure Convert 760 mmHg into kPa 2.5 atm into kPa 99572 Pa into kPa 450 kPa into atm
Vacuum Vacuum (Latin): vacant or void A space where there is no pressure, caused by the lack of any molecules. Vacuum is made by removing the gases from the contained volume. This is done by many different kinds of vacuum pumps.
Vacuum Gas particles create pressure in the container Vacuum No gas particles in the container No pressure Totally empty space
Properties of Gases Compressibility is how much the volume of matter decreases under pressure. Gases are easily compressed Distance between particles in a gas is large (the distance between particles 10 times the diameter of a particle at room temperature) The volume of particles in a gas is small compared to the overall volume of the gas.
Kinetic Molecular Theory Kinetic means motion. The energy an object has because of its motion is called kinetic energy . According to Kinetic Molecular Theory : All matter consists of tiny particles that are in constant motion.
Kinetic Molecular Theory of Gases The particles in gas are Small hard spheres with insignificant volume Gas particles are far apart Empty space between particles (10 times the size of particles). No attractive or repulsive forces between particles of gas. Gasses fill their containers regardless of the shape and volume. An uncontained gas can spreads into space without the limits
Gas Particles Motion Motion of the particles is rapid, constant and random. Particles travel in straight line path until they collide with another particle or object.
Average speed of some molecules at 25
Heavier molecules (carbon dioxide) have lower velocity (speed) Lighter molecules (hydrogen) have higher velocity. Watch the video: ttps :// www.youtube.com/watch?v=RmsqlEm968Y
What is a meaning of the word “elastic”?
Collisions between gas particles or collisions with the walls of the container are perfectly elastic . Elastic collision – total kinetic energy of the colliding bodies or particles is the same after the collision as it was before.
Elastic collision Energy can be transferred from one particle to another. But the total kinetic energy of two particles before the collision equals to their total kinetic energy after the collision. 1 2 1 2 Particle 2 with lower KE Particle 1 with higher KE KE increased after collision KE decreased after collision Total KE energy remains constant
Average Kinetic Energy and Kelvin Temperature The average kinetic energy of the particles depends only on temperature. is directly proportional to the temperature of gas in Kelvin. E = kT E – kinetic energy T – temperature in Kelvin k – Boltzmann constant Any two gases at the same temperature will have the same kinetic energy.
What can we say about KE of two gas samples at the same temperature? Any two gases at the same temperature will have the same kinetic energy. O 2 25 H 2 25
Any two gases at the same temperature will have the same kinetic energy .
Temperature What is temperature? Temperature is a measure of how hot or cold an object is. of the intensity of heat of the average kinetic energy of the particles in a sample of matter.
Measuring temperature: Kelvin Scale or Absolute Temperature Scale Kelvin ( absolute) scale: Celsius – Kelvin conversion formula: The zero point is an absolute zero. There is no negative temperature in Kelvin scale Freezing point of water is 273 K Boiling point of water is 373 K
Sir William Thomson, 1st Baron Kelvin 1824-1907 British mathematical physicist and engineer. Baron Kelvin is a title (like being knighted). Worked on thermodynamics, the transatlantic telegraph project , and refined the mariner's compass. Wrote of the need for a thermometric scale where there are no negative values.
Pressure vs. Volume at Constant Temperature
What do you think relationship between pressure and volume is? How do you think graph volume versus pressure will look like?
What is a meaning of word “direct”? What is a meaning of the word “inverse”?
Boyle’s Law For a given mass of gas at constant temperature, the volume of the gas varies (changes) inversely with pressure. If temperature (T) and the amount of gas in moles (n) are kept constant, as the pressure of a gas increases, the volume decreases. P 1 V 1 = P 2 V 2 P 1 initial pressure V1 initial volumeP2 final pressureV2 final volumeT is constantn (mol) is constant
Example Problem A balloon contains 30.0 L gas at 103 kPa . What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa ? Assume the temperature remains constant.
Charles Law For a given amount of gas and at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature. If pressure and amount of gas are kept constant, as temperature increases, volume increases. P is constant n ( mol ) constant V 1 initial volume T 1 initial temperature V 2 final volume T 2 final temperature
Example Problem A balloon inflated in a room at 24 has a volume of 4.00 L. The balloon is then heated to a temperature of 58 . What is the new volume if the pressure remains constant?
Discussion Question Gas particles move very fast. The average velocity of O 2 molecules in air (at 20 o C) is about 1050 mi/hr. If gas particles move so fast, why does it take so long for smells to migrate across a room?
Gay-Lussac Law For a given amount of gas the pressure of the gas is directly proportional to the Kelvin temperature if the volume remains constant. V is constant n ( mol ) is constant P 1 initial pressure T 1 initial temperature P 2 final pressure T 2 final temperature
Example Problem Aerosol cans carry warning on their labels that say not to incinerate them or store the cans above a certain temperature. This problem will show why it is dangerous to dispose of aerosol cans in a fire. The gas in a used aerosol can is at a pressure 103 kPa at 25 If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928 ?
Gas Properties Simulation https:// phet.colorado.edu/en/simulation/legacy/gas-properties
The Combined Gas Law There is a single expression that combines Boyle’s, Charles’s, and Gay-Lussac laws. The combined gas law allows to calculate the situations when only the amount of gas is constant.
The volume of a gas filled balloon is 30.0L at 313 K and pressure of 153 kPa . What would the volume be at standard temperature and pressure?
n is constant P 1 V 1 = P 2 V 2 T is constant, n is constant P is constant, n is constant V is constant, n is constant PV = nRT
Ideal Gases What do you think is an ideal gas? Ideal gas behaves ideally. An ideal gas follows the gas laws at all conditions of pressure and temperature. behaves according to kinetic molecular theory. Does the ideal gas exist? No. Real gas behaves as an ideal gas at High temperatures Low pressures Real gases differ most from an ideal gas at low temperature and high pressure (do not follow gas laws at these conditions.
Real versus Ideal Ideal Gas Gas described by Kinetic Molecular Theory Behaves ideally at all conditions of temperature and pressure Particles have insignificant v olume No attraction forces exist between gas particles Real Gases G ases that exist in reality Behave ideally only at high temperatures and low pressures (ordinary conditions) When compressed, the size of each particle is important L ower temperatures (around absolute zero), and high pressures cause the particles to slow down and experience attraction forces.
Ideal Gas Law The Ideal Gas Law relates pressure, volume, Kelvin temperature and number of moles of a gas.
Using the Ideal Gas Law to Find the Amount of Gas A deep underground cavern contains 2.24 L of methane gas CH 4 at a pressure of 1.50 kPa and a temperature of 315 K. How many kilograms of CH 4 does the cavern contain?
Partial Pressure T he pressure that would be exerted by one of the gases in a mixture if it occupied the same volume on its own .
Dalton’s Law of Partial Pressure The total pressure of a gas mixture is equal to the sum of all the partial pressures in the mixture P total = P 1 + P 2 + P 3 + . . .
Dalton’s Law Example Problem A gas mixture contains H 2 , He, Ne, and Ar. The total pressure of the mixture 93.6 kPa . The partial pressures of He is 15.4 kPa , Ne = 25.7 kPa , and Ar = 35.6 kPa. What is the partial pressure of hydrogen?
Diffusion Diffusion is the mixing of gas molecules by random motion under conditions where molecular collisions occur .
Unit Overview Why gases diffuse easily? The speed of gas particles is very fast. W hy does it take so long for smells to migrate across a room ? Why we cannot use Celsius scale and must use Kelvin temperature scale? At what conditions real gases behave as an ideal gas? Explain why at these conditions real gas behave as the ideal gas.
Figure out which formula to use 1. A sample of carbon dioxide occupies a volume of 3.50 L at 125 kPa . What pressure would the gas exert if the volume were decreased to 2.00 L ? 2. A sample of propane occupies 250.0 L at 125 kPa and 38 C. Find its volume at 100.0 kPa and 95 C. 3. Oxygen gas is at a temperature of 40C when it occupies a volume of 2.3 L. To what temp should it be raised to occupy a volume of 6.5 L?
Figure out which formula to use 5. Fluorine exerts a pressure of 1.2 atm. When the pressure is changed to 1.5 atm , its volume is 250. mL. What was the original volume? 6. The volume of a gas is 200.0 mL at 275 K and 92.1 kPa . Find its volume at STP. 7. What is a temperature of 3 mol sample of gas that is placed in the 39 L container at 2 atm ?
https://phet.colorado.edu/en/simulation/legacy/gas-properties
https:// www.youtube.com/watch?v=K6GyJBgBk2o&feature=iv&src_vid=GIoxY9kECRE&annotation_id=annotation_3655482367