Mind Catalyst Stick It! O With a partner, use the following scenarios as a guide to come up with the relationships of the gas properties. For each scenario, write the two properties and their relationship on a sticky note and place it on the front board! O Bicycle tires seem more flat in the winter than in summer O A can of soda explodes if left in the hot sun O You blow air into a balloon and it gets bigger
The Kinetic Molecular Theory and its Relation to the Gas Laws Robert Boyle Jacques Charles Amadeo Avogadro Joseph Louis Gay-Lussac
The Kinetic Molecular Theory of Gases O In the simulation, you personally observed the behavior of an ideal gas but not why they behave as they do O Why does a gas expand when heated at constant O pressure? Why does the pressure increase when a gas is compressed at constant temperature? O To understand the physical properties of gases, we need a model that helps us picture what happens to gas particles when conditions such as pressure or temperature change O This model is known as the kinetic-molecular theory of gases
Gases and the Kinetic Molecular Theory Model O All particles are in constant, random motion O All collisions between particles are perfectly elastic O The volume of the particles in a gas is negligible O The average kinetic energy of the molecules is in its Kelvin temperature
Why do We Care? O Assumptions of the KMT successfully account for the observed behavior of an ideal gas O In reality, real gases have a finite volume and exhibit attractive forces between other gas molecules O But now, we must ask the question: How do these assumptions explain your observations?
The KMT and the Relationship between Pressure and Volume O You observed that as the volume of the container decreased, the pressure of the gas increased (at constant temperature and amount of gas) O This is due to the gas particles hitting the wall more often O As a result, the force exerted on the walls of the container increases O This inverse relationship is referred to as Boyle s Law
Introducing Boyle s Law Volume (ml) Pressure (torr) P V (ml torr) 10.0 760.0 7.60 x 10 3 20.0 379.6 7.59 x 10 3 30.0 253.2 7.60 x 10 3 40.0 191.0 7.64 x 10 3 P PV = k V
O O O The KMT and the Relationship between Volume and Temperature You observed as heat was applied to the gas particles (at constant pressure and amount of gas), the temperature increased and volume of the container increased This is because the speed of the gas particles increased and thus, hit the walls more often and with more force O Only way to keep pressure constant is to INCREASE the VOLUME of the container! This direct relationship is referred to as Charles Law
Introducing Charles Law Volume (ml) Temperature (K) V/T (ml/k) 40.0 273.2 0.146 44.0 298.2 0.148 47.7 323.2 0.148 51.3 348.2 0.147 V T V T k
The KMT and the Relationship between Pressure and Temperature O You observed that when the temperature of a gas increases, the speeds of its particles increase O The particles are hitting the wall with greater force and greater frequency O Since the volume remains the same, this would result in INCREASED gas pressure O This direct relationship is referred to Amonton s Law
Introducing Amonton s Law P T k
The KMT and the Relationship Between Volume and the Amount of a Gas O You observed that an increase in the number of particles at the same temperature would cause the pressure to increase if the volume were held constant O The only way to keep constant pressure is to vary the volume the same way! O This direct relationship is referred to as Avogadro s Law O Another way to express this relationship is that equal volume of all ideal gases at the same temperature and pressure contain the same number of molecules O This relationship is important because you may think a small gas molecule would take up less space than a large gas molecule O But, it doesn t at the same temperature and pressure!
Introducing Avogadro s Law Gas Volume (ml) Mass (g) Moles, n V/n (L/mol) O 2 100.0 0.122 3.81 10-3 26.2 N 2 100.0 0.110 3.93 10-3 25.5 CO 2 100.0 0.176 4.00 10-3 25.0 V n V n k
Illustration of Avogadro s Law
O A Summary of the Four Gas Laws Boyle s law PV = k (at constant T and n) O O O Charles law Amonton s law Avogadro s law V T = k (at constant P and n) P T = k (at constant V and n) V n = k (at constant T and P)
The Ideal Gas Law O O Who s got time to remember all four of those relationships? NOT ME! So, the previous 4 relationships can be combined into one very important equation called the ideal gas law: PV = nrt O R is the combined proportionality constant called the universal gas constant O Always use the value 0.0821 L atm K mol for R O The ideal gas law is an equation of state for a gas O State of a gas is its condition at a given time O O A particular state of a gas is described by its pressure, volume, temperature, and number of moles A gas that obeys this equation is said to behave ideally
Practice! O A sample of hydrogen gas (H 2 ) has a volume of 8.56 L at a temperature of 0 C and a pressure of 1.5 atm. O Calculate the moles of H 2 molecules present in the sample.
The Molar Volume of a Gas at STP O Use PV = nrt to solve for the volume of one mole of gas at standard temperature pressure (STP) O Look familiar? O It s on your Mole Road Map! O This is the molar volume of a gas at standard temperature and pressure (STP) O The volume that one mole of any gas takes up at 0 C (273 K) and 1 atm
Practice! O What is the volume of 3.0 mol of nitrous oxide, NO 2(g), at STP?
The Molar Volume of a Gas at Standard Lab Conditions O Use PV = nrt to solve for the volume of one mole of gas at standard lab conditions (SLC) O This is the molar volume of a gas at standard lab conditions (SLC) O The volume that one mole of any gas takes up at 25 C (298 K) and 1 atm O Notice, the volume increased from that at STP! O Satisfies Charles s Law
Practice! O Suppose you have 44.8L of CH 4 (methane) gas at SLC O How many moles of methane gas are present? O What is the mass of the gas in grams? O How many molecules of the gas are present?
The Ideal Gas Law and Gas Stoichiometry Problems
Gas Stoichiometry O Use stoichiometry to solve gas problems only if gas is at STP or SLC conditions O Use the ideal gas law to convert quantities that are NOT at STP
Practice! O Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate (CaCO 3 ). O Calculate the volume of CO 2 at STP produced from the decomposition of 152 g CaCO 3 by the reaction: CaCO 3 s CaO s + CO 2 (g)
Practice! O A sample of methane gas (CH 4 ) having a volume of 2.80 L at 25 C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31 C and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. O Calculate the volume of CO 2 formed at a pressure of 2.50 atm and a temperature of 125 C
Numbered Heads Together Practice with the Ideal Gas Law
How to Play Numbered Heads Together O Members of learning teams (composed of 4 individuals) count off 1, 2, 3 or 4. O I present each learning team with an Ideal Gas Law problem to solve. O Learning teams discuss the question, and answer it together O Every group member must agree upon the answer O I then call a specific team number and individual number O The team members originally designated that number during the count off respond as the group spokesperson
Let s Begin O Calculate the volume in liters of 4.0 moles of oxygen gas at a temperature of 40.0 C and a pressure of 500.0 mm Hg
O 1.2 x 10 24 molecules of xenon gas occupy a volume of 20.0 liters at a temperature of 60.0 C. Determine the pressure in atm.
O If 5.0 X 10-2 moles of neon gas have a volume of 200.0 ml at a pressure of 50.0 torr, then calculate the centigrade temperature
O Calculate the number of molecules in a nitrogen gas sample that occupies a volume of 10.0 liters at a temperature of 60.0 C and a pressure of 5.0 atmospheres
Real-Life Applications of the Ideal Gas Law
Gas Laws are Everywhere! O As we have previously discussed, the behavior of gases can be observed on a daily basis O The science behind hot air balloons O A tire or ball gets flat in the winter O At higher elevations, potato chip bags and marshmallow bags tend to over-inflate O Packing lotion in a carry-on or in your luggage is a big mistake as the pressure inside the container is more than the pressure in the atmosphere while flying. End result: a big mess
Another Great Example Air Bags O Have you stopped to wonder how exactly air bags work and as a result, save lives? O With a partner, come up with some ideas on how you think air bags work O Try to think about what has to happen at the molecular level O Also, think about what makes them actually save lives? What is their purpose?
Time for Videos! Car Airbags Explained The Chemistry Behind Air Bags
Follow-Up Discussion O Based on what you observed in the videos, what features of an airbag make it effective in saving lives? O Discuss with a partner and be prepared to share with the class!