How do we explain gas behavior? Gas properties are explained by a model that describes the observed behavior of tiny gas particles. This is known as “The Kinetic Molecular Theory” or the “K-M” Theory.

Chapter 13 “Gases” What are the properties of gases?

Learning Target 13-1 Relate the behavior of gases to the Kinetic Molecular Theory (KMT) Learning Outcomes  Know and understand the postulates of the KMT.  Be able to use the KMT to explain what causes pressure in a sample of gas. Monday 4/13/14

How do we explain gas behavior? Gas properties are explained by a model that describes the behavior of the tiny particles of a gas. Gases have mass. It is easy to compress a gas. Gases fill their containers completely. Gases exert pressure.

The Kinetic-Molecular (K-M) Theory 6 Postulates: Gases consist of very small particles each of which has a mass. Gas particles themselves have no volume, but are spaced widely, with lots of empty space between them. Gas particles don’t repel or attract each other. Gas particles move in constant, rapid, random motion (straight lines). No kinetic energy is lost when particles collide with each other or wall (perfectly elastic). The average kinetic energy of the molecules of a gas is proportional to the temperature of the gas (measured in Kelvin). plets/KineticMolecularTheory/BasicConcepts.ht ml

13-2 Measuring Gases We must deal with four variables when looking at how gases behave:  Amount of gas (n, in moles) n = mass/molar mass  Volume of gas (V, in liters) 1 L = 1000mL = 1000 cm 3  Temperature (T, in kelvins) T(K) = T(°C)  Pressure (P, in atm, torr, kPa, etc.)

If scientists wanted to know the relationship between all of the variables in the gas laws (P,V, T, n), why do they set 1 (or more) as controls to study these relationships? How does this relate to the scientific method?

Learning Goals for “Gas Variables” Whole Class Discussion: 1.Understand the relationships between the 4 gas variables (n, P, V, and T) in how gases behave. 2.Understand the gas variable relationships with respect to the Kinetic Molecular Theory. Tuesday 4/14/14

Using the Kinetic Molecular Theory explain the behavior of the gas particles in Experiment B.

Using the KM Theory explain the increased volume in Experiment C. How does this differ and/or is similar to Experiment D? Using the KM Theory explain what is occurring with the increased volume in Experiment E.

Explain other phenomena that exists in the world around us related to gas behavior and explain it in terms of the KMT.

What are some practical uses of gas laws in the real world?

Oil Tanker Draw a model that explains what occurred with the oil tanker. Why did the oil tanker implode after steam cleaning? Explain in terms of the Kinetic Molecular Theory.

Learning Target: Be able to convert pressure values between common pressure units. Learning Outcome: Complete pressure conversion problems and manometer problems. Monday 4/20/15

How to Measure Pressure Pressure = Force / Area (newtons / meter 2 = pascals) Atmospheric pressure results from the mass of the air being attracted by Earth’s gravity.  The mass of the air attracted by gravity produces a force. 1 N = 1kg. m/s 2 Conversions:  1 atmosphere (atm) = kPa (1Pa = 1N/m 2 = 1kg/m. s 2 )  1 atmosphere = 760 mm Hg (same as torr)  1 atmosphere = lb/in 2

Tools for Measuring Pressure Barometer  Atmospheric pressure for predicting weather changes  Water vapor is lighter than nitrogen and oxygen. High water vapor content = Low barometric pressure Low water vapor content = High barometric pressure Pressure gauge  Tire pressure gauges or gas regulators

Tools for Measuring Pressure Manometer  Laboratory tool for working with gases

PROBLEMS The pressure in a certain tire is 109 kPa. What is the pressure of the air in the tire in atmospheres?

Manometer Measurements In an open-tube manometer:  If the gas pressure (P gas ) is greater than the atmospheric pressure (P atm ), then P gas = P atm + height difference  If the gas pressure is less than the atmospheric pressure, then P gas = P atm – height difference In a closed-tube manometer:  The P gas = the difference in Hg levels

Manometer Problem A gas container is fitted with a manometer. The level of the mercury is 15 mm lower on the open side. Using a laboratory barometer, you find that the atmospheric pressure is 750 mmHg. What is the pressure in atmospheres of the gas in the container? In kPa?

Exploring Gas Behavior (Class Activity) ts/KineticMolecularTheory/BasicConcepts.ht mlhttp:// ts/KineticMolecularTheory/BasicConcepts.ht ml Then go to “Maxwell Distribution,” followed by “Pressure” and “Pressure-Volume Relation.” Conclude with “Pressure-Temperature Relation.” Complete the exercise by working on the Boyle & Charles. QUESTION: What did you learn about gas behavior?

Learning Target: Know the variables in Boyle’s Law and how those variables are related. Know the variables of Charles’ Law and how they are related. Learning Outcome: Be able to use the KM Theory to explain Boyle’s and Charles’ Law. Be able to perform Boyle’s and Charles’ Law problems. Tuesday 4/21/14

13-3 The Gas Laws (1) Do you remember STP? SSTP = Standard Temperature & Pressure SSTP = 273 K (0°C) & 1 atm SSTP is important for measuring gas properties. GGases act “Ideal” at STP which the KM Theory is based off of.

Questions to ask: 1. What kind of problem is this/what gas equation? 2. What variables do I know? 3. Which variables do I solve for? 4. Are my units consistent? 5. Does my answer make sense?

Boyle’s Law The pressure and volume of a sample of gas are inversely proportional to each other at constant temperature. P 1 V 1 = P 2 V 2 Robert Boyle

Boyle’s Law

The Kinetic-Molecular (K-M) Theory 5 Postulates: Gas particles have no volume, but are spaced widely, with lots of empty space between them. Gas particles don’t repel or attract each other. Gas particles move in constant, rapid, random motion (straight lines). No kinetic energy is lost when particles collide with each other or wall (perfectly elastic). The average kinetic energy of the molecules of a gas is proportional to the temperature of the gas (measured in Kelvin). plets/KineticMolecularTheory/BasicConcepts.ht ml

Boyles Law Problem A gas occupies a volume of 458 mL at a pressure of 1.01 kPa and a temperature of 295 K. When the pressure is changed, the volume becomes 477 mL. If there is no change in temperature what is the new pressure?

A sample of Ne gas occupies L at atm. What is the its volume at 29.2kPa?

Learning Target: Know the variables in Charles’ Law and how those variables are related. Learning Outcome: Be able to use the KM Theory to explain Charles’ Law. Be able to perform Charles’ Law problems. Tuesday 4/15/14

Boyle’s Law and Manometer 1.A gas container is fitted with a manometer. The level of the mercury is 15mm lower on the open side. Using a barometer, you find that the atmospheric pressure is 750mmHg. What is the pressure of the gas in the container in kPa? L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas?

13-3 The Gas Laws (2) What happens when you change the temperature of a gas? EExamples: Hot air balloon inflating, automobile tires in very cold weather. Jacques Charles (1700s) studied the effect of temperature (T) on the volume (V) of a gas. Charles’ Law: The volume of a sample of gas is directly proportional to the Kelvin temperature at constant pressure. VV 1 T 2 = V 2 T 1 or

Charles’ Law

CHARLES’ LAW PROBLEM A gas sample at 83ºC occupies a volume of 1400 m 3. At what temperature will it occupy 1200 m 3. A gas can be used as a thermometer. If it is known that a sample of gas has a volume of 1.00 L at 235 K, what is the temperature if the volume of the gas is changed to 0.45 L at a constant pressure?

Learning Target: Know the variables in Combined Gas Law Equation and how those variables are related. Learning Outcome: Be able to use the KM Theory to explain Combined Gas Law Equation. Be able to perform Combined Gas Law problems. Monday 4/27/15

Demonstration What gas variables are associated with the demonstrations? How can this be explained using the KM Theory?

13-3 The Gas Laws (3) What happens to the pressure of a fixed volume of gas if you change the temperature? EExample: “Empty” aerosol can thrown into an incinerator. (Read the warning on the label!) Gay-Lussac (1700s-France) studied the effect of pressure (P) and temperature (T) on a fixed volume (V) of gas. Gay-Lussac’s Law: The pressure and temperature of a fixed volume of gas are directly proportional to each other.

Gay-Lussac’s Law

13-3 The Gas Laws (Combined) These Gas Laws seem complicated, but fortunately we can simplify things by combining the relationships into two simple expressions, the one first being: P1V1P1V1 = P2V2P2V2 T1T1 T2T2 This equation is used to solve “Combined Gas Law” problems, by simply “plugging in” the numbers! Just remember two things: “Go Kelvin!” (Convert temperature to kelvins.) Be sure all units are consistent for P and V.

PRACTICE PROBLEM The initial temperature of a 1.00 liter sample of argon is 20.° C. The pressure is decreased from 720 mm Hg to 360 mm Hg and the volume increases to 2.14 liters. What was the change in temperature of the argon?

Warm-Up A gas that has a volume of 28 L, a temperature of 45°C, and an unknown pressure has its volume increased to 34 L and its temperature decreased to 35°C. If I measure the pressure after the chance to be 2.0 atm, what was the original pressure of the gas?

Learning Target: Know the formula for the Ideal Gas Law and be able to use it to solve for P, V, n or T. Learning Outcome: Know the difference between Ideal and Real Gases. Be able to perform Ideal Gas Law problems. Tuesday 4/28/15

Ideal vs. Real Gases Ideal (KM Theory) Real Made up of small particles that have mass. Mostly empty space. Low density There are NO attractive or repulsive forces between particles. Particles have NO volume. Collisions are ELASTIC (no loss of total kinetic energy). SAME There are VERY SMALL attractive and repulsive forces between particles. Particles have a very small volume. Collisions are INELASTIC (When gas particles collide they will lose energy.

We are safe to use the Ideal Gas Equation (PV = nRT) to solve problems for real gases, except at low temperature and high pressure conditions where gases start to behave in a non-ideal manner.

13-3 The Gas Laws (4) Avogadro’s Law (1800’s): Equal volumes of gases at the same pressure and temperature contain an equal number of particles. 66.02 x particles/mol will have a volume of 22.4 L/mol at STP. 2 points: 1. All gases have the same behavior (KM Theory) 2. A gas with greater volume will have a greater # of particles.

13-4 The “Ideal Gas Law” The second equation that may be derived from the various gas laws is the “Ideal Gas Equation”: PV = nRT This describes the relationship among the four variables (P,V,n,T) of an ideal gas, where R is the gas constant.  R = atm-L/mol-K  R = Pa-m 3 /mol-K  R = J/mol-K Problems may be solved by simple substitution, but be careful to use consistent units.

But what is an “Ideal Gas”? Ideal Gas: one that is described by the postulates of the Kinetic-Molecular Theory. The gases we encounter are “real” – not “ideal”! However, most gases behave like ideal gases under ordinary conditions of temperature and pressure.  At low temperature and high pressure real gases behave in non-ideal ways. (Remember Bose- Einstein Condensate)

Deviations from Ideal Gas Behavior Occur Because: Kinetic-Molecular Theory makes two simplifying, but WRONG, assumptions:  Gas particles have no volume of their own.  Gas particles have no attraction for each other. But, as pressure increases…  …gas particles get closer together.  At very high pressure, the volume of the gas particles themselves become a significant part of the total volume, contrary to K-M Theory. As temperature decreases…  …gas particles slow down.  At very low temperature, attractive forces between gas particles become significant, contrary to K-M Theory, so gases liquefy.

13-3 The Gas Laws (5) Another relationship about gases was proposed by John Dalton. (Remember him? Why?) He proposed that gas particles in a mixture of gases act independently to exert pressure on the container. o Each gas in the mixture exerts the same pressure that it would if it was alone in the container. o This proposal was made before the Kinetic Molecular Theory was developed, so he didn’t really have its ideas to help him. Dalton’s Law of Partial Pressure: the sum of the partial pressures of all components of a gas mixture is equal to the total pressure of the gas mixture, or... P T = P 1 + P 2 + P 3 +.…. See sample problems.

Dalton’s Law of Partial Pressures Problem A flask contains a mixture of hydrogen and oxygen. The pressure being exerted by these gases is 7785 mmHg. If the partial pressure of the hydrogen in the mixture is 395 mmHg, what is the partial pressure of oxygen?  P T = P H2 + P O2  785mmHg = 395 mm Hg + P O2  P O2 = 390mmHg

13-5 How Gases Work: Lift Lifting Power  This is the result of low density of a gas, but the density must be lower than that of the air.  Low molar mass gases (H 2, He, NH 3, CH 4 ) may be used to gain lift.  Or the gas, usually air, may be heated.  Higher mass gases (CO 2, Kr) are too dense, so they sink in air. Can have disastrous effects.

13-5 How Gases Work: Effusion Effusion  Related to ‘diffusion’ (one gas moving through another).  Effusion is the gas movement through a tiny hole one particle at a time.  Small, light gases have greater speeds than large, heavy gases at a given temperature, so they effuse faster.  Graham’s Law of Effusion relates effusion to mass.