Chapter 14 “The Behavior of Gases”

Compressibility Gases can expand to fill its container, unlike solids or liquids Gases can expand to fill its container, unlike solids or liquids The reverse is also true: The reverse is also true: They are easily compressed, or squeezed into a smaller volume They are easily compressed, or squeezed into a smaller volume Compressibility is a measure of how much the volume matter decreases under pressure Compressibility is a measure of how much the volume matter decreases under pressure

Compressibility This is the idea behind placing “air bags” in automobiles This is the idea behind placing “air bags” in automobiles In an accident, the air compresses more than the steering wheel or dash when you strike it In an accident, the air compresses more than the steering wheel or dash when you strike it The impact forces the gas particles closer together, because there is a lot of empty space between them The impact forces the gas particles closer together, because there is a lot of empty space between them

Compressibility At room temperature, the distance between particles is about 10x the diameter of the particle At room temperature, the distance between particles is about 10x the diameter of the particle Fig. 14.2, page 414 Fig. 14.2, page 414 How does the volume of the particles in a gas compare to the overall volume of the gas? How does the volume of the particles in a gas compare to the overall volume of the gas?

Variables that describe a Gas The four variables and their common units: The four variables and their common units: 1. pressure (P) in kilopascals 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. amount (n) in moles The amount of gas, volume, and temperature are factors that affect gas pressure.The amount of gas, volume, and temperature are factors that affect gas pressure.

1. Amount of Gas When we inflate a balloon, we are adding gas molecules. When we inflate a balloon, we are adding gas molecules. Increasing the number of gas particles increases the number of collisions Increasing the number of gas particles increases the number of collisions thus, the pressure increases thus, the pressure increases If temperature is constant- doubling the number of particles doubles the pressure If temperature is constant- doubling the number of particles doubles the pressure

Pressure and the number of molecules are directly related More molecules means more collisions. More molecules means more collisions. Fewer molecules means fewer collisions. Fewer molecules means fewer collisions. Gases naturally move from areas of high pressure to low pressure because there is empty space to move into – a spray can is example. Gases naturally move from areas of high pressure to low pressure because there is empty space to move into – a spray can is example.

Common use? Aerosol (spray) cans Aerosol (spray) cans gas moves from higher pressure to lower pressure gas moves from higher pressure to lower pressure a propellant forces the product out a propellant forces the product out whipped cream, hair spray, paint whipped cream, hair spray, paint Fig. 14.5, page 416 Fig. 14.5, page 416 Is the can really ever “empty”? Is the can really ever “empty”?

2. Volume of Gas In a smaller container, the molecules have less room to move. In a smaller container, the molecules have less room to move. The particles hit the sides of the container more often. The particles hit the sides of the container more often. As volume decreases, pressure increases. (think of a syringe) As volume decreases, pressure increases. (think of a syringe)

3. Temperature of Gas Raising the temperature of a gas increases the pressure, if the volume is held constant. Raising the temperature of a gas increases the pressure, if the volume is held constant. The molecules hit the walls harder, and more frequently! The molecules hit the walls harder, and more frequently! Fig. 14.7, page 417 Fig. 14.7, page 417 Should you throw an aerosol can into a fire? What could happen? Should you throw an aerosol can into a fire? What could happen? When should your automobile tire pressure be checked? When should your automobile tire pressure be checked?

The Gas Laws These will describe HOW gases behave. These will describe HOW gases behave. Gas behavior can be predicted by the theory. Gas behavior can be predicted by the theory. The amount of change can be calculated with mathematical equations. The amount of change can be calculated with mathematical equations. You need to know both of these: the theory, and the math You need to know both of these: the theory, and the math

Robert Boyle ( ) Boyle was born into an aristocratic Irish family Became interested in medicine and the new science of Galileo and studied chemistry. A founder and an influential fellow of the Royal Society of London Wrote extensively on science, philosophy, and theology.

#1. Boyle’s Law Pressure x Volume = a constant Pressure x Volume = a constant Equation: P 1 V 1 = P 2 V 2 (T = constant) Equation: P 1 V 1 = P 2 V 2 (T = constant) Gas pressure is inversely proportional to the volume, when temperature is held constant.

Graph of Boyle’s Law – page 418

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Jacques Charles ( ) French Physicist French Physicist Part of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humansPart of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans This is how his interest in gases startedThis is how his interest in gases started It was a hydrogen filled balloon – good thing they were careful!It was a hydrogen filled balloon – good thing they were careful!

#2. Charles’s Law The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. This extrapolates to zero volume at a temperature of zero Kelvin.

Converting Celsius to Kelvin Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.) Reason? There will never be a zero volume, since we have never reached absolute zero. Kelvin =  C °C = Kelvin and

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Joseph Louis Gay-Lussac (1778 – 1850)  French chemist and physicist  Known for his studies on the physical properties of gases.  In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

#3. Gay Lussac’s Law The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. How does a pressure cooker affect the time needed to cook food? Sample Problem 14.3, page 423

#4. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Sample Problem 14.4, page 424

The combined gas law contains all the other gas laws! The combined gas law contains all the other gas laws! If the temperature remains constant... If the temperature remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

The combined gas law contains all the other gas laws! The combined gas law contains all the other gas laws! If the pressure remains constant... If the pressure remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Charles’s Law

u The combined gas law contains all the other gas laws! u If the volume remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac’s Law

5. The Ideal Gas Law #1 Equation: P x V = n x R x T Equation: P x V = n x R x T Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the temperature in Kelvin. Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the temperature in Kelvin. R =.o821 (L x atm) / (mol x K) R =.o821 (L x atm) / (mol x K) The other units must match the value of the constant, in order to cancel out. The other units must match the value of the constant, in order to cancel out. The value of R could change, if other units of measurement are used for the other values (namely pressure changes) The value of R could change, if other units of measurement are used for the other values (namely pressure changes)

We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: P x V P x V R x T R x T The Ideal Gas Law n =

Ideal Gases We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure An ideal gas does not really exist, but it makes the math easier and is a close approximation. An ideal gas does not really exist, but it makes the math easier and is a close approximation. Particles have no volume? Wrong! Particles have no volume? Wrong! No attractive forces? Wrong! No attractive forces? Wrong!

Ideal Gases There are no gases for which this is true; however, There are no gases for which this is true; however, Real gases behave this way at a) high temperature, and b) low pressure. Real gases behave this way at a) high temperature, and b) low pressure. Because at these conditions, a gas will stay a gas! Because at these conditions, a gas will stay a gas! Sample Problem 14.5, page 427 Sample Problem 14.5, page 427

#6. Ideal Gas Law 2 P x V = m x R x T M P x V = m x R x T M Allows LOTS of calculations, and some new items are: Allows LOTS of calculations, and some new items are: m = mass, in grams m = mass, in grams M = molar mass, in g/mol M = molar mass, in g/mol Molar mass = m R T P V Molar mass = m R T P V

Density Density is mass divided by volume Density is mass divided by volume.0.0 m Vso, m M P m M P V R T V R T D = =

Ideal Gases don’t exist, because: 1. Molecules do take up space 2. There are attractive forces between particles - otherwise there would be no liquids formed

Real Gases behave like Ideal Gases... When the molecules are far apart. When the molecules are far apart. The molecules do not take up as big a percentage of the space The molecules do not take up as big a percentage of the space We can ignore the particle volume. We can ignore the particle volume. This is at low pressure This is at low pressure

Real Gases behave like Ideal Gases… When molecules are moving fast When molecules are moving fast This is at high temperature This is at high temperature Collisions are harder and faster. Collisions are harder and faster. Molecules are not next to each other very long. Molecules are not next to each other very long. Attractive forces can’t play a role. Attractive forces can’t play a role.

#7 Dalton’s Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P P 1 represents the “partial pressure” or the contribution by that gas. P 1 represents the “partial pressure” or the contribution by that gas. Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.

If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: 2 atm + 1 atm + 3 atm = 6 atm Sample Problem 14.6, page

Diffusion is: Effusion: Gas escaping through a tiny hole in a container. Effusion: Gas escaping through a tiny hole in a container. Both of these depend on the molar mass of the particle, which determines the speed. Both of these depend on the molar mass of the particle, which determines the speed. u Molecules moving from areas of high concentration to low concentration. u Example: perfume molecules spreading across the room.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Molecules move from areas of high concentration to low concentration. Fig , p. 435

Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire… -Think of a nail in your car tire… Diffusion and effusion are explained by the next gas law: Graham’s

8. Graham’s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Derived from: Kinetic energy = 1/2 mv 2 Derived from: Kinetic energy = 1/2 mv 2 m = the molar mass, and v = the velocity. m = the molar mass, and v = the velocity. Rate A  Mass B Rate B  Mass A =

Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 With effusion and diffusion, the type of particle is important: With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Graham’s Law