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Chapter 14 The Behavior of Gases Pre-AP Chemistry Charles Page High School Stephen L. Cotton

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Section 14.1 The Properties of Gases OBJECTIVES: Explain why gases are easier to compress than solids or liquids are.

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Section 14.1 The Properties of Gases OBJECTIVES: Describe the three factors that affect gas pressure.

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

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Compressibility 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 The impact forces the gas particles closer together, because there is a lot of empty space between them

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Compressibility At room temperature, the distance between particles is about 10x the diameter of the particle Fig. 14.2, page 414 This empty space makes gases good insulators (example: windows, coats) How does the volume of the particles in a gas compare to the overall volume of the gas?

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Variables that describe a Gas 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.

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

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Pressure and the number of molecules are directly related More molecules means more collisions, and… 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.

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

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

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

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Section 14.2 The Gas Laws OBJECTIVES: OBJECTIVES: Describe the relationships among the temperature, pressure, and volume of a gas.

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Section 14.2 The Gas Laws OBJECTIVES: OBJECTIVES: Use the combined gas law to solve problems.

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

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Robert Boyle (1627-1691) 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.

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#1. Boyles Law - 1662 Pressure x Volume = a 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.

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Graph of Boyles Law – page 418 Boyles Law says the pressure is inverse to the volume. Note that when the volume goes up, the pressure goes down

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- Page 419

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Jacques Charles (1746-1823) French Physicist Part 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 started It was a hydrogen filled balloon – good thing they were careful!

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#2. Charless Law - 1787 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.

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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 + 273 °C = Kelvin - 273 and

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- Page 421

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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.

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#3. Gay-Lussacs Law - 1802 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? (Note page 422) Sample Problem 14.3, page 423

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#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

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

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

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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-Lussacs Law

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Section 14.3 Ideal Gases OBJECTIVES: OBJECTIVES: Compute the value of an unknown using the ideal gas law.

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Section 14.3 Ideal Gases OBJECTIVES: OBJECTIVES: Compare and contrast real an ideal gases.

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5. The Ideal Gas Law #1 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. R = 8.31 (L x kPa) / (mol x K) 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)

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We now have a new way to count moles (the amount of matter), by measuring T, P, and V. We arent restricted to only STP conditions: P x V R x T The Ideal Gas Law n =

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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 An ideal gas does not really exist, but it makes the math easier and is a close approximation. Particles have no volume? Wrong! No attractive forces? Wrong!

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

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

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Density Density is mass divided by volume m V so, m M P V R T D = =

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Ideal Gases dont exist, because: 1. 1. Molecules do take up space 2. 2. There are attractive forces between particles - otherwise there would be no liquids formed

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

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

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Section 14.4 Gases: Mixtures and Movements OBJECTIVES: Relate the total pressure of a mixture of gases to the partial pressures of the component gases.

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Section 14.4 Gases: Mixtures and Movements OBJECTIVES: Explain how the molar mass of a gas affects the rate at which the gas diffuses and effuses.

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#7 Daltons Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P 3 +... P 1 represents the partial pressure, or the contribution by that gas. Daltons Law is particularly useful in calculating the pressure of gases collected over water.

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Collecting a gas over water – one of the experiments in Chapter 14 involves this. Connected to gas generator

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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 434 1 2 3 4

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Diffusion is: 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. u Molecules moving from areas of high concentration to low concentration. u Example: perfume molecules spreading across the room.

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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. 14.18, p. 435

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

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8. Grahams Law 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 m = the molar mass, and v = the velocity. Rate A Mass B Rate B Mass A =

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Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 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. Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Grahams Law

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Chapter 14 The Behavior of Gases. Section 14.2 The Gas Laws l\

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