Honors Chem Ch. 10 Physical Characteristics of Gases 10.1 Kinetic Molecular Theory Pressure The Gas Laws Boyle, Charles, Gay-Lussac, combined, Dalton’s law of partial pressure

What is KMT? * Based on the research of Robert Boyle (1627 – 1691) A theory that envisions molecules in motion Best describes properties and behaviors of gases * Imagines particles of a gas like billiard balls, moving and crashing into each and the walls of a container in a three-dimensional space.

Kinetic Theory and a Model for Gases Kinetic Molecular Theory (as stated in Prentice Hall text): »The particles in a gas are considered to be small, hard spheres with an insignificant volume. »The motion of the particles in a gas is rapid, constant, and random. »All collisions between particles in a gas are perfectly elastic The word kinetic refers to motion. –The energy an object has because of its motion is called kinetic energy. –According to the kinetic theory, all matter consists of tiny particles that are in constant motion.

Kinetic Theory and a Model for Gases a) Particles in a gas are in rapid, constant motion. b) Gas particles travel in straight-line paths c) The gas fills the container 13.1

Principles of KMT (as stated in Hein-Arena text) 1. Gases consist of tiny (submicroscopic) particles.

2. Gas particles are very far apart; the volume occupied by a gas consists mostly of empty space (typically about 99.9% empty). 3. Gas particles are not attracted to each other (like ions are.)

4. Gas particles move randomly in all directions, traveling in straight lines. * Gas molecules travel at very high speeds, about 6000 km/hr (~2700 mi/hr) The higher the average speed of the particles, the higher the temperature of that substance.  Absolute temperature: T based on average particle speed; measured in Kelvin (K)  Absolute zero (0 K): particles are not moving; there is no T below 0 K. K = °C + 273

6. Gas particles collide with each other and with the walls of the container without losing energy. Pressure = the collision of gas particles with a surface

Nature of gases based on KMT Expand: completely fill any container Fluid: particles glide past each other. Low density: particles so far apart. Compressibility: particles can be crowded together. Diffusion: spontaneous mixing caused by random motion, (depends on speed, diameter and attractive forces.) Effusion: particles under pressure pass through a tiny opening.

Properties of Gases In organized soccer, a ball that is properly inflated will rebound faster and travel farther than a ball that is under-inflated. If the pressure is too high, the ball may burst when it is kicked. You will study variables that affect the pressure of a gas.

Compressibility Compressibility is a measure of how much the volume of matter decreases under pressure. When a person collides with an inflated airbag, the compression of the gas absorbs the energy of the impact.

Factors Affecting Gas Pressure The amount of gas, volume, and temperature are factors that affect gas pressure. Four variables are generally used to describe a gas. The variables and their common units are –pressure (P) in kilopascals –volume (V) in liters –temperature (T) in kelvins –the number of moles (n).

Factors Affecting Gas Pressure Collisions of particles with the inside walls of the raft result in the pressure that is exerted by the enclosed gas. Increasing the number of particles increases the number of collisions, which is why the gas pressure increases.

Gas Pressure –Gas pressure results from the force exerted by a gas per unit surface area of an object. –An empty space with no particles and no pressure is called a vacuum. –Atmospheric pressure results from the collisions of atoms and molecules in air with objects. –Gas pressure is the result of simultaneous collisions of billions of rapidly moving particles in a gas with an object. 13.1

Temperature of a Gas Directly related to the average kinetic energy(k) As the temperature is increased, the speed of the particles increase. (k increases.) k= ½ mv 2 ( where m=mass of particle and v= average velocity of particles) Absolute zero (0 K, or –273.15°C) is the temperature at which the motion of particles theoretically ceases. Particles would have no kinetic energy at absolute zero. Absolute zero has never been produced in the laboratory.

Kinetic Energy and Temperature 13.1 Average Kinetic Energy and Kelvin Temperature The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance. The particles in any collection of atoms or molecules at a given temperature have a wide range of kinetic energies. Most of the particles have kinetic energies somewhere in the middle of this range.

Measuring Pressure The atmospheric pressure can be measured by using “ barometer”. A manometer is used to measure the pressure of a gas in a closed container. Units of pressure: Pascal, mm Hg, atm, torr STP: Standard Temperature and Pressure, 1 atm and 0°C. RTP: Room temp and pressure 25 ° C, 1 atm Pressure is equal to force/unit area SI units = Newton/meter 2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa = kPa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

Pressure Conversions A. What is 475 mm Hg expressed in atm? 1 atm 760 mm Hg B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 760 mm Hg 14.7 psi = 1.52 x 10 3 mm Hg = atm 475 mm Hg x 29.4 psi x

A barometer is a device that is used to measure atmospheric pressure Developed by Torricelli in 1643 P= h.d.g, where, p= pressure h= height of the mercury column d= density of the liquid g= acceleration due to gravity= 9.8 m/s^2 Would a mercury barometer or a water barometer be taller? Why? Density of Mercury: 13.6 g/cm^3 Density of Water: 1.0 g/cm^3 Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink)

Open Tube Manometer Manometer: is used to measure the gas pressure. Manometers have a U tube connected on one side to the gas flask and is either open or closed on other side. The U-tube is filled with Mercury and the pressure is calculated using the formula p=h.d.g, where h is the difference in the height of two arms in U tube.

Boyle’s Law: Pressure and Volume There is an inverse relationship between the pressure & volume of a gas if amount (moles, n) & temperature remain constant.

Boyle’s Law: Pressure and Volume If the temperature is constant, as the pressure of a gas increases, the volume decreases. Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.

Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

Charles’s Law: Temperature and Volume Volume varies directly with the kelvin temp. (n & P are constant)

Charles’s Law: Temp. and Volume As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant. Charles’s law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

Gay-Lussac’s Law: Pressure and Temperature When a gas is heated at constant volume, the pressure increases. A pressure cooker demonstrates Gay- Lussac’s Law.

Gay-Lussac’s Law: Pressure and Temperature As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant. Gay-Lussac’s law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.

The Combined Gas Law Weather balloons carry data-gathering instruments high into Earth’s atmosphere. At an altitude of about 27,000 meters, the balloon bursts.

Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyle’s Law Charles’ Law Gay-Lussac’s Law

The Combined Gas Law The combined gas law describes the relationship among the pressure, temperature, and volume of an enclosed gas. The combined gas law allows you to do calculations for situations in which only the amount of gas is constant.

Combined Gas Law Problem A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ??

Calculation P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ?? P 1 V 1 P 2 V 2 T 1 = T 2 P 1 V 1 T 2 = P 2 V 2 T 1 T 2 = P 2 V 2 T 1 P 1 V 1 T 2 = 3.20 atm x 90.0 mL x 302 K atm x mL T 2 = 604 K = 331 °C = 604 K

Summary Gases: relationship between pressure, volume, temperature, and number of moles Boyle’s Law: pressure is inversely proportional to volume as pressure goes up; volume goes down Charles’ Law: volume is directly proportional to temperature as volume goes up; temperature goes up Gay-Lussac’s Law: pressure is directly proportional to temperature Combined Gas Law:

Behavior of Real Gases Deviate from ideality at conditions of high pressures and low temperatures or when the total volume of gas in itself is very small. In a real gas, especially at high pressures and low temperatures, intermolecular forces can not be completely ignored. These forces are important any time two molecules move close together.

Ideal Gases and Real Gases There are attractions between the particles in an ideal gas. Because of these attractions, a gas can condense,or even solidify, when it is compressed or cooled. Real gases differ most from an ideal gas at low temperatures and high pressures

Ideal Gases and Real Gases

Dalton’s Law The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P When H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.

GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H kPa P H2 = 91.7 kPa Dalton’s Law Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. Look up water-vapor pressure on p.899 for 22.5°C. Sig Figs: Round to least number of decimal places. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P H torr P gas = torr A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places. Dalton’s Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.