You can predict how pressure, volume, temperature, and number of gas particles are related to each other based on the molecular model of a gas.

The Kinetic Molecular Theory 1.) Gas particles are in constant motion and move in a straight line until they hit another gas particle or the side of the container. 2.) There are not attractive or repulsive forces between the gas particles. 3.) The volume of the actual gas particle is assumed to be zero, since it is insignificant to the volume of the whole sample of gas.

The Kinetic Molecular Theory (cont.) 4.) The temperature is an indirect measure the average kinetic energy of all the gas particles in the sample. Kinetic Energy = ½ (mass) x (velocity) 2 5.) There is no exchange of energy when 2 gas particles collide, the collision is totally elastic. (Just like when two billiard balls collide.)

Pressure Pressure = Force Applied / Area (P = F / A) When the gas molecules collide with the inside wall of the container, it exerts a force over an area. Therefore there is always an internal pressure on a gas.

Measuring Pressure Pressure can be measured using a device called a manometer.

Measuring Pressure Atmospheric Pressure can be measured using a device called a barometer.

Units for Measuring Pressure Pascal (Pa) – Metric System unit for pressure Atmosphere (atm) Pounds per square inch (psi) Torricelli (torr) Millimeter of Mercury (mm Hg) 1 atm = 101,300 Pa = kPa = 14.7 psi = 760 torr = 760 mm Hg

Pressure Conversions 1 atm = 101,300 Pa = kPa = 14.7 psi = 760 torr = 760 mm Hg Convert 0.75 atm into mm Hg. Convert 32.0 psi into kPa.

Robert Boyle (1627 – 1691) An English scientist whose work revolved around trying to discover the relationship between the pressure and volume of a gas.

Boyle’s Law If the pressure exerted on a gas increases, the volume of the gas will proportionally decrease. What is the relationship between the pressure exerted on a gas and its volume?

Boyle’s Law The product of the pressure and volume of a gas must always be a constant as long as the temperature and # of moles of gas remain constant. Pressure x Volume = constant Pressure (initial) x Volume (initial) = Pressure (final) x Volume (final) P 1 V 1 = P 2 V 2

Boyle’s Law Initially, a 3.0 L expandable tank of gas is under a pressure of 13 atm. What would be the volume of the tank if the pressure inside the tank is reduced to 5.0 atm. The temperature and # of moles of gas remain constant.

Jacques Charles (1746 – 1823) A French scientist, inventor, and avid balloonist. He was interested in discovering the affect that the temperature had on the volume of a gas.

Charles’ Law The volume of a gas divided by its Kelvin temperature must remain constant. As long as the pressure and # moles of gas does not change. Volume = constant Temperature Volume (initial) = Volume (final) Temperature (initial) Temperature (final) V 1 = V 2 T 1 T 2 Temperature must be in Kelvins!

Charles’ Law This is how absolute zero was determined. Is it possible?

Charles’ Law Problem A balloon has a volume of 1.0 L at 23.0°C. What is the volume of the balloon if the temperature decreases to -10.0°C? Assume that the pressure and # of moles of gas particles remains constant.

Combined Gas Law (Boyle’s and Charles’ Law) P 1.V 1 = P 2.V 2 T 1 T 2 The number of moles of gas must remain constant.

Combined Gas Law (Boyle’s and Charles’ Law) A 2.0 L balloon initially at Standard Temperature and Pressure (STP) is heated to °C and pressurized to 1.5 atmospheres. Calculate the new volume of the balloon.

Joseph Louis Gay-Lussac (1778 – 1850) French Chemist and Physicist who discovered th relationship between the pressure and the temperature of a gas.

Joseph Louis Gay-Lussac (1778 – 1850) Gay-Lussac’s Law P 1 = P 2 T 1 T 2 The volume and number of moles of gas must remain constant.

Gay-Lussac’s Law Initially, a sample of gas has a temperature of 10.0°C. It is then pressurized from 740. mm Hg to 800. mm Hg. What will be the new temperature of the gas if the volume and number of moles of gas remain constant?

The Ideal Gas Law The only gas law that incorporates moles into it. PV = nRT P = Pressure (atm or kPa) V = Volume (L) n = # of moles of gas particles R = The Gas Law Constant ( L.atm) mol.K T = Temperature (K)

The Ideal Gas Law What volume would grams of CO 2 occupy at 0.00°C and 1.00 atmosphere?

The Ideal Gas Law What is pressure of 10.0 grams of NH 3 in a 5.0 L tank at 50.0°C?

John Dalton ( ) What did he not do?

Dalton’s Law of Partial Pressures The partial pressure (p gas X ) of a gas is the pressure that the gas exerts when it is part of a mixture of gases. Right now, the room that we are sitting in contains nitrogen gas, oxygen gas, water vapor, and trace amount of other gases atm O atm N atm CO atm trace gases = 1.0 atm (atmospheric pressure)

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the gases that make up the gas mixture. p gas 1 + p gas 2 + p gas 3 + ……… = P total

Graham’s Law of Effusion Effusion – The movement of a gas molecule through a small hole so its velocity may be measured. Diffusion – The movement of gas particles from an area of high concentration to an area of low concentration. What causes a gas particle to diffuse?

Graham’s Law of Effusion What is diffusion?

Graham’s Law of Effusion A heavier gas particle will travel slower than a lighter gas particle. KE = ½ mass x velocity 2 If the kinetic energy is the same for a heavy and a light gas particle, then the velocity of the heavier one will be less than the velocity of the lighter one.

Graham’s Law of Effusion The rate at which a ligher gas will travel faster than a heavier gas is equal to the inverse square root of the molar mass of the gases. Rate of light gas = √ (molar mass of heavy gas) Rate of heavy gas √ (molar mass of light gas)

Graham’s Law of Effusion Which molecule will diffuse faster, H2 or O2? How many times faster will the ‘faster’ molecule diffuse compared to the slower one?