Kinetic-Molecular Theory and Gas Laws Kinetic-Molecular Theory and Gas Laws

Properties of Gases highly compressible and low density – due to the large spaces between gas particles highly compressible and low density – due to the large spaces between gas particles indefinite shape – will take shape of its container indefinite shape – will take shape of its container indefinite volume – will occupy the entire volume of its container indefinite volume – will occupy the entire volume of its container high fluidity – the particles easily glide by one another, allow the gas to flow high fluidity – the particles easily glide by one another, allow the gas to flow

Kinetic-Molecular Theory and Gases 1. Gas is composed of particles either molecules or atomseither molecules or atoms (Ex: O 2 or Ar)(Ex: O 2 or Ar) 2. Gas particles do not attract or repel one another. Like billiards balls, they bounce off of one anther after a collisionLike billiards balls, they bounce off of one anther after a collision

Kinetic-Molecular Theory and Gases 3. Gas particles are in constant, random motion they move in straight line pathsthey move in straight line paths only changing direction when they collide with one another or walls of containeronly changing direction when they collide with one another or walls of container 4. All gas particle collisions are elastic collisions energy transferred from one particle to another without a loss of kinetic energy.energy transferred from one particle to another without a loss of kinetic energy.

5. The amount of kinetic energy, how fast the particles move, depends on temperature. –Higher temperature, move faster –Lower temperature, move slower –At absolute zero (0 K – lowest possible temperature) – NO movement Effusion – gradual movement of a gas through a small opening Diffusion – gradual mixing of gases due to constant random motion

Standard Temperature and Pressure Temperature Temperature 0 o C = 273 K –Temperature conversion examples: What is 25 o C in Kelvin? What is 345 K in Celsius? Pressure units are: Pressure units are: kPa = 760 mm Hg = 760 torr = 1 atm –Pressure conversion example: If a barometer at you home reads mmHg, what is the atmospheric pressure in kPa?

Dalton’s Law of Partial Pressures Total pressure (P total ) of a mixture of gases is equal to the sum of the pressures of each of the gases Equation P total = P gas 1 + P gas 2 + P gas If a gas is collected over water, as the gas is collected some of the water is evaporated and joins the gas. – –Thus the pressure in the collection container is the sum of the gas and the water. – –To find the pressure of just the gas, the pressure of the water needs to be subtracted. P gas = P total - P water vapor

Examples… A scuba tank contains a mixture of gases including 0.42 atm N 2, 205 torr O 2 and 35.5 kPa CO 2. What is the total pressure inside the tank in atmospheres? Oxygen gas was collected over water at 16 o C. Total volume of gas is 188 mL at pressure of 92.3 kPa. What is the pressure of the O 2 ? (at 16 o C, vapor pressure = 1.82 kPa)

Boyle’s Law the volume of a gas is inversely proportional to pressure, at constant temperature the volume of a gas is inversely proportional to pressure, at constant temperature - if volume increases, then - if volume increases, then pressure decreases - if volume decreases, then - if volume decreases, then pressure increases Equation Equation P 1 · V 1 = P 2 · V 2 Example: A sample of neon gas occupies a volume of 2.8 L at 1.8 atm. What would its volume be at 1.2 atm? Example: A sample of neon gas occupies a volume of 2.8 L at 1.8 atm. What would its volume be at 1.2 atm?

Charles’ Law volume of a gas is directly proportional to temperature (in Kelvin), at constant pressure volume of a gas is directly proportional to temperature (in Kelvin), at constant pressure –if temperature doubles, then volume also doubles Equation Equation V 1 = V 2 T 1 T 2 Example: A sample of nitrogen occupies a volume of 250 mL at 25 °C. What volume will it occupy at 95 °C? Example: A sample of nitrogen occupies a volume of 250 mL at 25 °C. What volume will it occupy at 95 °C?

Gay-Lussac’s Law the pressure of a gas is directly proportional to absolute temperature (Kelvin), at constant volume the pressure of a gas is directly proportional to absolute temperature (Kelvin), at constant volume –if temperature doubles, then pressure also doubles Equation Equation P 1 = P 2 T 1 T 2 Example: If a gas is cooled from K to K and the volume is kept constant, what final pressure would result if the original pressure was mmHg? Example: If a gas is cooled from K to K and the volume is kept constant, what final pressure would result if the original pressure was mmHg?

Combined Gas Law relationship of pressure, volume, and temperature (in Kelvin) of a sample of gas with constant mass relationship of pressure, volume, and temperature (in Kelvin) of a sample of gas with constant mass Equation: P 1 ·V 1 = P 2 ·V 2 Equation: P 1 ·V 1 = P 2 ·V 2 T 1 T 2 T 1 T 2 Example: Example: An unopened, cold 2.00 L bottle of soda contains 46.0 mL of gas confined at a pressure of kPa at a temperature of 5.0°C. If the bottle is dropped into a lake and sinks to a depth at which the pressure is 154 kPa and a temperature of 2.1°C, what will be the new volume of the gas?

Ideal Gas Law Equation: P V = n R T Equation: P V = n R T P = pressure P = pressure V = volume (in liters) V = volume (in liters) n = number of moles n = number of moles T = temperature (in Kelvin) T = temperature (in Kelvin) R = ideal gas constant (pick which one based on the unit of pressure) R = atm·L R = 62.4 mmHg·L mol·K mol·K R = kPa·L mol·K Example: Example: Calculate the number of moles of gas contained in a 3.0L vessel at 33°C and a pressure of 1.50 atm.

equal volumes of gases at the same temperature & pressure contain equal numbers of particles equal volumes of gases at the same temperature & pressure contain equal numbers of particles At STP, one mole of any gas… At STP, one mole of any gas… 1 mol = x particles = Molar Mass in grams = 22.4 L Examples: – –Determine the volume occupied by 2.5 mol of a gas at STP. – –What volume will g of krypton occupy at STP? Avogadro’s Principle

Gas Stoichiometry coefficients in balanced chemical equations represent number of: – moles of each substance – liters of gases, assuming pressure and temp. remain constant Example C 3 H 8 (g)+ 5 O 2 (g) 3 CO 2 (g)+ 4 H 2 O (g) 1 mol 5 mol 3 mol 4 mol 1 L 5 L 3 L 4 L

Volume–Volume Problems use the balanced equation to find volume ratio Example: If 1.78 L of oxygen reacts, what volume of nitrogen will be produced? NH 3 (g) + O 2 (g) N 2 (g) + H 2 O (l) 1.78 L O 2 2 N 2 = 1.19 L N 2 3 O 2