Gas Laws. The kinetic theory of matter states that particles which make up all types of matter are in constant motion.

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1 Name Period Gas Laws Kinetic energy is the energy of motion of molecules. Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule is very far from other atoms or molecules. Virtually all of the volume of a gas is empty space. The kinetic theory of matter states that particles which make up all types of matter are in constant motion. The kinetic theory of gases assumes the following: 1. Gases consist of particles in constant, random motion. They continue in a straight line until they collide with something usually each other or the walls of their container. 2. No molecular forces are at work. This means that there is no attraction or repulsion between the particles. 3. Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions. 4. The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and kinetic energy of the gas refer to the average of these speeds. 5. The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move. 6. All gases at a given temperature have the same average kinetic energy. 7. Lighter gas molecules move faster than heavier molecules. Temperature is a measure of the average kinetic energy of the particles of a substance. Kelvin K= C Kelvin: temperature scale with no negative signs 0 K = absolute zero (Temperature at which all kinetic motion ceases)

2 STP (Standard Temperature and Pressure) means pressure is equal to 1 atm and temperature is 273 K. Barometer: Instrument used to measure atmospheric pressure Melting point: temperature at which a solid has enough energy to become a liquid Boiling point: temperature at which a liquid has enough energy to become a gas Condensation point: temperature at which gas becomes a liquid Boiling Point: vapor pressure of the liquid = surrounding pressure of the liquid At 1 atm water boils at 100 C BUT water can boil at much lower temperatures!!! Deposition: Gas becomes a solid (frost) Sublimation: solid becomes a gas (dry ice) Three units used to measure atmospheric pressure are pascals (Pa) millimeter of mercury (mm Hg) atmospheres (atm) 1 atm = 760 mm Hg 1 atm = kpa 1 atm = 760 torr 1 atm = inches Hg 1 kpa = 1000 Pa

3 Examples Convert 825 mm Hg to atm Convert 1.07 atm to kpa Convert 125 kpa to torr Convert 8.20 x 10 6 Pa to inches of Hg The three factors which determine the physical behavior of gases are: 1. Pressure 2. Temperature 3. Volume

4 Gas Laws Boyle's law states that for a given mass of gas at a constant temperature, the volume of a gas varies inversely with pressure. That is if we increase pressure the volume decreases and vice versa. If we increase the volume the pressure decreases and vice versa. P1 x V1 = P2 x V2 Examples A balloon is filled with helium gas at 1.0 atm of pressure and has a volume of 32.0L. Assuming constant temperature, what will its volume be if it rises in the atmosphere to a height where the pressure is 0.75 atm? Calculate the final pressure of a gas (in kpa) when the volume of the container increases from 250 ml to 1.0 L. The gas is initially at 3.75 atm. Assume constant temperature.

5 Charles' law states that the volume of a fixed mass of gas is directly proportional to its temperature (K) if the pressure is kept constant. That is if we increase temperature volume increases and vice versa. V1/T1= V2/T2. Examples: A balloon is inflated to a volume of 1.0 L in a room at 298 K. What is final temperature if the volume decreases to 250 ml while the pressure remains constant? A gas has a volume of L at a temperature of 20.0 C. At constant pressure, what will the volume of the gas be if the temperature changes to 30.0 C?

6 Gay-Lussac's law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant. P1/T1 =P2/T2 Examples: A tank of nitrogen gas has a temperature of 273 K and a pressure of 3.30 atm. Assuming constant volume, if the temperature rises to 293 K, what will the resulting pressure be? A mass of air has a pressure of 0.25 atm at 101 o C. What will the temperature be if the pressure is increased to 750 mm Hg while the volume remains constant?

7 Boyles, Charles, and Gay-Lussacs Law each have one factor which is held constant and does not appear in the equations (use this to help remember which equation to use). But what if all the factors change? Then the combined gas law is used. P1 x V1 /T1 = P2 x V2 /T2. Examples: A cylinder of compressed nitrogen has a volume of 20.0 L at atm and 273K. If all the gas of the cylinder is used to fill an inert atmosphere which has a volume of L and a temperature of 225K, what will the pressure be? Calculate the volume of a gas present at STP if the gas starts off with a volume of 225 ml at 123 kpa and 25 o C.

8 Avogadro s Gas Law: a gas at constant temperature and pressure The volume is directly proportional to the number of moles v 1 / n 1 = v 2 /n grams of helium gas is in a 5.4 L balloon. If 7.5 grams of helium are added to the balloon, what will the volume increase to? A 5.5L tank can hold 2.5 kg of oxygen. How many kg of oxygen can a 6.5 L tank hold?

9 The ideal gas law mathematical expression that relates the moles of a gas (indicated in the equation by the variable "n") to T,V and P. It uses the ideal gas constant (R). PV = nrt P = pressure, in atm V = volume, in L n = number of moles, in moles R = ideal gas constant L atm/k mol T = temperature, in K The units must be the same as the R to put it into the ideal gas law equation. If not then you must convert each unit first before putting it into the equation. Example: In an industrial reaction 12.4 mol of nitrogen are produced filling a 60.0 L reaction vessel at K. If nitrogen is the only gas producing the pressure what would the pressure be?

10 What is the volume, in ml, of moles of a gas that is at 940 mm Hg and 25 o C? How many grams of nitrogen monoixide gas are present in a 750 ml container at 12 o C and 115 kpa? What is the density of oxygen gas at atm and 42 C?

11 Dalton's law of partial pressures states that at constant temperature and volume, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures. a partial pressure is the pressure exerted by one of the gases in the mixture. Ptotal = P1 + P2 + P3... Examples: Calculate the total pressure of a mixture of gases where the partial pressures are: 425 mm Hg of O 2, 215 mm Hg of N 2 and 240 mm Hg of CO 2. What is the percent of each gas in the mixture? A 2.0 L contains of mixture of nitrogen and oxygen gas at 25 C. The total pressure is 1.7 atm. The mixture contains moles of nitrogen. Calculate the partial pressure of oxygen and the moles of oxygen.

12 A 472 ml of a gas is collected over water at 32 C at a pressure of 94.9 kpa. What volume does the gas occupy if the pressure is increased to 115 kpa? Stoichiometry and Gas Laws Calculate the volume of oxygen gas produced at 1.50 atm and 28 C by the decomposition of 10.5 g potassium chlorate. How many liters of oxygen gas will be needed to combust 8.50 g of butane at 1.25 atm and 25 C?

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