Kinetic Molecular Theory and Properties of Gases

I. Kinetic Molecular Theory of Gasses *What does the word kinetic mean? A.This theory is based on speculations about the behavior of individual gas molecules and attempts to explain the behavior of an ideal gas.

A magnified view of a flask of air. What is between the dots (the air molecules)?

II. Implications of Kinetic Molecular Theory A.The meaning of temperature – The higher the temp. the faster the particles move. B.The relationship between pressure and temperature – the higher the temp. the faster the particles move, the more pressure is exerted. C.The relationship between volume and temperature – as long as pressure is held constant, the faster moving particles make the volume increase to keep the pressure constant.

Implications (cont.) Volume of individual gas particles is considered to be negligible. The collision of the gas particles with the walls of the container causes pressure. Particles assumed to exert no forces on each other. Average Kinetic Energy of the gas particles is directly proportional to the Kelvin temperature.

Pressure force a gas exerts on its surroundings due to collisions of gas molecules with the surroundings. A barometer is – an instrument used to measure atmospheric pressure

Units of pressure 1. mm Hg or torr 2. atmospheres (atm) 3. pascals (Pa) Standard Pressures: 1 atm = 760 mm Hg = 760 torr = 101,325 Pa Example Conversions

The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a can, and then turning off the heat and sealing the can. Hmco Photo Files

As the water boiled in the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple. Hmco Photo Files

Pressure Conversion Examples Convert 0.87 atm to kPa. Convert 659 mmHg to atm Convert 976 torr to kPa.

Units of Temperature Celcius Water boils at 100 o C Water freezes at 0 o C Kelvin Water boils at 373 K Water freezes at 273 K What is the connection between o C and Kelvin? K = o C + 273

An illustration of Boyle's Law.

A plot of P versus V from Boyle ’ s Law

II. Pressure and Volume: Boyle ’ s Law A. When pressure increases, volume will decrease if the temperature and amount of gas remain constant. Due to this fact we say that pressure and volume are inversely proportional. B. If a change in the pressure of volume of a gas occurs, that gasses new pressure or volume can be determined using: *Boyle ’ s Law: P 1 V 1 = P 2 V 2

Boyle’s Law Examples What is the new volume if a 1.3 L volume of gas at 1.2 atm is exposed to a pressure of 3.4 atm? What is the original pressure if 0.45 L of gas is changed to 1.4 L and a final pressure of 568 torr?

The air in a balloon expands when it is heated. This means that some of the air escapes from the balloon, lowering the air density inside and thus making the balloon buoyant.

III. Volume and Temperature: Charles ’ s Law A.Temperature is a measure of kinetic energy. The gas particles will move faster and want to spread farther apart. Therefore, increasing the volume they occupy. B.At a temperature of 0 K, all motion stops. This temperature is known as absolute zero.

III. Volume and Temperature: Charles ’ s Law As the temperature of a gas increases, the volume of the gas will increase if the pressure and amount of the gas are held constant. Due to this fact we say that temperature and pressure are directly proportional. Charles ’ s Law:

An increase in temperature results in an increase in volume if pressure and amount remain constant.

Plots of V (L) versus T (ºC) for several gases.

Plots of V versus T, using the Kelvin scale for temperature.

Charles’ Law Examples What is the volume of a gas at a constant pressure of 1.0 atm if the temperature rises from 25 o C to 45 o C? What is the new temperature of a gas at 0.73 liters and a constant pressure of 1.0 atm if the original volume is 1.3 liters and temperature of 25 o C?

A.As the number of moles of gas increases, the volume of the gas increases assuming that the temperature and pressure of the gas remain constant. Due to this fact we say that that the number of moles of gas and the volume of a gas are directly proportional. B. Avogadro ’ s Law: where n is the number of moles of gas. IV. Volume and Moles: Avogadro ’ s Law

The relationship between volume V and number of moles n.

Avogadro’s Law Examples If you have 3.4 grams of CO 2 in a 4.5 Liter container, what is the new volume if you add moles of CO 2 at constant temperature and pressure? How many grams of CO 2 is contained in 32.7 liters at STP?

Combined Gas Law The combined gas law is used to calculate the change in either pressure, volume or temperature of a gas if the amount of gas remains constant.

Combined Gas Law Example If you have 3.4 liters of a gas at STP, what is the volume of the gas if you move it to an environment where the pressure is 578 torr and 30 o C?

1 mole of a gas at 273 K and 1 atm (STP) occupies 22.4 L Let ’ s calculate what that number will be, using P x V n x T atm * L/mole * K 62.4 mmHg * L/mole * K 62.4 Torr * L/mole * K 8.31 kPa * L/mole * K

V. Ideal Gas Law A.PV = nRT, where R is the universal gas constant (R = L atm/K mol) Note: the units of pressure, volume, and Temperature that you plug into the above equation must match the corresponding units in the R value) Example

Ideal Gas Law Example If you have 8.32 grams of SO 2 at 30 o C and a pressure of 780 torr, what is the volume of SO 2 ?

B. The ideal gas law has limitations, It assumes the following: That real gases do not stick together. That real gases do not have elastic collisions. That real gases have no volume

C.It is important to note that the ideal gas law is an approximation. Real gases may deviate from the way this model says that they should behave.Real gases may deviate from the way this model says that they should behave. But the model gets closer to real gases when the gas is at extremely low pressures and/or high temperatures.But the model gets closer to real gases when the gas is at extremely low pressures and/or high temperatures.ExamplePractice

The production of oxygen by thermal decomposition of KClO 3.

VI. Dalton ’ s Law of Partial Pressures This law applies when there is a mixture of gasses. A. The ____________________ of a gas is the pressure that the gas would exert if it were alone in the container. B. Dalton ’ s law says that the total pressure of a mixture of gases in a container is equal to the sum of the partial pressures of the gasses in the container: P total = P 1 + P 2 + P 3 + …..however many gasses there are.

When two gases are present, the total pressure is the sum of the partial pressures of the gases.

The total pressure of a mixture of gases depends on the number of moles of gas particles (atoms or molecules) present, not on the identities of the particles.

Laws and Models: A review It is important to note that the ideal gas law, and all the other laws, are approximations. Real gases may deviate from the way this model says that they should behave, but the model is closer to real gases when the gases are at extremely low pressures and/or high temperatures.

X. Gas Stoichiometry Remember…Stoichiometry is all about using a mole ratio. Well…how can you get moles of gas from other information given about the gas? Answer: often you can use PV = nRT to find moles of the gas given before doing a mole ratio.