Active Chemistry Kinetic Molecular Theory and the Gas Laws

Phases of Matter There are four phases of matter: 1. Solid 2. Liquid 3. Gas 4. Plasma The state of matter depends on the motion of the molecules that make it up.

Solids Solids are objects that have definite shapes and volumes. The atoms or molecules are tightly packed, so the solid keeps its shape. The arrangement of particles in a solid are in a regular, repeating pattern called a crystal. Microscopic picture of a solid.

Liquids The particles in a liquid are close together, but are able to move around more freely than in a solid. Liquids have no definite shape and take on the shape of the container that they are in. Microscopic picture of a liquid.

Gases A gas does not have a definite shape or volume. The particles of a gas have much more energy than either solids or liquids and can move around freely. Microscopic picture of a gas.

Plasma Plasma is a gas-like mixture of positively and negatively charged particles. It is found in stars, such as the sun, and in fluorescent lighting. Plasma occurs when temperatures are high enough to cause particles to collide violently and be ripped apart into charged particles.

Postulates of KMT A gas consists of a collection of small particles traveling in straight-line motion. The molecules in a gas occupy no volume (that is, they are points spread far apart). Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during the collision). There are no attractive or repulsive forces between the molecules. The average kinetic energy of a molecule is proportional to the Temperature. Molecules can collide with each other and with the walls of the container. Collisions with the walls account for the pressure of the gas.

At the same temperature, lighter gases move faster than heavier gases.

Do you remember which is the standard unit???? Temperature Temperature is a measure of the amount of the average kinetic energy of the particles in matter. The more kinetic energy the particles have, the higher the temperature. The temperature of particles are usually recorded in one of three ways: 1. Fahrenheit (ºF) 2. Celsius (ºC) 3. Kelvin (K) Do you remember which is the standard unit????

Fahrenheit Developed by Daniel Gabriel Fahrenheit, who is best known for inventing the alcohol thermometer and mercury thermometer in the early 1700’s. It is based on 32º for the freezing point of water and 212º for the boiling point of water. The interval between the freezing and boiling points are divided into 180 parts. The conversion to Celsius is: ºF = (9/5 ºC) + 32

Celsius Scale developed by Anders Celsius in the early to mid-1700’s, working from the invention of Fahrenheit's thermometers. The Celsius scale is based on 0º for the freezing point of water and 100º as the boiling point. The interval between the freezing and boiling points are divided into 100 parts. The conversion to Fahrenheit is: ºC= (5/9)(ºF-32) The conversion to Kelvin is: K=ºC +273

Kelvin Developed by William Thompson Kelvin in 1848, Kelvin is a temperature scale having an absolute zero below which temperatures do not exist. At 0K, all molecules cease any type of motion (as in the temperature of outer space). It corresponds to a temperature of -273°C. The Kelvin degree is the same size as the Celsius degree, so the freezing point of water is at 273K and the boiling point is at 373K.

The Behavior of Gases The behavior of gases can be explained by the way their particles interact with each other and the environment around them. The particles are constantly colliding with one another and other objects. Since the molecules have mass, there is a certain amount of pressure being applied. As the volume of the gas and/or the temperature of the gas change, so does its behavior.

Gas Laws The result of a force distributed over an area. SI unit for pressure = pascal (Pa) = N/m2 (one kilopascal = kPa= 1000 Pa)

Factors that Affect Pressure of an Enclosed Gas Temperature Volume Number of Particles

Temperature Raising the temperature of a gas will increase its pressure if the volume of the gas and the number of particles are constant

Volume Reducing the volume of a gas increase its pressure if the temperature of the gas and the number of particles are constant.

Number of Particles Increasing the number of particles will increase the pressure of a gas if the temperature and the volume are constant.

General Properties of Gases There is a lot of “free” space in a gas. Gases can be expanded infinitely. Gases fill containers uniformly and completely. Gases diffuse and mix rapidly.

Real Gases Ideal Gas Real Gas . No intermolecular small attraction attraction between between particles particles Gas particles have Gas particles have no volume a volume

This implies: If the volume of space occupied is large and the pressure is low, the behavior of a gas is very close to that of an ideal gas. We will not deal with gases at conditions that make them non-ideal in this class.

Atmospheric Pressure The pressure the earth’s atmosphere exerts due to its weight.

Pressure Pressure of air is measured with a BAROMETER Column height measures Pressure of atmosphere 1 standard atmosphere (atm) = 760 mm Hg = 101.3 kPa (SI unit is PASCAL)

Measuring Pressure of confined gas Manometer- Instrument used to measure gas pressure Filled with Mercury

Pressure Conversions 1.00 atm = 101.3 kPa 1.00 atm = 760. mmHg 101.3kPa = 760. mmHg

Pressure Conversions 475 mm Hg x = 0.625 atm 29.4 kPa x = 221 mm Hg A. What is 475 mm Hg expressed in atm? 1.00 atm 760 mm Hg B. The pressure of a tire is measured as 29.4 kPa. What is this pressure in mm Hg? 101.3kPa 475 mm Hg x = 0.625 atm 29.4 kPa x = 221 mm Hg

Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (ml, L, cm3, etc) T = temperature (K) ALL temperatures MUST be in Kelvin to calculate other variables!!! No Exceptions! n = amount (moles) P = pressure (atm, mmHg, kPa)

Standard Conditions Standard Temperature: 273 K Standard Pressure: 1.00 atm (atmosphere) 760 mm Hg 760 torr 101.3 kPa (kilopascal) Referred to as STP- Standard Temperature and Pressure

Pressure and Volume Click here for Demonstration

This is an relationship Pressure and Volume When temperature and the # of particles are kept constant in a closed container: As Volume decreases, Pressure or As Volume increases, Pressure This is an relationship increases decrease inverse

Boyle’s Law P1 • V1 = P2 • V2 P α 1/V This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. P1 • V1 = P2 • V2 Robert Boyle (1627-1691)

A Graph of Boyle’s Law

Boyle’s Law If the gas is compressed to half the volume it had, twice as many molecules are present in any given volume. Twice as many impacts per second on the walls of the container results in doubling the pressure.

Boyle’s Law Example A balloon filled with Helium has a volume of 457ml at standard atmospheric pressure. After the balloon is released, it reaches an altitude of 6.3km where the pressure is only 65.5kPa. What is the volume of the balloon at this altitude? P1 • V1 = P2 • V2

Temperature Scales and Interconversions Kelvin ( K ) - The “Absolute temperature scale” begins at absolute zero and only has positive values. Celsius ( oC ) - The temperature scale used by science, formally called centigrade and most commonly used scale around the world, water freezes at 0oC, and boils at 100oC.

Temperature Conversions Formulas K = 0C + 273 0C = K - 273

Temperature Conversions Ex. 1: The boiling point of Liquid Nitrogen is –1950C, what is the temperature in Kelvin? Formula: K = 0C + 273 K = -195 + 273 = 78.0 K (3 Sig Dig)

Temperature Conversions Ex. 2 The normal body temperature is 310. K, what is it in Celsius? Formula: 0C = K - 273 0C = 310. – 273 = 37.0 0C

Temperature and Volume Click here for Demonstration

Volume and Temperature Pressure and the # of particles are constant then As Temperature decreases, Volume _________ or As Temperature increases, Volume __________ This is a relationship decreases increases direct

Charles’ Law Example A quantity of gas occupies a volume of 506 cm3 at a temperature of 147oC. Assuming that the pressure remains constant, at what temperature will the volume of the gas be 604 cm3? V1 = 506cm3 V2= 604cm3 T1 = 147oC + 273 = 420K T2= ??

A Graph of Charles’s Law

V1 V2 T1 T2 = Charles Law If n (moles) and P are constant, then V α T V and T are directly proportional. If one temperature goes up, the volume goes up! Jacques Charles (1746-1823) V1 V2 T1 T2 =

Pressure and Temperature Volume and the # of particles are constant then: As Temperature decreases, pressure _______ or As Temperature increases, pressure ________ This is a relationship decrease increase direct

Charles’ Law Doubling the Kelvin temperature of a gas makes the gas expand resulting in doubling the volume of the gas

= Gay-Lussac’s Law P1 P2 T1 T2 If n and V are constant, then P α T P and T are directly proportional. If one temperature goes up, the pressure goes up! P1 P2 T1 T2 =

Guy Lussac’s Law Doubling the Kelvin temperature of a gas doubles the average kinetic energy of its molecules. Faster moving molecules strike the wall of the container more often and with more force doubling the Pressure.

Gas Pressure Volume Temperature Number Law of moles (P) (V) (T) (n) Boyles   Charles   Gay-   Lussac

Confusing?

P1V1 P2V2 T1 T2 = Combined Gas Law All 3 Laws can be found from this one! =

Combined Gas Law P1V1 P2V2 T1 T2 Boyle’s Law – Temperature constant =

Combined Gas Law P1V1 P2V2 T1 T2 Charles’ Law – Pressure constant =

Combined Gas Law P1V1 P2V2 T1 T2 Gay-Lussac’s Law – Volume constant =

IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory. BE SURE YOU KNOW THIS EQUATION!

The Ideal Gas Law PV = nRT P = pressure (in atmospheres) V = volume (in Liters) n = number of moles R = Universal Gas Law Constant (.0821 L atm/mol K) T = Temperature (in Kelvins)

Using PV = nRT How much N2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 oC? Solution 1. Get all data into proper units V = 27,000 L T = 25 oC + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm And we always know R, 0.0821 L atm / mol K

Using PV = nRT PV = nRT RT RT How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC? Solution 2. Now plug in those values and solve for the unknown. PV = nRT RT RT n = 1.1 x 103 mol (or about 30 kg of gas)

Using Ideal Gas Law Example What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm and temperature of 20oC? Ans: V = nRT/P V = (2.3 mol)(.0821 L atm/mol K)(293K) 1.2 atm = 46.0 L

Deviations from Ideal Gas Law Real molecules have volume. The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves. There are intermolecular forces. An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions. Otherwise a gas could not condense to become a liquid.

Dalton’s Law of Partial Pressures The % of gases in air Partial pressure (STP) 78.08% N2 593.4 mm Hg 20.95% O2 159.2 mm Hg 0.94% Ar 7.1 mm Hg 0.03% CO2 0.2 mm Hg PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2 Total Pressure = 760 mm Hg

Dalton’s Law of Partial Pressures 2 H2O2 (l) ---> 2 H2O (g) + O2 (g) 0.32 atm 0.16 atm What is the total pressure in the flask? Ptotal in gas mixture = PA + PB + ... Therefore, Ptotal = PH2O + PO2 = 0.48 atm Dalton’s Law: total P is sum of PARTIAL pressures.

Dalton’s Law John Dalton 1766-1844

Health Note When a scuba diver is several hundred feet under water, the high pressures cause N2 from the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2 in scuba tanks used for deep descents.

Collecting a gas “over water” Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

Table of Vapor Pressures for Water

Solve This! 768 torr – 17.5 torr = 750.5 torr A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the gas? 768 torr – 17.5 torr = 750.5 torr

GAS DENSITY Low density 22.4 L of ANY gas AT STP = 1 mole High density

Gases and Stoichiometry 2 H2O2 (l) ---> 2 H2O (g) + O2 (g) Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the volume of O2 at STP? Bombardier beetle uses decomposition of hydrogen peroxide to defend itself.

Gases and Stoichiometry 2 H2O2 (l) ---> 2 H2O (g) + O2 (g) Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the volume of O2 at STP? Solution 1.1 g H2O2 1 mol H2O2 1 mol O2 22.4 L O2 34 g H2O2 2 mol H2O2 1 mol O2 = 0.36 L O2 at STP

Gas Stoichiometry: Practice! A. What is the volume at STP of 4.00 g of CH4? B. How many grams of He are present in 8.0 L of gas at STP?