Starter  Describe the differences between various states of matter

Physical Characteristics of Gases Kinetic Molecular Theory

The Kinetic Molecular Theory  based on the idea that particles are constantly moving  can be applied to solid, liquid, or gas  provides a model of ideal gas behavior so only an approximation

Gases consist of tiny particles that are very far apart  most volume is empty space-low density  allows gases to be easily compressed All collisions between particles and container walls are elastic  there is no net loss of energy when particles collide  total kinetic energy stays constant even though it can be transferred between particles

Particles are in continuous, rapid, random motion  since they are moving, they have KE  KE overcomes their attractive forces No forces of attraction or repulsion  like billiard balls  bounce apart immediately

Average kinetic energy depends on temperature  KE increases as temperature increases  KE = ½mv 2 where m = mass of particle where m = mass of particle where v = velocity of particle where v = velocity of particle  so at the same T, lighter particles have higher speeds than heavier ones  velocity and temperature are directly proportional

Real vs. Ideal Gases  ideal gas is defined by the KMT  most gases behave close to the ideal when high temperature – so they have enough KE to overcome attractive forces high temperature – so they have enough KE to overcome attractive forces low pressure – so they are very spread out low pressure – so they are very spread out  Gases with little attraction are more ideal (monatomic gases)

Physical Characteristics of Gases Pressure

Pressure  P : force per unit area on a surface  Newton – SI unit for force (1 kg*m/s 2 )  why would shoes with smaller diameter heel not be allowed on gym floor?  As surface area decreases, pressure increases  Pressure exerted by a gas depends on volume volume temperature temperature number of molecules number of molecules

Measuring Pressure  barometer instrument used to measure atmospheric pressure instrument used to measure atmospheric pressure first one created by Torricelli in early 1600s first one created by Torricelli in early 1600s glass tube filled with mercury is inverted in a dish glass tube filled with mercury is inverted in a dish mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish

Measuring Pressure  manometer: measures pressure of gas in a container measures pressure of gas in a container gas has less pressure than atmosphere if the Hg is closer to chamber gas has less pressure than atmosphere if the Hg is closer to chamber gas has more pressure than atmosphere if the Hg is further from chamber gas has more pressure than atmosphere if the Hg is further from chamber

Units of Pressure  millimeters of mercury (mmHg) from mercury barometer from mercury barometer  torr (torr) from Toricelli inventing barometer from Toricelli inventing barometer  atmosphere of pressure (atm)  Pascal (Pa) = 1N/m 2 (SI unit) named after French scientist named after French scientist 1 atm = 760 mmHg = 760 torr = kPa

Practice Conversions  Convert atm to mmHg mmHg torr torr kPa kPa

Practice Conversions  Convert kPa to atm atm mmHg mmHg torr torr

Temperature Scales

Convert the following to K or 0 C  0 0 C  5 K  20 0 C  C  100 K  C

Starter The pressure of a gas is measured as 49 torr. Convert this pressure to atmospheres, kiloPascals, and mmHg. Pull out your homework so I can check it.

Starter: Pressure Conversions The pressure of a gas is measured as 49 torr. Represent this pressure in atmospheres, Pascals, and mmHg.

Physical Properties of Gases Gas Laws: Relationships between volume, temperature, pressure, and amount of gas.

Boyle’s Law: P and V  as one increases, the other decreases  inversely proportional  pressure is caused by moving molecules hitting container walls  If V is decreased and the # of molecules stays constant, there will be more molecules hitting the walls per unit

Boyle’s Law: P and V  Boyle’s Law: the V of fixed mass of gas varies inversely with P at a constant T.  PV = k  k is a constant for a certain sample of gas that depends on the mass of gas and T  What kind of graph is V vs. P?  If we have a set of new conditions for the same sample of gas, they will have same k so:

Boyle’s Law

Boyle’s Law: P and V  Discovered by Irish chemist, Robert Boyle  Used a J-shaped tube to experiment with varying pressures in multistory home and effects on volume of enclosed gas

Example: Boyle’s Law Consider a 1.53-L sample of gaseous SO 2 at a pressure of 5.6 x 10 3 Pa. If the pressure is changed to 1.5 x 10 4 Pa at constant temperature, what will be the new volume of the gas?

Charles’ Law: V and T  if P is constant, gases expand when heated  when T increases, gas molecules move faster and collide with the walls more often and with greater force  to keep the P constant, the V must increase

Charles’ Law: V and T  Problem: if we use Celsius, we could end up with negative values from calculations in gas laws for volumes  we need a T system with no negative values: Kelvin Temperature Scale starts at ° C = absolute zero = 0 K starts at ° C = absolute zero = 0 K lowest possible temperature lowest possible temperature balloon going into liquid nitrogen

Charles’ Law: V and T  Charles’ Law: the V of fixed mass of gas at constant P varies directly with Kelvin T.  V = kT  k is a constant for a certain sample of gas that depends on the mass of gas and P  What kind of graph is V vs. T?  If we have a set of new conditions for the same sample of gas, they will have same k so:

Charles’ Law  discovered by French physicist, Jacques Charles in 1787  first person to fill balloon with hydrogen gas and make solo balloon flight

Example: Charles’ Law & Temp. A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?

Pressure vs Volume vs Temp P V V T T P P/V = k T/V = k P/T = k

Equations on your reference sheets

Physical Characteristics of Gases Dalton’s Law of Partial Pressure

 John Dalton responsible for atomic theory responsible for atomic theory also studied gas mixtures also studied gas mixtures  the P of gas mixture is the sum of the individual pressures of each gas alone  the P that each gas exerts in the mixture is independent of the P that are exerted by other gases

Dalton’s Law of Partial Pressure  the total P of a mixture of gases is equal to the sum of partial P of component gases, no matter how many different gases  P T = P 1 + P 2 + P 3 + …  Partial Pressure- P of each gas in mixture

Why?  the particles of each gas in a mixture have an equal chance to hit the walls  so each gas exerts P independent of that exerted by other gases  total P is result of the total # of collisions per unit of wall area

Water Displacement  gas produced is less dense than water so it replaces the water in the bottle  gas collected is not pure because it contains vapor from the water P T = P gas + P water equal to atmospheric pressure set for a certain T

Example  Oxygen gas from decomposition of KClO 3 was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0 ° C respectively. If the partial pressure of water vapor is 17.5 torr at 20.0 ° C. What was the partial pressure of oxygen collected?  P T = P O2 + P H2O  torr = P O  P O2 = torr

Example  Find the partial pressure by 2 gases (A and B) mixed if the overall pressure is 790 mmHg. The percent by volume is A: 20% and B: 80%.  P T = P A + P B = 790 mmHg  A: 0.20 x 790 = 158 mmHg  B: 0.80 x 790 = 632 mmHg

Starter  How many grams of NO gas are in 6200 mL of gas at STP?

Molecular Composition of Gases Ideal Gas Law

 relationship among P, V, T, and number of moles of gas (n)  combination of all the laws we learned  helps us approximate “real” gas behavior  where R: ideal gas constant R: ideal gas constant L atm/mol K (use most often) L atm/mol K (use most often) J/mol K (only for when P is in Pascals) J/mol K (only for when P is in Pascals)  check units before using equation

Example  What is the P in atm exerted by a mol sample of nitrogen gas in a 10.0 L container at 298 K?

Example  What is the volume in liters of mol of oxygen gas at 20.0°C and atm?

Example  What mass of chlorine gas is in a 10.0 L tank at 27°C and 3.50 atm?

Finding Molar Mass  mass of one mole of substance  units : g/mol  represented by M

Finding Molar Mass  At 28°C and atm, 1.00 L of gas has a mass of 5.16g. What is the molar mass?

Finding Density

Finding Molar Mass  The density of dry air at sea level (with pressure of exactly 1 atm) is g/L at 15°C. What is the molar mass of air?

Finding Density  What is the density of carbon monoxide gas at STP?

Finding Density  A sample of gas has a mass of 50.0 g and volume of 26.0 L at 25C and 1.2 atm. What is the molar mass of the gas?