States of Matter & Gas Laws Chapters 13 & 14

Kinetic Theory of Matter All particles are moving all the time.

Gases No definite shape or volume Easily compressible

What do we know about gas particles? Can be either molecules or atoms; e.g. He, O2, C3H8 Very far apart from one another. Between particles is empty space. No attractive or repulsive forces between particles. Move randomly. Move at high speeds (O2 at 20oC moves at 1700 km/h). Travel in straight paths. Only change direction when collide with another particle/object. Collide elastically (no kinetic energy lost).  Ideal Gas

Gas Pressure The force exerted by a gas per unit of surface area.  Created by the collision of gas particles with a surface.

Vacuum empty space  no particles no pressure A vacuum pump is a device that removes gas molecules from a sealed volume in order to leave behind a partial vacuum

Atmospheric Pressure Atmospheric Pressure: created by the gases that make up Earth’s atmosphere.  Atmospheric pressure decreases as elevation increases (lower density of gases).  Measured using a Barometer.

Units of Pressure SI Unit = pascal (Pa) Other units: atmospheres (atm) millimeters of mercury (mmHg) torr pounds per square inch (psi) Standard Pressure: 101.3 kPa = 1 atm = 760 mmHg = 760 torr = 14.7 lb/in2 (psi) Rmv psi

Pressure Conversion Practice 7.31 psi = _______ mmHg 1140 torr = _______ kPa 19.0 psi = ________ kPa 202 kPa = ________ atm Rmv psi

Temperature Temperature: average kinetic energy of particles The faster the particles are moving, the higher the temperature. Kelvin temperature is directly proportional to the average kinetic energy of the particles of the substance. Particles at 200K have twice the average KE of particles at 100K. Absolute Zero: KE = 0; all motion of particles stops We have only produced 0.5 nanokelvin.  TK = TC + 273

Relative Density of States of Matter GENERAL TREND: In order from most dense to least dense: solid, liquid, gas Exception: Water is most dense at 4oC (liquid).

Phase Change Review Melting: solid  liquid Vaporization: liquid  gas Evaporation: occurs only at surface of liquid Boiling: bubbles of vapor form within the liquid when the temperature of the liquid is increased Condensation: gas  liquid Freezing: liquid  solid

Gas Laws P1V1 = P2V2 T1 T2 (FOR A FIXED AMOUNT OF GAS) Cool Program Gas Laws (FOR A FIXED AMOUNT OF GAS) P1V1 = P2V2 T1 T2 (COMBINED GAS LAW)

Boyle’s Law Units: Pressure – Volume – Boyle’s Law: At constant temperature, the pressure and volume of a gas are inversely proportional. P1V1 = P2V2 Graph: Units: Pressure – Volume –

Boyle’s Law

Boyle’s Law Conceptual Problems If the volume of a gas is decreased by half, what happens to its pressure? If the pressure tripled, what must have happened to the volume of the gas? If the volume doubles, what happens to pressure?

Boyle’s Law Math Problems The volume of a gas at 99 kPa is 300 mL. If the pressure is increased to 188 kPa, what will be the new volume? The pressure of a sample of helium in a 1.0-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.0-L container? *Both Pressures must be in the same unit. Both Volumes must be in the same unit.

Cartesian Diver How does it work???

Charles’s Law Units: Volume – Temperature – Charles’s Law: At constant pressure, the volume of a gas is directly proportional to its Kelvin temperature. V1 = V2 T1 T2 Graph: Units: Volume – Temperature –

Charles’s Law

Liquid Nitrogen

Charles’s Law Conceptual Problems If the temperature of a gas is doubled, what must happen to volume in order for pressure to remain constant? If the volume of a gas decreases to one-third its original volume, what happens to the temperature in order for pressure to remain constant?

Charles’s Law The Math… The Celsius temperature of a 3.0-L sample of gas is lowered from 80oC to 30oC. What will be the resulting volume of this gas? A gas at 89oC occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?

Gay-Lussac’s Law Gay-Lussac’s Law: At constant volume, the pressure of a gas is directly proportional to its Kelvin temperature. P1 = P2 T1 T2

Gay-Lussac’s Law What happens to pressure if temperature increases and volume is held constant? The pressure in an automobile tire is 1.88 atm at 25oC. What will be the pressure if the temperature warms up to 37oC?

Combined Gas Law Combined Gas Law: for a fixed amount of gas. P1V1 = P2V2 T1 T2   STP = 273 K (0 oC), 1 atm

Combined Gas Law Conceptual Problems What happens to temperature if volume and pressure are both doubled? What happens to pressure if volume and temperature are both tripled? What must happen to volume if pressure is halved and temperature is doubled?

Combined Gas Law Math Problems A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36oC. If it is released and rises to an elevation at which the pressure is 0.9 atm and the temperature is 28oC, what will be the new volume of the balloon? At STP, a sample of gas occupies 30 mL. If the temperature is increased to 30 oC and the entire gas sample is transferred to a 20 mL container what will be the gas pressure inside the container?

Ideal Gas Law Ideal Gas Law – Amount of Gas Varies PV = nRT n = number of moles R = 0.0821 L*atm/mol*K = 62.4 L*mmHg/mol*K = 8.31 kPa*L/mol*K

Ideal Gas Law What pressure is exerted by 0.450 mol of a gas at 25oC if the gas is in a 0.650-L container? Determine the volume occupied by 0.582 mol of a gas at 15oC if the pressure is 81.8 kPa.

Avogadro’s Law Avogadro’s Law n1 = n2 V1 V2

Avogadro’s Law Assuming that pressure and temperature remain constant, what happens to the volume of a gas if the number of moles doubles? If you have two moles of a gas in a 4-liter container, how many moles of the gas would you have to release in order for the gas to occupy a 3- liter container and retain the same pressure and temperature.

Mixtures of Gases Dalton’s Law of Partial Pressures: the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture. Ptotal = P1 + P2 + P3 + … Partial Pressure of a Gas: the portion of the total pressure contributed by a single gas.

Dalton’s Law of Partial Pressures What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mmHg and the partial pressure of helium is 439 mmHg?