KINETIC MOLECULAR THEORY

Phase Changes Requiring Energy

Melting The process by which a solid becomes a liquid The melting point is the temperature at which the solid becomes a liquid

Melting

Vaporization The process by which a liquid changes to a gas or vapor Evaporation is vaporization that occurs only on the surface of a liquid Vapor Pressure is the pressure of vapor above a liquid As heat is added to a liquid the vapor pressure increases The Boiling Point is the temperature at which vapor pressure is equal to atmospheric pressure

Vaporization

Sublimation The process by which a solid changes directly into a gas

Phase Changes that Release Energy

Freezing The process by which liquid becomes a solid The freezing point is the temperature at which a liquid becomes solid

Freezing

Condensation The process by which gas becomes liquid

Condensation

Deposition The process by which vapor turns to a solid without moving through a liquid phase

Phase Diagrams The triple point is the temperature and pressure at which all three phases can exist at once The critical point is the temperature and pressure above which the substance can only exist as a gas

States/Phases of Matter

Solids Most ordered state of matter Strong attractive forces between particles Definite shape Fixed volume Particles in constant vibrational motion

Liquids Less ordered than solids, but more ordered than gasses Some attractive forces between particles Able to take the shape of the container Fixed volume Constantly in fluid motion, meaning they flow about freely

Gasses Very disordered Behavior of gasses is described by the Kinetic-Molecular Theory and the Gas Laws

Assumptions made by KMT Particle Size- gasses are made up of small particles separated by empty space no attractive forces between particles Particle Motion- constant random motion collisions between particles are elastic, meaning kinetic energy is conserved

Assumptions made by KMT Particle Energy Kinetic Energy of a Gas Particle= ½ mass * velocity2 All particles of a gas have the same mass, but not the same velocity Not all particles have the same Kinetic Energy

4 Variables Affecting Gasses

Temperature Temperature is the average kinetic energy of particles When performing calculations, it is important to use the Kelvin scale Conversion Factor: °C + 273 = Kelvin (K) Note that NO DEGREE SYMBOL is used with Kelvin

Volume Volume is the space occupied by an “object” (an object can be solid, liquid, or gas Conversion Factor: 1L = 1000mL = 1000cm3

Pressure Pressure is the force per unit area Conversion Factor: 1ATM = 760mmHg = 101.3kPa = 14.7psi

mole Number of Particles The unit used to talk about the number of particles is the mole Conversion Factor: for any given substance, 1 mole=molar mass

Standard Temperature and Pressure STP 0 Kelvin 1 atmosphere of Pressure

Diffusion/Effusion Diffusion is the movement of gas particles from an area of greater concentration to an area of lower concentration (down a concentration gradient) Effusion is diffusion through a small opening

Graham’s Law of Effusion Graham’s Law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight Equation for Graham’s Law: Is used to compare the effusion/diffusion rates for two gasses Heavier particles diffuse more slowly

Example 1: Ammonia (NH3) has a molar mass of 17.0g/mole; hydrogen chloride (HCl) has a molar mass of 36.5g/mole. What is the ratio their diffusion rates?

Example 2: What is the rate of effusion for a gas that has a molar mass twice that of a gas that effuses at a rate 3.6mol/min?

Example 3: Calculate the molar mass of a gas that has a rate of effusion four times that of CO2.

Dalton’s Law of Partial Pressures Each gas in a mixture exerts pressure independently of the other gasses present Dalton’s Law states that the total pressure of a mixture of gasses is equal to the sum of the pressures of all the gasses in the mixture Ptotal = P1 + P2 + P3 + … Pn

Example 1: Find the total pressure for a mixture that contains four gasses with a partial pressure of 5.00kPa, 4.56kPa, 3.02kPa, and 1.20kPa.

Example 2: A mixture of oxygen (O2), carbon dioxide (CO2) and nitrogen (N2) has a total pressure of 0.97 atm. What is the partial pressure of O2 if the partial pressure of CO2 is 0.70 atm and the partial pressure of N2 is 0.12 atm?

The Gas Laws

Relationships Between Variables

Pressure and Volume Graph Direct or Inverse? Description: one goes up, the other goes down Mathematical Formula: P1V1=P2V2 Gas Law: Boyle’s Law Pressure Volume

Pressure and Temperature Graph Direct or Inverse? Description: one goes up, the other goes up Mathematical Formula: P1/T1 = P2/T2 Gas Law: Charles’s Law Temperature Pressure

Volume and Temperature Graph Direct or Inverse? Description: one goes up, the other goes up Mathematical Formula: V1/T1 = V2/T2 Gas Law: Gay-Lussac’s Law Temperature Volume

The Combined Gas Law The combined gas law states the relationship among pressure, volume, and temperature of a fixed amount of gas Equation for the Combined Gas Law: *where temperature MUST be in KELVIN Or simplified:

Example 1: A gas at 110kPa and 30.0°C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80.0°C and the pressure increased to 440kPa, what is the new volume?

Example 2: A helium-filled balloon at sea level has a volume of 2.1L at 0.998 atm and 36°C. If it is released and rises to an elevation at which the pressure is 0.900atm and the temperature is 28°C, what will be the new volume of the balloon?

Example 3: A sample of helium gas in a balloon is compressed from 4.0L to 2.5 L. If the pressure of the gas in the 4.0L volume is 210kPa, what will the pressure be at 2.5L?

Example 4: The volume of a gas at 99.0kPa is 300.0mL. If the pressure is increased to 188kPa, what will the new volume be?

Example 5: A gas sample at 40.0 °C occupies a volume of 2.32 L. If the temperature is raised to 75.0 °C, what will be volume be, assuming the pressure remains constant?

Example 6: A gas at 89°C occupies a volume of 0.67L. At what Celsius temperature will the volume be increased to 1.12L?

Example 7: The pressure of a gas in a tank is 3.20 atm at 22.0°C. If the temperature rises to 60.0°C, what will be the gas pressure in the tank?

Example 8: A gas in a sealed container has a pressure of 125kPa at a temperature of 30°C. If the pressure in the container is increased to 20kPa, what is the new temperature?

Avogadro’s Principle and Molar Volume

Avogadro’s Principle Avogadro’s principle states that equal volumes of gasses at the same temperature and pressure contain equal number of particles One mole = 6.022 x 1023 particles

Molar Volume The molar volume of a gas is the volume that one mole of a gas occupies at standard temperature and pressure STP= 1atm of pressure, 0 Kelvin The molar volume for any gas at STP is 22.4L Conversion factor: 22.4 L /1 mole This conversion factor can be used to find… The number of moles in a gas sample The mass of a gas sample The number of particles in a gas sample

Example 1: Calculate the volume that 0.881 moles of a gas will occupy at STP.

Example 2: Calculate the volume that 2000g of methane gas (CH4) will occupy at STP.

Ideal Gas Law The ideal gas law describes the physical behavior of an ideal gas in terms of the pressure, volume, temperature, and number of moles of gas present Equation for the Ideal Gas Law: Where… P= pressure (MUST be in ATM) V= volume (MUST be in LITERS) n= # of moles R= ideal gas constant, (0.0821 L*atm/mol*K) T= temperature (MUST be in KELVIN)

Example 1: If the pressure exerted by a gas at 25°C in a volume of 0.044L is 3.81 atm, how many moles are present in the gas?

Example 2: Determine the Celcius temperature of 2.49 moles of gas contained in a 1.00L vessel at a pressure of 143kPa.

Example 3: Calculate the volume of a 0.323 mol sample of gas will occupy at 265K and a pressure of 0.900atm.