Chapter 6 The States of Matter Examples of Physical Properties of Three States of Matter 1
Three States of Matter Solids: Fixed shape, fixed volume, particles are held rigidly in place. Liquids: Variable shape, fixed volume, particles are held loosely together. Gases: Variable shape, variable volume, particles are not attracted to each other. 6.2 The Kinetic Molecular Theory of Matter Postulate 1: Matter is made up of tiny particles called molecules. Postulate 2: The particles of matter are in constant motion and therefore possess kinetic energy. Postulate 3: The particles possess potential energy as a result of repelling or attracting each other. Postulate 4: The average particle speed increases as the temperature increases. Postulate 5: The particles transfer energy from one to another during collisions in which no net energy is lost from the system. 2
6.3 The Solid State The solid state is characterized by a high density, a definite shape that is independent of its container, a small compressibility, and a very small thermal expansion. 6.4 The Liquid State The liquid state is characterized by a high density, an indefinite shape that depends on the shape of its container, a small compressibility, and a small thermal expansion. 3
6.5 The Gaseous State The gaseous state is characterized by a low density, an indefinite shape that depends on the shape of its container, a large compressibility, and a moderate thermal expansion. A Kinetic Molecular View of Solids, Liquids, and Gases 4
6.6 The Gas Laws The gas laws are mathematical equations that describe the behavior of gases as they are mixed, subjected to changes in pressure, temperature, volume, or amount. Pressure Pressure the force per unit area. 5
Conversion of Pressure Units The barometer reading for today is inches of Hg. Express this pressure in terms of: atm torr mmhg Temperature The temperature of a gas sample is a measurement of the average kinetic energy of the gas molecules in the sample. The Kelvin temperature scale is used in all gas law calculations. Absolute Zero: The temperature at which all motion stops (0 K). On the Celsius scale, absolute zero is equal to -273ºC. 6
6.7 Pressure, Temperature, and Volume Relationships Mathematical equations relating the pressure, temperature, and volume of gases are called gas laws. Boyle s Law Boyle's law describes the pressure and volume behavior of a gas sample that is maintained at constant temperature. Mathematically, Boyle's law is written as follows: k v P = or PV = In these equations, P is the pressure, V is the volume, and k is an experimentally determined constant. This relationship leads to the following equation: k P 1 V 1 = P 2 V 2 7
Charles s Law V V = k' T = T k' The Combined Gas Law PV = k' ' T 8
The relationship between the volume and pressure of a gas. Boyle s Law The relationship between the volume and temperature of a gas. Charles s Law 9
Gas Law Examples A gas sample has a volume of 2.50 liters when it is at a temperature of 30.0ºC and a pressure of 1.80 atm. What volume, in liters, will the sample have if the pressure is increased to 3.00 atm, and the temperature is increased to 100ºC? A gas occupies 3.8 L at 0.70 atm. If the volume is expanded, at a constant temperature, to 6.5 L, then what is the final pressure? A constant volume of oxygen gas, O 2, is heated from 120 o C to 212 o C. The final pressure is 20.3 atm. What was the initial pressure? 6.8 The Ideal Gas Law Avogadro s law states that equal volumes of gases measured at the same temperature and pressure contain equal numbers of molecules. STP (standard temperature and pressure) = 0ºC (273 K) and 1.00 atm Molar volume at STP: 1 mole of any gas has a volume of 22.4 L at STP. 10
The Ideal Gas Law PV= nrt In this equation, P, V, and T are the same as in the previous gas laws. The number of moles of gas is represented by n and R is the universal gas constant. A commonly-used value for R is: L atm 0.0821 mol K Given the units of R, what are the units for P, V, and T? Ideal Gas Law Calculations Example 1: A 2.50 mole sample of gas is confined in a 6.17 liter tank at a temperature of 28.0ºC. What is the pressure of the gas in atm? Example 2: A 4.00 g sample of gas is found to exert a pressure of 1.71 atm when confined in a 3.60 L container at a temperature of 27ºC. What is the molecular weight of the gas in grams per mole? 11
Real Gases At high temperatures and low pressures most gases behave ideally. Consider gases at high pressure. The effect of molecular volume on measured gas volume. 12
The effect of intermolecular attractions on measured gas pressure. (Real) Non Ideal At high pressures we can no longer say the attractions between gases are negligible. We can no longer say the volume of the gaseous particles themselves is negligible. Thus our ideal gas law equation, PV = nrt has to have some correction factors, a and b. ( P + an 2 / V 2 )( V - nb ) = nrt 13
PV RT 1.0 H 2 He Ideal gas CH 4 CO 2 CH 4 PV RT 2.0 1.5 1.0 0.5 0 10 20 P ext (atm) H 2 CO 2 He PV/RT > 1 Effect of molecular volume predominates PV/RT < 1 Effect of intermolecular attractions predominates Ideal gas 0.0 0 200 400 600 800 1000 P ext (atm) 6.11 Changes in State Changes in state are often accomplished by adding or removing heat from a substance. Adding heat to a substance is classified as an endothermic (heat gained) process. Removing heat from a substance is classified as an exothermic (heat released) process. 14
Endothermic and Exothermic Processes Endothermic processes: Vaporization a liquid is changed to a gas. Sublimation a solid is changed to a gas. Fusion a solid is changed to a liquid. Exothermic processes: Condensation a gas is changed to a liquid. Deposition a gas is changed into a solid. Freezing a liquid is changed into a solid. 6.12 Evaporation and Vapor Pressure Vapor pressure is the pressure exerted by a vapor that is in equilibrium with its liquid. 15
What Can Effect Vapor Pressure Vapor pressure is dependent on the intermolecular forces of the substance. Stronger IMFs lead to lower vapor pressures and weaker IMFs lead to higher vapor pressures. For example, when comparing substances with similar molecular weights those that have dipole forces compared to dispersion forces will have lower vapor pressures. Also, if comparing substances with similar IMFs then the substance with a higher molecular weight will have stronger IMFs and therefore a lower vapor pressure. 6.13 Boiling and the Boiling Point The boiling point the temperature at which the vapor pressure of the liquid is equal to the atmospheric pressure. The normal or standard boiling point is the temperature at which the vapor pressure of a liquid is equal to 1 standard atmosphere (760 torr). A low vapor pressure would equate to a high boiling point. The temperature would have to increase considerably in order to have enough gas sitting above the liquid so the pressure would equal the atmospheric pressure. 16
Variation of Water Boiling Point with Elevation 6.14 Sublimation and Melting Sublimation is the endothermic process in which a solid is changed directly to a gas without first becoming a liquid. Most solids melt before appreciable sublimation takes place. Melting point the temperature at which a solid becomes a liquid. At the melting point, the disruptive forces are strong enough to partially overcome the cohesive forces holding the particles together. 17
6.15 Energy and the States of Matter At 760 torr, constant heat is applied until a 1 g sample of ice at -20ºC is converted to steam at 120ºC. This is a five step process: (AB) heating ice to melting point, (BC) melting ice, (CD) heating liquid to boiling point, (DE) boiling water, and (EF) heating steam. Which of the physical changes are endothermic or exothermic? Endothermic Melting Sublimation Vaporization Exothermic Freezing Deposition Condensation 18
Energy Calculations for Changes in State The energy (heat) associated with steps AB, CD, and EF depends on the mass of the substance, the change in temperature, and the specific heat. The specific heat is the amount of heat required to raise the temperature of exactly 1 g of a substance exactly 1ºC. A lower specific heat indicates very little heat is needed to raise the temperature and vice versa. Heat = (specific heat)(mass)( T) The energy associated with steps BC and DE are know as the heat of fusion and the heat of vaporization, respectively. Heats of Fusion and Vaporization The heat of fusion of a substance is the amount of heat required to melt exactly 1g of a solid substance at constant temperature. The heat of vaporization of a substance is the amount of heat required to vaporize exactly 1g of a liquid substance at constant temperature. For water the heats of fusion and vaporization are 80 cal/g and 540 cal/g. 19
Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Temperature (ºC) 130 100 0 GAS GAS LIQUID H 0 vap LIQUID LIQUID SOLID H 0 fus 40 Heat removed SOLID Example of Energy Required to Change Ice into Steam Calculate the amount of heat needed to convert 52.6g of ice at -20ºC to steam at 120ºC. Specific Heats: Ice (0.51 cal/g o C), water (1.00 cal/g o C), and steam (0.48 cal/g o C) Heat of fusion: 80 cal/g Heat of vaporization: 540 cal/g 20