8 - 1 Pressure and Moving Molecules Pressure is defined by The atmosphere exerts pressure because of the weight and the average kinetic energy of molecules which make up the mixture of gases. P= F A = N m2m2

8 - 2 Normal atmospheric pressure (1 atm) is and is exerted in all directions. The following series of slides show how to determine the pressure of a confined gas using a manometer. To determine the pressure, the difference in height of mercury levels must be known as the atmospheric pressure. P = 760 mm Hg = 76 cm Hg = kPa

collected O 2 Hg P = kPa What Pressure is the Gas Exerting? Δ h = 30. mm Hg

8 - 4 The diagram indicates that the atmospheric pressure is supporting both the gas and the column of mercury. P atm = P g + P Hg PgPg = kPa mm Hg × kPa 760 mm Hg PgPg 97.3 kPa =

collected O 2 What Pressure is the Gas Exerting? Hg P = kPa Δ h = 30. mm Hg

8 - 6 The diagram indicates that the collected O 2 is supporting both the column of mercury and the atmospheric pressure. P g = P atm + P Hg PgPg = kPa mm Hg × kPa 760 mm Hg PgPg 105 kPa =

collected O 2 What Pressure is the Gas Exerting? Δ h = 0 P = kPa Hg

8 - 8 The diagram indicates that the collected O 2 and the atmospheric exert equal pressure because Δ h = 0. P g = P atm = kPa

8 - 9 Liquid Vapor Equilibrium. When the molecules are first put into the box, the rate of evaporation is greater than the rate of condensation. After a period of time, the rate of evaporation is equal to the rate of condensation. liquid

When the rate of evaporation equals the rate of condensation, there is said to be a dynamic equilibrium between the liquid and its vapor. H 2 O(l) H 2 O(g) At a given temperature, there some molecules moving much faster than others and have enough energy to overcome the surface tension and cohesion to enter the gaseous phase.

There is always vapor pressure above the surface of the water created by the molecules which have evaporated. The vapor pressure of water increases with an increase in temperature. The following graph illustrates that chloroform boils at ≈ 61°C, ethyl alcohol boils at ≈ 78°C, and water boils at 100°C.

The graphs also indicate that the vapor pressure of a liquid is a function of intermolecular forces. chloroformethyl alcohol water

More Liquid Vapor Equilibrium The graphs clearly show that as the temperature increases, the vapor pressure increases. Vapor pressure depends on the intermolecular forces present in the liquid and temperature. Vapor pressure is independent of the volume of liquid or vapor present and the surface area of the liquid.

At some temperature, the vapor pressure will equal the atmospheric pressure. This is the point at which boiling begins and bubbles of water vapor will form along the bottom and sides of the container. A substance can boil at any temperature if the applied pressure is changed but there is only one normal boiling point.

The normal boiling point is the temperature at which the liquid vapor pressure is equal to the standard pressure, kPa. As a substance is heated at its normal boiling point, the temperature remains the same because the additional energy goes into increasing the potential energy of the molecules.

Molecules possess both kinetic energy (KE) and potential energy (PE). During a change of phase (state), there can be no change in temperature until the change of phase is complete. The KE of molecules depends on their translational (straight line) speed and the PE depends on the rotational and vibrational modes.

State of Matter Terms Sublimation is a solid changing to a vapor without first passing through the liquid state. Melting and fusion are opposite processes. Evaporation and vaporization are synonymous terms. Condensation and liquefaction are synonymous terms.

Melting and Freezing Points As the temperature of a substance is lowered, so is the KE of the molecules. At a particular temperature, the intermolecular forces will be sufficiently strong enough to pull the molecules into a more orderly arrangement. Most substances contract as they freeze but water is an important exception.

Each water crystal is made up of six water molecules forming a hexagonal structure which is filled with empty space. To adjust for the required angles, the water molecules must move further apart causing the water to expand upon solidifying. Water has its maximum density at 4°C which is 1.00 gm/cm 3.

The normal freezing point is the temperature at which the solid and the liquid phase are in a dynamic equilibrium at 1 atm. H 2 O(l) H 2 O(s) The temperature will not drop below the melting/freezing point until the change of state is complete.

Phase Changes Every phase change is accompanied by an energy change. A quantity called the heat of fusion is involved when either melting or freezing takes place. Δ H fus = 6.01 kJ/mol When 1.00 mol of water is frozen, 6.01 kJ of energy is given off (exothermic).

Similarly, when 1.00 mol of ice melts, 6.01 kJ of energy is absorbed (endothermic). A quantity called the heat of vaporization is involved when either vaporization or condensation takes place. Δ H vap = 40.7 kJ/mol When 1.00 mol of water is vaporized, 40.7 kJ of energy is absorbed (endothermic).

Similarly, when 1.00 mol of water vapor condenses, 40.7 kJ of energy is given off (exothermic). The Δ H fus and Δ H vap are different values for different substances. Their values can be found in a table of thermochemistry data. Also, Δ H fus and Δ H vap are extensive physical properties because they are mass dependent.

 The Δ H vap > Δ H fus because when ice melts the water molecules are close enough to experience intermolecular attractions.  When water molecules vaporize additional energy is added to completely overcome attractive intermolecular forces. The following heating curve shows the energy changes when 1.00 g of ice is heated from -5.0 °C to °C.

Heating Curve for 1.00 g of Water A B C D E F ice warming ice melting water warming water boiling water vapor warming

Heat Calculations The following calculations determine the amount of heat absorbed when 1.00 g of ice is heated from -5.0 °C to °C. Segment AB – ice warming qgqg = m × c × ΔTΔT qgqg = 1.00 g H 2 O × 2.09 J g H 2 O °C × 5.0 °C qgqg = 10. J

Segment BC – ice melting q g = m × Δ H fus q g = 1.00 g H 2 O × 6.01 kJ 1 mol H 2 O × g H 2 O q g = kJ There is no Δ T because there is a change of state.

Segment CD – water warming qgqg = m × c × ΔTΔT qgqg = 1.00 g H 2 O × 4.18 J g H 2 O °C × °C qgqg = 418 J Note that the specific heat for ice and water are not the same.

Segment DE – water vaporizing q g = m × Δ H vap q g = 1.00 g H 2 O × 40.7 kJ 1 mol H 2 O × g H 2 O q g = 2.26 kJ There is no Δ T because there is a change of state.

Segment EF – water vapor warming qgqg = m × c × ΔTΔT qgqg = 1.00 g H 2 O × 1.84 J g H 2 O °C × 60.0 °C qgqg = 110. J Note that the specific heat for ice, water, and water vapor is not the same.

q AB + q BC + q CD +q DE + q EF qgqg = qgqg =10. J kJ × 10 3 J 1 kJ J kJ × 10 3 J 1 kJ J qgqg = 3130 J

Heat Calculations Wrap Up In the previous slides, water in the gaseous state is referred to as a vapor and not a gas.  The term vapor refers to a substance that is not in the gaseous state at standard conditions (P = 1 atm, T = 25°C = 298 K).  Water is such an example while oxygen is referred to as a gas.

Heat absorbed or liberated is an extensive physical property because it depends on the amount of mass present. Heat is an example of a state function.  A state function is not dependent on the path or the number of steps involved.  The total amount of heat is simply the sums of the heat involved in each step.

The formulas used in the previous example are:  q g = m × c × Δ T  q g = m × Δ H fus  q g = m × Δ H vap

q g = m × c × Δ T This equation is used to determine the amount of heat absorbed or liberated when there is no change of state. c is the symbol for specific heat.  Specific heat is the amount of heat gained or liberated when 1.0 g of the substance is heated or cooled by 1.0 °C.

 Specific heat is a physical intensive property because it is not dependent on the amount of matter.  Specific heat is dependent on the type of substance.  Different substances have different specific heats with water having one of the highest at 4.18 J/g°C.  A consequence of this is that it takes a long time for water to heat up and cool down.

 Specific heat also depends on the state of matter. Ice, liquid water, and water vapor have different specific heats.

Phase Diagram A phase diagram summarizes the conditions of pressure and temperature under which an equilibrium exists between the different states of matter. In the following diagram, the line from A to D represents the vapor pressure of the liquid. C represents the normal boiling point because the pressure is 1.00 atm.

Phase Diagram For Water. Triple Point Critical Point

D represents the critical point – the critical temperature and critical pressure.  Critical temperature is the maximum temperature at which it is possible to liquefy a gas by increasing the pressure. Above this temperature, no amount of pressure will liquefy the gas.  Critical pressure is the pressure that is needed at the critical temperature.

Line segment AB represents the change in the melting point of the solid with an increase In pressure.  In the case of water, line AB slopes slightly to the left as the pressure is increased.  An increase in pressure usually favors the formation of a solid except in the case of water.

 Water is abnormal because when it freezes, it expands rather than contracts. A represents the triple point because the three phases of water are in equilibrium at this temperature and pressure. For water to exist as a liquid, the pressure must exceed 4.58 torr.