8 - 1 pressure and moving molecules pressure is defined by the atmosphere exerts pressure because of...
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8 - 1
Pressure and Moving MoleculesPressure and Moving Molecules
Pressure is defined by
The atmosphere exerts pressure because ofthe weight and the average kinetic energy
ofmolecules which make up the mixture ofgases.
P =FA =
Nm2
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Normal atmospheric pressure (1 atm) is
and is exerted in all directions.
The following series of slides show how todetermine the pressure of a confined gasusing a manometer.
To determine the pressure, the difference inheight of mercury levels must be known asthe atmospheric pressure.
P =760 mm Hg=76 cm Hg =101.3 kPa
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.
collected O2
Hg
P = 101.3 kPa
What Pressure is the Gas What Pressure is the Gas Exerting?Exerting?
Δh = 30. mm Hg
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The diagram indicates that the atmosphericpressure is supporting both the gas and thecolumn of mercury.
Patm = Pg + PHg
Pg
=
101.3 kPa -30. mm Hg ×101.3 kPa
760 mm Hg
Pg 97.3 kPa
=
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.
collected O2
What Pressure is the Gas What Pressure is the Gas Exerting?Exerting?
Hg
P = 101.3 kPa
Δh = 30. mm Hg
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The diagram indicates that the collected O2
is supporting both the column ofmercury and the atmospheric pressure.
Pg = Patm + PHg
Pg
=
101.3 kPa+30. mm Hg ×101.3 kPa
760 mm Hg
Pg 105 kPa
=
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.
collected O2
What Pressure is the Gas What Pressure is the Gas Exerting?Exerting?
Δh = 0
P = 101.3 kPa
Hg
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The diagram indicates that the collected O2
and the atmospheric exert equal pressurebecause Δh = 0.
Pg = Patm = 101.3 kPa
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Liquid Vapor EquilibriumLiquid 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
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When the rate of evaporation equals the rate
of condensation, there is said to be a dynamic
equilibrium between the liquid and its vapor.
H2O(l) H2O(g)
At a given temperature, there somemolecules moving much faster than othersand have enough energy to overcome thesurface tension and cohesion to enter thegaseous phase.
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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 thatchloroform boils at ≈ 61°C, ethyl
alcohol boilsat ≈ 78°C, and water boils at 100°C.
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.
The graphs also indicate that the vapor pressureof a liquid is a function of intermolecular forces.
Vapor Pressure vs Temperature
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90 100
Temperature (oC)
Vap
or
Pre
ssu
re (
kPa)
chloroform ethyl alcohol water
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More Liquid Vapor EquilibriumMore Liquid Vapor Equilibrium
The graphs clearly show that as thetemperature increases, the vapor pressureincreases.
Vapor pressure depends on theintermolecular forces present in the liquidand temperature.
Vapor pressure is independent of the volume
of liquid or vapor present and the surfacearea of the liquid.
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At some temperature, the vapor pressure will
equal the atmospheric pressure.
This is the point at which boiling begins andbubbles of water vapor will form along thebottom and sides of the container.
A substance can boil at any temperature ifthe applied pressure is changed but there isonly one normal boiling point.
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The normal boiling point is the temperature at
which the liquid vapor pressure is equal tothe standard pressure, 101.3 kPa.
As a substance is heated at its normal boiling
point, the temperature remains the samebecause the additional energy goes intoincreasing the potential energy of themolecules.
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Molecules possess both kinetic energy (KE)and potential energy (PE). During a changeof phase (state), there can be no change intemperature until the change of phase iscomplete.
The KE of molecules depends on theirtranslational (straight line) speed and the
PEdepends on the rotational and vibrationalmodes.
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State of Matter TermsState of Matter Terms
Sublimation is a solid changing to a vaporwithout first passing through the liquid
state.
Melting and fusion are opposite processes.
Evaporation and vaporization aresynonymous terms.
Condensation and liquefaction aresynonymous terms.
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Melting and Freezing PointsMelting and Freezing Points
As the temperature of a substance islowered, so is the KE of the molecules.
At a particular temperature, theintermolecular forces will be sufficientlystrong enough to pull the molecules into amore orderly arrangement.
Most substances contract as they freeze butwater is an important exception.
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Each water crystal is made up of six watermolecules forming a hexagonal structurewhich is filled with empty space.
To adjust for the required angles, the watermolecules must move further apart causingthe water to expand upon solidifying.
Water has its maximum density at 4°C which
is 1.00 gm/cm3.
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The normal freezing point is the temperature
at which the solid and the liquid phase are in
a dynamic equilibrium at 1 atm.
H2O(l) H2O(s)
The temperature will not drop below themelting/freezing point until the change ofstate is complete.
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Phase ChangesPhase Changes
Every phase change is accompanied by anenergy change.
A quantity called the heat of fusion is involved
when either melting or freezing takes place.
ΔHfus = 6.01 kJ/mol
When 1.00 mol of water is frozen, 6.01 kJ ofenergy is given off (exothermic).
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Similarly, when 1.00 mol of ice melts,6.01 kJ of energy is absorbed
(endothermic).
A quantity called the heat of vaporization isinvolved when either vaporization orcondensation takes place.
ΔHvap = 40.7 kJ/mol
When 1.00 mol of water is vaporized, 40.7 kJ
of energy is absorbed (endothermic).
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Similarly, when 1.00 mol of water vaporcondenses, 40.7 kJ of energy is given off(exothermic).
The ΔHfus and ΔHvap are different values fordifferent substances. Their values can befound in a table of thermochemistry data.
Also, ΔHfus and ΔHvap are extensive physicalproperties because they are massdependent.
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The ΔHvap > ΔHfus 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 energychanges when 1.00 g of ice is heated from-5.0 °C to 160. 0 °C.
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Heating Curve for 1.00 g of WaterHeating Curve for 1.00 g of WaterTemperature vs Time
-20.000.00
20.0040.0060.0080.00
100.00120.00140.00160.00180.00
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00
Time (min)
Tem
per
atu
re (
°C)
A
B C
D E
F
icewarming
icemelting
water warming
water boiling
water vaporwarming
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Heat CalculationsHeat Calculations
The following calculations determine theamount of heat absorbed when 1.00 g of
ice isheated from -5.0 °C to 160.0 °C.
Segment AB – ice warmingqg = m × c × ΔT
qg =1.00 g H2O ×2.09 J
g H2O °C× 5.0 °C
qg = 10. J
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Segment BC – ice melting
qg = m
× ΔHfus
qg = 1.00 g H2O ×6.01 kJ
1 mol H2O× 1 mol H2O
18.02 g H2O
qg = 0.334 kJ
There is no ΔT because there is a change of state.
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Segment CD – water warming
qg = m × c × ΔT
qg =1.00 g H2O ×4.18 J
g H2O °C×100.0 °C
qg = 418 J
Note that the specific heat for ice and water arenot the same.
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Segment DE – water vaporizing
qg =m ×ΔHvap
qg =1.00 g H2O× 40.7 kJ1 mol H2O
× 1 mol H2O18.02 g H2O
qg =2.26 kJ
There is no ΔT because there is a change of state.
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Segment EF – water vapor warming
qg = m × c × ΔT
qg =1.00 g H2O ×1.84 J
g H2O °C× 60.0 °C
qg =110. J
Note that the specific heat for ice, water, and water vapor is not the same.
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qAB + qBC + qCD +qDE + qEFqg =
qg =10. J + 0.334 kJ ×103 J1 kJ
+ 418 J +
2.26 kJ ×103 J1 kJ
+ 110. J
qg = 3130 J
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Heat Calculations Wrap UpHeat Calculations Wrap Up
In the previous slides, water in the gaseousstate 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.
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Heat absorbed or liberated is an extensivephysical property because it depends on
theamount 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.
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The formulas used in the previous exampleare:
qg = m × c × ΔT
qg = m × ΔHfus
qg = m × ΔHvap
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qg = m × c × ΔT
This equation is used to determine theamount of heat absorbed or liberated whenthere 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.
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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.
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Specific heat also depends on the state of matter. Ice, liquid water, and water vapor have different specific heats.
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Phase DiagramPhase Diagram
A phase diagram summarizes the conditionsof pressure and temperature under which anequilibrium exists between the differentstates of matter.
In the following diagram, the line from A to Drepresents the vapor pressure of the liquid.
C represents the normal boiling pointbecause the pressure is 1.00 atm.
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Phase Diagram For WaterPhase Diagram For Water
.
Triple Point
Critical Point
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D represents the critical point – the criticaltemperature 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.
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Line segment AB represents the change inthe melting point of the solid with an
increaseIn 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.
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Water is abnormal because when it freezes, it expands rather than contracts.
A represents the triple point because thethree phases of water are in equilibrium atthis temperature and pressure.
For water to exist as a liquid, the pressuremust exceed 4.58 torr.