Heat Added (Joules)

Tem

pera

ture

˚C

Now let’s apply the heat stuff to real-world stuff like phase changes and the energy or cost it takes to carry it out. A “heating curve”.......a plot of temperature of a substance vs heat added to a substance.

Here’s the same curve now applying the conservation of energy (sum of the heats)

Ice

Ice + Water mix

Water

SteamHeating solid ice to 0˚C

Heat Added (kJ/mole)4.12 38 79.3 305 309

Tem

pera

ture

˚C

Melting solid ice to 0˚C water

Heating water to boiling 100˚C

Boiling all water to steam 100˚C

Heating steam past

100˚C

0

-100

100

220

q = sice mice !T

q = mice !Hfus

q = sH2O mH2O !T

q = mH2O !Hvap

q = sstm mstm !T

Phase transition

Phase transition

A

B C

D E

F

Temperature does not change during a phase transition.

Temperature does not change during a phase transition.

Water + steam mix

Calculate the amount of heat required to convert 500 grams of ice at -20.0˚C to steam at 120.˚C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g ˚C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kJ/mol respectively.

n∑

i=1

qi = 0 sum the q’s baby

q = si mi ΔT

qsolid=>liquid = (# moles) ΔH˚fusion

qliquid=>gas = (# moles) ΔH˚vaporization

for heating non-phase transitions

for phase transitions

Calculate the amount of heat required to convert 500 grams of ice at -20˚C to steam at 120˚C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g ˚C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kJ/mol respectively.

1. Heat ice from -20˚C to ice at 0˚C = 500. g x 2.06 J/g ˚C x 20˚C 2. Melt ice at 0˚C to water at 0˚C = 500. g/(18 g/mol) x 6.02 kJ/mol 3. Heat water from 0˚C to water at 100˚C= 500. g x 4.18 J/g ˚C x 100˚C 4. Evap water at 100˚C to vap at 100˚C = 500. g/(18 g/mol) x 40.7 kJ/mol5. Heat vap from 100˚C to vap at 120˚C = 500. g x 1.84 J/g ˚C x 20˚C

1. = 20.6 kJ2. = 167.2 kJ3. = 209.0 kJ4. = 1130.5 kJ5. = 18.4 kJ

Total = 1545.6 kJ

Bunker fuel C, coal and rice hulls are the most widely used fuels in the Philippines (world too) used in create steam in nearly all industries worldwide.

Look up the heating value of each of these fuels. By hook or by crook find the price per liter or price per kg of each of these fuels. Which fuel is the cheapest fuel to produce steam? What is the approximate cost to produce a MT steam at 120˚C starting from 24˚C assuming the efficiencies of all the heating processes are the same, and the cost of boilers are the same as well?

Unfortunately not everything is simple economics. What other factors might one consider with each of these fuels assuming 15MT of steam is produced per day 7 days a week, 30 days a month and 12 months a year?

The equilibrium vapor pressure is the pressure exerted by a vapor over its liquid phase (measured under vacuum) when dynamic equilibrium exists between condensation and evaporation.

Evaporation

Liquid

Vapor Pressure

Liquid

The concept of vapor pressure

In open containers, molecules that have enough KE can overcome IMF’s at the surface and “evaporate” into the atmosphere.

In closed containers, molecules vaporize and condense until there is no further change in concentration in each phase. This forms an equilibrium “vapor pressure” over the liquid.

Dynamic chemical equilibrium is reached when there is no net change in the number of molecules: the rate of evaporation and the rate of condensation are equal.

Molecules in liquid begin to vaporize

Molecules vaporizing and condensing at such a rate

that no net change in numbers occure

At the melting point a solid begins to change into a liquid as heat is added. As long no heat is added or removed melting (red arrows) and freezing (black arrows) occur at the same rate an the number of particles in the solid remains constant.

Dynamic equilibria is also reached in melting and sublimation and also in most chemical reactions.

Reaction Rate of the forward reaction =

aA + bB cC + dDReactants Products

= Rate of Reverse reaction

Because kinetic energy (of molecules in any phase) depends on temperature, so does vapor pressure of a liquid.

At higher temperatures,a larger fraction of moleculeshave enough KE to escape the liquid phase.

More molecules escape at high temp

KE = Ek = 32 RT

Kinetic Energy Temperature

Relates molecular properties of molecules to bulk properties that we observe!

The vapor pressure of a pure liquid (bulk property) depends on the intermolecular forces between molecules. The stronger the attractive forces in the liquid phase the lower the vapor pressure--and the less volatile it is.

Which of the following has the highest vapor pressure at 1 atm?

Which is the least volatile at 1 atm?

.66 atm

2 atm

water boils at 75˚Cat 300 torr = .4 atm

Vapor Pressure of Some Liquids

The following diagram shows a close-up view of part of the vapor-pressure curves for a solvent (red curve) and a solution of the solvent with a second liquid (green curve). Which solvent is more volatile?

The boiling point of a pure liquid is the temperature at which the equilibrium vapor pressure of a liquid over its liquid phase is equal to the external pressure on the liquid.

The normal boiling point is the temperature at which a liquid boils when the external pressure is 1 atm.

Evaporation Boiling

Vapor pressure plotted as a function of temperature

ln (vapor pressure) plotted as a function of 1/Temp

If we plot vapor pressure vs temperature we observe a linear relationship between ln P and 1/T.

• The Clausius-Claperyron equation relates the vapor pressure (P) of a pure liquid to the liquid’s temperature (T) and the liquids molar heat of vaporization (∆Hvap).

• By taking measurements at two temps, we get:

slope = ∆Hvap/R

1/T

ln P

ln

P2P1

= -ΔHvapR

1T2

−1T1

y = m x + b

ln P = -ΔHvap

R1T

+ C

(note R = 8.31 J/K mol)

Vapor pressure of pure etOH is 115 torr at 34.9˚C. If ΔHvap = 40.5 kJ/mol calculate the temperature when the vapor pressure of etOH is 760 torr. R is the gas constant given at 8.314 J/mol K