Thermodynamics

Introduction

Entropy vs. Enthalpy

TS ArleneHurricane Katrina (Cat 5)

Thermodynamics• Transport, transformation and effect(s) of an organic

compound depend on which environmental compartment it settles in.

• Examples:– Compounds can be transported long distances in air or

water, but if they remain sorbed to organic matter, their movement is limited. (Like a “Broken down Mac Truck”)

– CCl2F2 may undergo reductive dehalogenation in anaerobic aqueous environments, but due to its very high vapor pressure, it stays in the atmosphere, which is oxidative. Thus CCl2F2 is very persistent and eventually reaches the stratosphere, where it causes ozone depletion.

Thermodynamics• Quantifies a compound’s affinity for the

environmental compartments which are available to it.

• Also implies the amount of energy necessary to move a chemical into a different compartment

• Can predict the direction of phase transfer– Example: Are PBDEs absorbing into or volatilizing

out of the water of the Hudson River Estuary?– Does not tell us anything about kinetics of phase

transfer

Equilibrium is related to kinetics

Simple reversible reaction

dt

dBBkAk

dt

dA ][][ 11

At equilibrium, there is no change in concentrations:

0dt

dB

dt

dA thus ][][ 11 BkAk

eqKk

k

A

B

1

1

][

][ Example: sorption of PCBs to organic matter. Keq is large, implying that sorption is fast and desorption is slow

BAk

k

1

1

In addition,

• Kinetic expressions for things like air-water exchange include the thermodynamic constant (Henry’s law constant).

• Sometimes equilibrium can be related to kinetics via Linear Free Energy Relationships

Chemical potential ()• Energy status of molecules in a system (e.g.

Benzene in water)– Internal energies

• Chemical Bonds, vibrations, flexations, rotations.

– External Energies• Whole molecule transitions, orientations• Interactions of molecule with surroundings

• Energy status is a function of:– Temperature– Pressure– Chemical composition

• “Average energy per molecule”

Chemical potential = free energy added to system with each added increment of i

ji

i nPTn

G,,

Where = chemical potential (kJ/mol)G = free energy (kJ)ni = moles of component (i)nj = moles of component (j)

iii nnTPG ),,(

The total free energy is the sum of the contributions from all the different components present:

iiii STHG

If two populations of chem (for example, the chemical coexists in two separate phases): each will have its own value of 1 and 2

1: liquid 2: gas

1 2

Start: liquid benzene (1) and very little vapor benzene (2)

Initial disequilibrium: 1 2 (1 > 2)

Open stopcock. Benzene volatilizes. Net movement of benzene to the right.

1 decreases, 2 increases until they are equal. No net movement of benzene

• No way to directly measure chemical potential.

• Can only determine differences in , based on the tendencies of a chemical to move from one situation to another.

• Need a reference point, like sea level or absolute zero.

• often: select pure liquid chem. as reference

Fugacity = urge to flee

• Fugacity is how happy the chemical is in its environment

• Fugacity is like temperature.• At equilibrium, everything has the same

fugacity (temperature) even though they may contain different concentrations (amounts) of the chemical (heat).

Fugacity vs. Temperature

A liter of waterStart:T = 0ºCfbenzene = 0 (no chemical present)Add:2100 Joules of heat to raise temperature by 1 ºC

0.022 moles benzene to raise fugacity to 104.1 Pa.

A liter of airStart:T = 0ºCfbenzene = 0 (no chemical present)Add:0.001 Joules of heat to raise temperature by 1 ºC

0.0051 moles benzene to raise fugacity to 104.1 Pa.

Reference statesFor gases, ideal behavior is assumed, so

a compound’s fugacity is equal to its partial pressure:

iig pf

We use the gas phase as our reference state.

As a result, fugacity is given in units of pressure, often Pa.

Pressure (and therefore f ) is easy to measure, unlike

For pure solid (s) or liquid (L), the fugacity is:

isisis pf *iLiLiL pf *

Where describes the nonideal behavior resulting from molecule-molecule interactions. For pure solid or liquid, is assumed to equal one.

In a mixture (i.e. aqueous solution):

iLiliLiLiliLiL fxpxf **

aqueous solutions of organic chemicals are usually not ideal. 1 (the * means we are using the pure liquid as our reference state)

Activity coefficients:solute => hexane benzene diethylether ethanol

solvent

n-hexadecane ~1 ~1 ~1 35

CHCl3 1.8 0.8 0.3 4.5

ethanol 12 5.4 n.a. 1

water 460,000 2500 130 3.6

Activity coefficient and chemical potential

 

** ln

iLp

fRT il

iLil

chemical potentialin solution

chemical potentialof pure liquid (ideal)

fugacity relative to ideal

ililiLil xRT ln* mole fraction

il

activity coefficient

Phase transfer processes(or: where the rubber hits the road)

Consider a chemical (A) equilibrating between air and water:

Aa Aw

AaAaALAa xRT ln*

AwAwALAw xRT ln*

Note: still using pure liquid as

reference state

At equilibrium, is equal in the two phases

After some rearranging you get:

RT

RTRT

x

x AwAa

Aw

Aa lnlnln

RT

RTRT

Aw

AaAwAa

ex

x lnln

entropic and

enthalpic terms

ba

dc

BA

DCK

dDcCbBaA

][][

][][

Recall

RT

STH

RT

G

Aaw eeK

'

contributions from enthalpy and entropy terms

Temperature dependence of K

R

S

RT

H

RT

STHK

R

S

RT

H

RT

STHK

T

T

22

22

11

11

ln

ln

211

2 11ln

TTR

H

K

K

T

T