lecture 27 thermodynamics: enthalpy, gibbs free energy...
TRANSCRIPT
Physical Principles in BiologyBiology 3550
Fall 2017
Lecture 27
Thermodynamics: Enthalpy, Gibbs Free Energy
and Equilibrium Constants
Wednesday, 1 November
c©David P. GoldenbergUniversity of Utah
The Second Law of Thermodynamics
For a spontaneous process:
∆Suniv = ∆Ssys + ∆Ssurr
Entropy change for the system (constant T):
∆Ssys =qrevT
= nk lnΩ2
Ω1
Entropy change for the surroundings:
∆Ssurr = − q
T
q is heat absorbed for specified process.
Flow of heat to surroundings represents an increase in entropy of thesurroundings.
Entropy of the system can decrease in a spontaneous process, if thereis a flow of heat to the surroundings.
Thermodynamics and Chemical Reactions
A −−−−−− B
Changes in potential energy:
Forming a chemical bond reduces potential energy of molecules andreleases energy.
Breaking a chemical bond increases potential energy of molecules andabsorbs energy.
If the potential energy is released, where can that energy go?• Thermal energy (temperature) increases.
• Heat flows out of the system. (q < 0)
• Work is done by the system. (w < 0)
• Some combination of the above.
J. Willard Gibbs
1839–1903
Arguably the first great American theoretical scientist.
Consolidated thermodynamics into a consistent theory.
Applied thermodynamics to chemistry.
Also made important contributions in math and optics.
A New State Function: Enthalpy (H)
Enthalpy, H , is closely related to the internal energy, E .
H = E + PV
The product PV has the units of energy or work.
For a process at constant pressure:
∆H = ∆E + P∆V
P∆V is work due to a change in volume at constant pressure.
Two new quantities:• wp = −P∆V = work done on system in constant pressure process
• qp = heat absorbed by system in constant pressure process
From the first law:
∆E = qp + wp = qp − P∆V
∆H = ∆E + P∆V = qp
A New State Function: Enthalpy (H)
Two consistent definitions for ∆H at constant pressure:
∆E minus work due to volume change
∆H = ∆E + P∆V
= ∆E − wp
If there is no volume change, then wp = 0, and ∆H = ∆E .
The heat absorbed during the constant pressure process:
∆H = qp
Chemical and biochemical reactions are usually studied underconditions of constant (or nearly constant) pressure, and ∆V is usuallyvery small.
∆H can be experimentally measured.
Measuring ∆H with a Calorimeter
Water
Reaction
Thermometer
Insulation
If ∆H < 0, heat flows from the reaction vessel and warms the water.
If ∆H > 0, heat flows into the reaction vessel, and water temperaturedecreases.
∆H = −∆Twater
mass of water (g)(in calories)
Clicker Question #1
Which of the following is true at constant pressure?
Choose two.
1 ∆H = ∆E + P∆V
2 ∆H = ∆E + V∆P
3 ∆H = qrev
4 ∆H = wrev
5 ∆H = qp
6 ∆H = wp
The Gibbs Free Energy
G = H − TSsys
For a process at constant temperature:
∆G = ∆H − T∆Ssys
For a process at constant temperature and constant pressure:
∆G = qp − T∆Ssys
Since ∆Ssurr = −q/T , qp = −T∆Ssurr at constant pressure.
∆G = −T∆Ssurr − T∆Ssys = −T (∆Ssurr + ∆Ssys)
= −T∆Suniv
Or, ∆Suniv = −∆G/T
The Gibbs Free Energy is Used to Apply the Second Law
From the previous slide:
∆Suniv = −∆G/T
If ∆G < 0• ∆Suniv > 0, and the process will be spontaneous.
If ∆G > 0• ∆Suniv < 0, and the reverse process will be spontaneous.
If ∆G = 0• ∆Suniv = 0, and the process is reversible.
(Can be pushed in either direction.)
• ∆G = 0 defines a system at equilibrium.
All based on state functions of the system!
Don’t have to worry about the surroundings.
Clicker Question #2
Which of the following is true at constant pressureand constant temperature?
Choose two.
1 ∆G = ∆H − T∆Suniv
2 ∆G = ∆H − T∆Ssys
3 ∆G = −T∆Ssurr − T∆Ssys
4 ∆G = T∆Ssurr − T∆Ssys
5 ∆G = −T∆Ssurr − qp/T
What About Free Energy as Energy Available to do Work?
The change in Helmholtz free energy, as previously defined:
∆F = wrev
The maximum work available from a process.
From the first law:
∆E = qrev + wrev
wrev = ∆E − qrev
∆F = ∆E − qrev
For a constant-temperature process:
∆Ssys =qrevT
qrev = T∆Ssys
∆F = ∆E − T∆Ssys
The Helmholtz Free Energy
For a constant temperature process:
∆F = ∆E − T∆Ssys
The standard definition of the Helmholz free energy:
F = E − Ssys
Compare to:
∆G = ∆H − T∆S
Since ∆H = ∆E − wp (a few slides back):
∆G = ∆F − wp
wp is work due to volume change at constant pressure.
The Helmholtz Free Energy
From previous slide:
∆G = ∆F − wp
If volume change is small and wp can be ignored:• ∆G = ∆F
• If ∆G < 0: Process is favorable, and maximum work availablefrom the process = −∆F = −∆G
• If ∆G > 0: Process is unfavorable, and minimum work requiredto drive the process = ∆F = ∆G
Commonly made assumptions for chemical reactions indilute solutions:
• P∆V = −wp ≈ 0
• ∆H ≈ ∆E
• ∆G ≈ ∆F
The Equilibrium Constant for a Chemical Reaction
A −−−−−− B
The reaction can occur in either direction. (at least in principle)
The probability that any molecule of A will be converted to a moleculeof B is the same as for any other molecule of A.
• The total rate of conversion of A to B is proportional to the concentrationof A.
• Similarly, the total rate of conversion of B to A is proportional to theconcentration of B.
A differential equation:
d [A]
dt= −kf [A] + kr[B]
The constants kf and kr are called rate constants.
The Equilibrium Constant for a Chemical Reaction
A −−−−−− B
From the previous slide: d [A]
dt= −kf [A] + kr[B]
Similarly:d [B]
dt= kf [A] − kr[B] = −
d [A]
dt
Whatever the starting concentrations, [A] and [B] will eventually adjustso that they no longer change.
At equilibrium:d [A]
dt= −
d [B]
dt= 0
− kf [A] + kr[B] = 0
The Equilibrium Constant for a Chemical Reaction
A −−−−−− B
At equilibrium:
d [A]
dt= −
d [B]
dt= −kf [A]eq + kr[B]eq = 0
[A]eq and [B]eq are the concentrations of A and B at equilibrium.
Rearranging:
kr[B]eq = kf [A]eq
[B]eq
[A]eq=
kfkr
= Keq
Keq is defined as the equilibrium constant.
The Equilibrium Constant for a Chemical Reaction
A −−−−−− B Keq =[B]eq
[A]eq
At equilibrium, a little bit of work can push the reaction in eitherdirection.
This defines the condition where ∆G = 0
Definition of ∆G for a chemical reaction:
The free energy change for converting one mole of reactants to onemole of products, at specified concentrations, without significantlychanging concentrations(!).
Implies a very, very large volume!
Or, a mechanism that restores concentrations continuously.