Transcript Review - University of Illinois at Urbana–Champaign

Free energy and work
qirreversible
we can measure T, P, V and n
q = CT mass
qreversible
constant P
qP = n CPT
= H
ideal gas, CP = 5/2 R
constant V
qV = n CVT
= E
ideal gas, CV = 3/2 R
constant T (ideal gas)
q = PV
constant T
qr = nRTln(V2/V1)
qr = TS
Free energy and work
we can measure T, P, V and n
max + w
wmax = wuseful
PV
max
wuseful
wPV
wPV = -Pext  V
max = G
wuseful
E = q + w
max
+ wPV
E = qr + wuseful
max
+ wPV
H - PV = qr + wuseful
max - P V
H - PextV = qr + wuseful
ext
max
H = TS + wuseful
max = G
H - TS = wuseful
wmax
wmax= - nRT ln(V2/V1)
reversible conditions
Free energy and work
E = q + w = qr + wr
max + w
q + wuseful + wPV = qr + wuseful
PV
max
q + wuseful = qr + wuseful
max - w
q - qr = wuseful
useful
under constant P and T
max
if wuseful = wuseful
if wuseful = 0
max
wuseful
= q - qr
max + q
q = wuseful
r
q P = G + TS = H
q = qr
q P = TS
Standard Gibbs Free Energy
Go = Ho - TSo
Go = - 30.5 kJ/mol
Go < 0 spontaneous
Go > 0 non-spontaneous Go = + 16.7 kJ/mol
Go = 0 equilibrium
Go = - 13.8 kJ/mol
glucose + phosphate  glucose-6-phosphate + H2O
ATP + H2O  ADP + phosphate
glucose + ATP  ADP + glucose-6-phosphate
Non-standard conditions
Q = reaction quotient =
m
[products] initial
n
[reactants]initial
K = equilibrium constant = [products]mequilibrium
[reactants]nequilibrium
G = - RT ln ( K /Q)
K>Q
K<Q
K=Q
G < 0 spontaneous
G > 0 non-spontaneous
G = 0 equilibrium
Go
G = - RT ln(K/Q)
Impose Standard conditions:
[reactants]initial = 1(M or atm) = [products]initial
Q= 1
G = - RT ln(K)
o
Standard Free Energy
Non-Standard Conditions
G = Go + RT ln Q
G = - RT ln (K/Q)
Go = - RT ln K
ln (a/b) = ln a - ln b
G = - RT ln (K/Q) = -RT ln K + RT ln Q
Go = - RT ln(K)
glucose + phosphate  glucose-6-phosphate + H2O
standard conditions non-spontaneous
Go = 16.7 kJ/mol = -RT ln K
-RT
-RT
K = 1.2 x 10-3
G = - RT ln ( K /Q)
-3
Q
<
K
<
1.2
x
10
G < 0
non-standard conditions
[products] initial
Q
=
start with no product spontaneous
[reactants]initial
Non-Standard Conditions
G = Go + RT ln Q
2NO2 (g)
Initially [NO2] = 0.3 M
N2O4 (g)
[N2O4] = 0.5 M
Will more products or reactants be formed?
Q = 0.5 /0.32 = 5.6
Non-Standard Conditions
G = Go + RT ln Q
2NO2 (g)
Initially [NO2] = 0.3 M
N2O4 (g)
[N2O4] = 0.5 M
Gorxn = Gof products - Gof reactants
= 97.8 - 2(51.3) = - 4.8 kJ/mol
Grxn= -4.8 +(8.314 x 10-3)(298)ln 5.6 = -0.5 kJ/mol
More a) product will be formed
b) reactant
G = -RT ln (K/Q)
A +B  C
K = [C]e Q = [C]i
[A]e[B]e [A]i[B]i
Le Chatelier’s Principle
Add A
Add B
Remove A
a)
decrease
increase Q
b)G
decrease
>
<0
K/Q > 1
increase Q
K/Q < 1
Temperature dependence of K
exothermic reaction
at low T
at high T
favor a) forward reaction
reversereaction
favor b)reverse
endothermic reaction
at low T
at high T
heat = product
heat = reactant
favor reverse reaction
favor forward reaction
Temperature dependence of K
Go = -RT ln K
Go =  Ho - TSo
-RT ln K =  Ho - TSo
o 1 + So
H
ln K =
+R
T
R
ln K
m x
b
y
exothermic
increase T
Ho < 0
decrease K
1/T
T
Temperature dependence of K
Go =  Ho - TSo
Go = -RT ln K
-RT ln K =  Ho - TSo
o 1 + So
H
ln K =
-R
T
R ln K
m x
b
y
endothermic H > 0
increase T increase K
1/T
T