Download Slides for lecture 7 - Aleksey Kocherzhenko

General Physical Chemistry I
Lecture 7
Aleksey Kocherzhenko
February 26, 2015"
Last time…"
The first law of thermodynamics"
The change in the internal energy of a system: "dU
= dA + dq
Work performed on the system (positive)
Heat transferred"
or by the system (negative) "
to the system (positive) or from the
The first law of thermodynamics"
system to the surroundings (negative)"
Verbal statement: The
"
change in the internal energy of the system is the sum
of the heat transferred to the system and the work performed on it"
An isolated system does not exchange
energy with its surroundings, neither as
heat, nor as work: dq
" = dA = 0
) dU = 0
The first law of thermodynamics is
the law of energy conservation:
energy can be converted from one
form to another, but it cannot be
created or destroyed"
à Perpetual motion machines that perform more work
than they use energy cannot be created"
Internal energy as a state function"
The internal energy only depends
on the initial and final state of the
system (not on how it transferred
from one to the other)"
Ø  Quantities like that are referred
to as state functions!
Ø  Work is not a state function:
as we have seen, it depends on
the path by which the system got
from the initial to the final state
(it is a process function)!
Enthalpy"
Many processes, particularly chemical reactions, occur at
constant pressure (in open vessels), not at constant volume"
à Transferred heat ≠ change in internal energy"
Ø  Heat transfer in such processes is conveniently
characterized in terms of the enthalpy, defined as:!
H = U + pV
Positive for endothermic reactions !
At constant pressure:" dH
= dU + pdV
Negative for exothermic reactions!
At constant pressure, the heat
transferred to the system is
equal to the change in enthalpy "
Ø  The enthalpy is defined in terms of state functions only ( U,
and thus it is itself a state function"
p, V
),
Ø  Like the internal energy, the enthalpy is an extensive quantity: it depends
on the amount of substance, and molar enthalpy can be defined"
Heat capacity"
Heat capacity"
The heat capacity of a system is the amount of energy
that needs to be transferred to a system"
dq
to achieve a unit change in its temperature:" C =
dT
Specific heat capacity (per unit mass):"
C
Cs =
m
Extensive property:
heating more substance
requires more energy"
Molar heat capacity (per mole):"
C
Cm =
⌫
Heat capacity depends on the conditions under which the substance is heated"
(the reasons for this are discussed in detail in PChem II) "
à  Commonly reported are the molar heat capacity @ constant pressure,"Cp,m
or @ constant volume, CV,m (or respective specific heat capacities)"
Ø  Heat capacities for all monoatomic perfect gasses are similar"
Ø  The heat capacity of a sample can be measured using a calorimeter, where
a known amount of energy is transferred to a sample and the change in its
temperature is detected"
Heat capacity at constant p and constant V!
At constant volume:"
CV =
✓
@q
@T
◆
=
V
✓
@U
@T
◆
At constant pressure:"
Cp =
V
The heat capacities at constant volume
and constant pressure are tangents to
functions U (T ) and H (T ), respectively"
✓
@q
@T
◆
=
p
✓
@H
@T
◆
à generally, the heat capacity
is temperature-dependent"
p
Heat capacity for a perfect gas!
At constant volume:"
CV =
✓
@q
@T
Enthalpy:" H
)
◆
=
V
✓
@U
@T
◆
At constant pressure:"
Cp =
V
= U + pV
(for a perfect gas only):"
✓
@q
@T
◆
=
p
✓
Perfect gas law:" pV
@H
@T
@H
@U
=
+ ⌫R
@T
@T
) Cp = CV + ⌫R
Or, for molar heat capacities:"
Cp,m = CV,m + R
This relation between heat capacities at constant pressure
and constant volume is valid for perfect gasses only"
p
= ⌫RT
H = U + ⌫RT
Differentiating both sides with temperature:"
◆
Heat capacity for a perfect gas!
At constant volume:"
CV =
✓
@q
@T
◆
=
V
✓
@U
@T
◆
At constant pressure:"
Cp =
V
✓
@q
@T
◆
Relation between molar heat capacities of a perfect gas:" Cp,m
=
p
✓
@H
@T
◆
= CV,m + R
Calculate the actual values of the molar heat capacities at constant volume
and at constant pressure for a monoatomic perfect gas! "
(Hint: use the equipartition principle)"
Energy per degree of freedom:"
E1 = 12 kB T
Energy per atom of perfect gas:"
Eatom = 32 kB T
Energy per mole of perfect gas:"
Em = NA · 32 kB T = 32 RT
For a perfect gas, "Um
= Em ) CV,m =
) Cp,m = CV,m +
p
@Um
3
=
@T V
2R
R = 32 R + R = 52 R
Thermochemistry"
Thermochemistry"
Some definitions:"
Ø  Heat of reaction: The heat change in the transformation of reactants
at given fixed temperature and pressure to products
at the same temperature and pressure"
Ø  Exothermic reaction: system transfers heat to the surroundings"
Ø  Endothermic reaction: system absorbs heat from the surroundings"
The first law of thermodynamics requires
that if a forward reaction is exothermic,
the reverse reaction must be endothermic:"
forward H
=
reverse H
All reactants and products are in their standard
states (at pressure 1 bar) at the same T "
Changes in enthalpy in a reaction are reported under standard conditions
(1 bar and some temperature): the standard enthalpy of the reaction, " r H
Enthalpy of a phase transition"
Ø  Phase: is a state of matter that is uniform in composition and physical state"
Ø  Phase transition:
a process in which a substance
goes from one phase to another "
Solid"
Liquid"
Only He has"
two different"
liquid states"
Gas"
All substances
have just one
gas phase"
Many substances have more
than one solid phase: e.g., C:
graphite and diamond"
All processes at same temperature"
The enthalpy change of a process is the sum of enthalpy changes for the steps (observed
or hypothetical) into which it may be divided"
Enthalpies of some phase transitions"
H2O (l) à H2O (g)"
vap H
(298 K) = 44 kJ/mol
H2O (g) à H2O (l)"
44 kJ/mol
cond H (298 K) =
H2O (s) à H2O (l)"
fus H (273 K) = 6 kJ/mol
H2O (s) à H2O (g)"
sub H (273 K) = 51.07 kJ/mol
vap H (273 K) =
sub H (273 K)
fus H
vap H (273 K) ?
(273 K)
Enthalpy of ionization"
@ 1 bar and 25 °C"
Enthalpy of ionization:
Enthalpy that accompanies the removal of
an electron from an atom in the gas phase"
First, second, … enthalpies of ionization
correspond to the removal of 1, 2, … e–’s"
For atom in a solid: enthalpy of sublimation
+ enthalpy of ionization (in gas phase)"
How much heat is necessary to turn
1 g of solid Mg into a gas of Mg2+ ions
and e–’s @ 1 bar and 25 °C? "
MMg = 24.31 g/mol
Enthalpy of e– gain: enthalpy of adding an e– to form a negative ion"
Standard enthalpy of formation"
Change of enthalpy when 1 mole of a
compound is formed from its constituent
elements, with all substances in their
standard states at 1 bar "
reactants"
products"
aA + bB à cC + dD"
Stoichiometric coefficients "
r Hm
=c
f Hm
(C) + d
f Hm
(D)
a
f Hm
(A)
f Hm
(B)
b
Standard states for:"
Ø  A gas: a pressure of 1 bar"
Ø  A solute in an ideal solution: a concentration of exactly 1 M under p = 1 bar"
Ø  A pure substance or a solvent in a condensed state (liquid or solid):
the pure liquid or solid under p = 1 bar"
Ø  For an element: the form in which the element is most stable under a pressure
of 1 bar [Exception: P – most stable form at 1 bar is black P, but white P is used
as the reference state for zero enthalpy of formation]"
Bond enthalpy"
Bond enthalpy: the enthalpy that accompanies the breaking of a chemical bond"
Ø  For polyatomic molecules, average bond enthalpy can be defined"
Ø 
Hr
estimated by counting the total number of bonds broken and formed "
HCl (g) à H(g) + Cl(g)"
Hr = +431 kJ
Breaking a bond always requires energy à all bond enthalpies are positive"
Complication: bond enthalpy depends on molecule in which a bond is broken"
Mean bond enthalpy"
Example: dissociation of water into atoms"
H2O(g) à 2H(g) + O(g) "
H2O(g) à HO(g) + H(g) "
HO(g) à H(g) + O(g) "
Hr = +927 kJ
Hr1 = +499 kJ
Hr2 = +428 kJ
Mean bond enthalpy: average of bond enthalpies
over a related series of compounds"
Kirchhoff’s law"
The difference between the enthalpies of a reaction at two
temperatures, T1 and T2 , is the difference in the enthalpies
of heating the products and reactants from T1 to" T2
rH
Gustav Kirchhoff"
(T2 )
rH
(T1 ) =
ZT2
r Cp,m dT
=
Cp,m (T2
✓
◆
T1
@H
C
=
since we have established that" p
@T p
T1 )
Nearly constant within a wide range of T
"
r Cp,m
=
X
i
Sum over
products"
(i)
ai Cp,m
X
(j)
bj Cp,m
j
Sum over
reactants"
Stoichiometric
coefficients "