Download Chemistry and the material world

Chemistry and the material world
123.102
Unit 4, Lecture 2
Matthias Lein
Thermodynamics
Definitions of Work, Heat and Energy
adiabatic and non-adiabatic paths
state functions
internal energy
the first law of thermodynamics
heat capacity
enthalpy – energy at constant pressure
Standard enthalpy changes
Hess' law and its applications
Thermodynamic builds on Work, Heat and Energy:
E.g.: Work is done, when a process can be used to change the
height of a weight somewhere in the surrounding.
To measure the amount of work we use the definition:
work = force × way
If a builder pulls a bucket of bricks with a pulley from the ground
floor to the roof he has to exert a certain force. The higher he
pulls the bucket, the more work is done.
Energy is the ability to perform work
If we do work on an otherwise isolated system, the system's
ability to perform work itself is increased i.e. its energy is
increased. If a system does work, its energy is decreased
because the system's ability to perform work is decreased.
Experiments have shown that work is not the only way to
change a system's energy.
If there is a temperature difference between the system and its
surrounding, the system's energy will change when the
temperatures start to equilibrate.
If the energy of a system changes because of a temperature
difference we speak of heat-flow.
Systems which allow heat-flow are called diathermic, systems
which do not allow heat-flow are called adiabatic.
Thermos flasks are good approximations to adiabatic systems if the
heat-flow is very slow compared to the
time-scale of the experiment.
Heat-flow is usually measured by
observing temperature changes in the
surrounding. Often in a calorimeter.
The first law of thermodynamics:
If a system is changed from one state to another in an adiabatic
but otherwise arbitrary way, the work is always the same
irrespective of the method used.
If we assume a system goes from an initial state with the
internal energy Ui to a final state with the internal energy Uf, it
could be also assumed that the work wad for this process
depends on the way the system takes from the initial state to
the final state and which intermediate states are visited.
But:
The first law of thermodynamics states that the work is always:
wad = Uf – Ui
Important:
The “height”-differences are independent of the way you take,
they only depend on the “height” of the initial state and the
“height” of the final state.
This “height” is called the internal energy of the system U
Any function (like U) that only depends on the difference
between an initial and a final state and not on the path taken is
called a state-function.
Let us look at a another process:
If we assume a system going from the same initial state to the
same final state, but now along a non-adiabatic way. That means
that the system is in thermal contact with its surrounding and heat
is allowed to flow.
The energy difference ΔU will be the same (because it depends
only on the state and not the way) but the work done doesn't
necessarily have to be the same.
The difference between the energy difference ΔU and the work w is
then called the heat q:
q = ΔU - w
This way the first law of thermodynamics gives us a fundamental
definition of heat because we can measure ΔU for a process that
takes s system from an initial to a final state by measuring wad for
the adiabatic path and w for the non-adiabatic path.
q = wad – w
Finally, from the first law of thermodynamics also follows that the
internal energy of an isolated system cannot change. Because for
an isolated system there is w = 0 and q = 0 and with ΔU = q + w it
follows that ΔU = 0.
The state of an isolated system can undergo change but the
energy remains the same.
The energy of an isolated system is constant
Sign convention:
For the internal energy: ΔU = q + w we will use the sign for q and w
in the following way
If the internal energy is decreased by work being done by the
system or heat flowing out of the system w (and or q respectively)
will be negative.
If the internal energy is increased by work being done to the
system or heat flowing into the system w (and or q respectively) will
be positive.
More conventions:
–
SI unit of energy
● Joule
● 1 J = 1 kg m2 s-2
● 1 kJ = 103 J
–
Thermodynamic equations require the temperature in kelvin
● Temperature difference (ΔT) of 1 K is numerically equal to
ΔT of 1 °C
Compression and expansion work:
The work done if a piston moves
against
a
constant
outside
pressure is given by:
w = - pout ΔV
ΔV is positive for an expansion of
gas (Vfinal – Vinitial) work is negative
for this process.
Note that the work is only
determined
by
the
outside
pressure even though it is the
inside pressure that drives the
piston.
●
Heat Capacity
–
–
–
–
Heat and temperature are not the same
thing
Heat is a transfer of energy due to a
temperature difference
q = CΔT
q - heat (J)
C - heat capacity (J K-1)
●
Heat Capacity
–
–
–
Heat capacity depends on the size of
the sample
A property with a value that depends on
the size of the sample is an extensive
property
A property with a value independent of
the size of the sample is an intensive
property
●
Heat Capacity
–
Divide heat capacity (extensive
property) by the mass of the sample to
form specific heat capacity (intensive
property)
–
c - specific heat capacity (J g-1 K-1)
Divide by amount instead of mass to
form molar heat capacity (J mol-1 K-1)
–
●
Heat Capacity
q = cmΔT
If a gold ring with a mass of 5.50 g changes
in temperature from 25.0 to 28.0 °C, how
much heat has it absorbed?
m = 5.50 g c = 0.129 J g–1 K–1 ΔT = 3 K
q = cmΔT
= (0.129 J g-1 K-1) × (5.50 g) × (3 K)
= 2.1 J
• The determination of heat
– Calorimeter
• Apparatus designed to
minimise heat loss
between the system
and surroundings
– Bomb calorimeter
• System remains at
constant volume
• ΔU = q + w
• ΔU = qv
●
Enthalpy: the heat of reaction at
constant pressure
ΔU = q + w
ΔU = qp – pΔV
–
–
Inconvenient as need
to know ΔV
Define a new thermodynamic
property called enthalpy (H)
ΔH = qp
●
Enthalpy: the heat of reaction at
constant pressure
H = U + pV
ΔH = ΔU + pΔV
–
Substituting ΔU = qp – pΔV gives
ΔH = qp – pΔV + pΔV
ΔH = qp
●
Enthalpy: the heat of reaction at
constant pressure
–
–
–
–
–
The heat of reaction at constant
pressure is equal to ΔH
The heat of reaction at constant volume
is equal to ΔU
ΔH > 0 reaction is endothermic
ΔH < 0 reaction is exothermic
The difference between ΔH and ΔU for
a reaction is pΔV
●
Standard enthalpy change
N2(g) + 3H2(g)  2NH3(g) ΔHθ = –92.38 kJ
–
–
–
The above is a thermochemical
equation
Always gives the physical states of the
reactants and products
Its value of ΔHθ is only true when
coefficients of reactants and products
are numerically equal to the number of
moles of the corresponding substances
●
Hess’s law
–
–
Method for combining known
thermochemical equations in a way that
allows us to calculate ΔHθ for another
reaction
One step
C(s) + O2(g)  CO2(g) ΔHθ = –393.5 kJ
–
Two step
Step 1:
C(s) + ½O2(g)  CO(g) ΔHθ = – 110.5 kJ
Step 2: CO(g) + ½O2(g)  CO2(g)ΔHθ = – 283.0 kJ
●
Hess’s law
2Fe(s) + 3CO2(g)  Fe2O3(s) + 3CO(g) ΔHθ = +26.7 kJ
3CO(g) + O2(g)  3CO2(g)
ΔHθ = -849.0 kJ
2Fe(s) + O2(g)  Fe2O3(s)
ΔHθ = -822.3 kJ
– Rules for manipulating thermochemical
equations:
1. When an equation is reversed the sign of
ΔHθ must also be reversed.
Fe2O3(s) + 3CO(g)  2Fe(s) + 3CO2(g) ΔHθ = -26.7 kJ
2Fe(s) + 3CO2(g)  Fe2O3(s) + 3CO(g) ΔHθ = +26.7 kJ
●
Hess’s law
2Fe(s) + 3CO2(g)  Fe2O3(s) + 3CO(g) ΔHθ = +26.7 kJ
3CO(g) + O2(g)  3CO2(g)
ΔHθ = -849.0 kJ
2Fe(s) + O2(g)  Fe2O3(s)
ΔHθ = -822.3 kJ
– Rules for manipulating thermochemical
equations:
2. Formulae can be cancelled from both
sides of an equation only if the substance
is an identical physical state.
●
Hess’s law
2Fe(s) + 3CO2(g)  Fe2O3(s) + 3CO(g) ΔHθ = +26.7 kJ
3CO(g) + O2(g)  3CO2(g)
ΔHθ = -849.0 kJ
2Fe(s) + O2(g)  Fe2O3(s)
ΔHθ = -822.3 kJ
– Rules for manipulating thermochemical
equations:
3. If all the coefficients of an equation are
multiplied or divided by the same factor,
the value of ΔHθ must likewise be
multiplied or divided by that factor.
CO(g) + ½O2(g)  CO2(g)
ΔHθ = -283.0 kJ
3CO(g) + 3/2O2(g)  3CO2(g)
ΔHθ = -849.0 kJ
●
Standard enthalpy of combustion
– ΔcHθ
– Enthalpy change at temperature T when
1 mole of a substance is completely
burned in pure oxygen gas
– Combustion reactions are always
exothermic
– ΔcHθ always negative
–
kJ mol–1
●
Standard enthalpy of formation (ΔfHθ)
Enthalpy change when 1 mole of
substance is formed at 105 Pa and the
specified temperature from its elements in
their standard states
– An element is in its standard state when it
is in its most stable form and physical
state at 105 Pa and the specified
temperature
– ΔfHθ for the elements in their standard
states are 0
–
●
Standard enthalpy of formation
–
–
aA + bB  cC + dD
ΔH θ c Δf HCθ  d Δf H Dθ  a Δf H Aθ  b Δf H Bθ
Hess’s law equation
Use either enthalpies of combustion or enthalpies of
formation
●
Bond enthalpies
–
–
A bond enthalpy is the enthalpy change
on breaking 1 mole of a particular
chemical bond to give electrically neutral
fragments
Atomisation enthalpy (ΔatH) is the
enthalpy change that occurs on rupturing
all the chemical bonds in 1 mole of
gaseous molecules
●
Bond enthalpies and Hess’s law
●
Lattice enthalpies and Hess’s law – the Born Haber cycle
– Lattice enthalpies for ionic solids calculable using
Hess’s law and thermodynamic data
Today we covered
Definitions of Work, Heat and Energy
adiabatic and non-adiabatic paths
state functions – that do not depend on the path
internal energy – ΔU = q + w
the first law of thermodynamics – conservation of energy
heat capacity – q = CΔT to connect heat flow and temperature
enthalpy – energy at constant pressure ΔH = ΔU + pΔV = qp
Standard enthalpy changes
Hess' law and its applications