Aka the Law of conservation of energy, Gibbs in 1873 stated energy cannot be created or destroyed, only transferred by any process

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1st Law of Thermodynamics

• Aka the Law of conservation of energy, Gibbs in
  1873 stated energy cannot be created or
  destroyed, only transferred by any process
• The net change in energy is equal to the heat
  that flows across a boundary minus the work done
  BY the system
• DU q w
• Where q is heat and w is work
• Some heat flowing into a system is converted to
  work and therefore does not augment the internal
  energy

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Directionality from the 2nd Law

• For any spontaneous irreversible process, entropy
  is always increasing
• How can a reaction ever proceed if order
  increases?? Why are minerals in the earth not
  falling apart as we speak??

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NEED FOR THE SECOND LAW

• The First Law of Thermodynamics tells us that
  during any process, energy must be conserved.
• However, the First Law tells us nothing about in
  which direction a process will proceed
  spontaneously.
• It would not contradict the First Law if a book
  suddenly jumped off the table and maintained
  itself at some height above the table.
• It would not contradict the First Law if all the
  oxygen molecules in the air in this room suddenly
  entered a gas cylinder and stayed there while the
  valve was open.

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MEANING OF ENTROPY AND THE SECOND LAW

• Entropy is a measure of the disorder (randomness)
  of a system. The higher the entropy of the
  system, the more disordered it is.
• The second law states that the universe always
  becomes more disordered in any real process.
• The entropy (order) of a system can decrease, but
  in order for this to happen, the entropy
  (disorder) of the surroundings must increase to a
  greater extent, so that the total entropy of the
  universe always increases.

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3rd Law of Thermodynamics

• The heat capacities of pure crystalline
  substances become zero at absolute zero
• Because dq CdT and dS dq / T
• We can therefore determine entropies of formation
  from the heat capacities (which are measureable)
  at very low temps

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Free Energy

• Still need a function that describes reaction
  which occurs at constant T, P
• G U PV TS H TS
• (dH dU PdV VdP)
• The total differential is
• dG dU PdV VdP TdS SdT
• G is therefore the energy that can run a process
  at constant P, T (though it can be affected by
  changing P and T)
• Reactions that have potential energy in a system
  independent of T, P ? aqueous species, minerals,
  gases that can react

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• Can start to evaluate G by defining total
  differential as a function of P and T
• dG dU PdV VdP TdS SdT
• Besides knowing volume changes, need to figure
  out how S changes with T
• For internal energy of a thing
• dU dqtot PdV determining this at constant
  volume ? dU CVdT
• where CV is the heat required to raise T by 1C

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Increasing energy with temp?

• The added energy in a substance that occurs as
  temperature increases is stored in modes of
  motion in the substance
• For any molecule modes are vibration,
  translation, and rotation
• Solid ? bond vibrations
• Gases ? translation
• Liquid water complex function

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Heat Capacity

• When heat is added to a phase its temperature
  increases (No, really)
• Not all materials behave the same though!
• dqCVdT ? where CV is a constant (heat capacity
  for a particular material)
• Or at constant P dqCpdT
• Recall that dqpdH then dHCpdT
• Relationship between CV and Cp

Where a and b are coefficients of isobaric
thermal expansion and isothermal compression,
respectively
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Enthalpy at different temps

• HOWEVER ? C isnt really constant.
• C also varies with temperature, so to really
  describe enthalpy of formation at any
  temperature, we need to define C as a function of
  temperature
• Maier-Kelley empirical determination
• Cpa(bx10-3)T(cx10-6)T2
• Where this is a fit to experimental data and a,
  b, and c are from the fit line (non-linear)

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Does water behave like this?

• Water exists as liquid, solids, gas, and
  supercritical fluid (boundary between gas and
  liquid disappears where this happens is the
  critical point)
• Cp is a complex function of
• T and P (H-bond affinities),
• does not ascribe to Maier-
• Kelley forms

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Heats of Formation, DHf

• Enthalpies, H, are found by calorimetry
• Enthalpies of formation are heats associated with
  formation of any molecule/mineral from its
  constituent elements

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Calorimetry

• Measurement of heat flow (through temperature)
  associated with a reaction
• Because dH q / dT, measuring Temperature change
  at constant P yields enthalpy

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Problem When 50.mL of 1.0M HCl and 50.mL of 1.0M
NaOH are mixed in a calorimeter, the temperature
of the resultant solution increases from 21.0oC
to 27.5oC. Calculate the enthalpy change per
mole of HCl for the reaction carried out at
constant pressure, assuming that the calorimeter
absorbs only a negligible quantity of heat, the
total volume of the solution is 100. mL, the
density of the solution is 1.0g/mL and its
specific heat is 4.18 J/g-K.
qrxn - (cs solution J/g-K) (mass of solution g)
(DT K) - (4.18 J/g-K) (1.0g/mL)(100 mL) (6.5
K) - 2700 J or 2.7 kJ DH 2.7 kJ Enthalpy
change per mole of HCl (-2.7 kJ)/(0.050 mol)
- 54 kJ/mol
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• Hesss Law
• Known values of DH for reactions can be used to
  determine DHs for other reactions.
• DH is a state function, and hence depends only on
  the amount of matter undergoing a change and on
  the initial state of the reactants and final
  state of the products.
• If a reaction can be carried out in a single step
  or multiple steps, the DH of the reaction will be
  the same regardless of the details of the process
  (single vs multi- step).

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• CH4(g) O2(g) --gt CO2(g) 2H2O(l) DH -890
  kJ
• If the same reaction was carried out in two
  steps
• CH4(g) O2(g) --gt CO2(g) 2H2O(g) DH -802
  kJ
• 2H2O(g) --gt 2H2O(l) DH -88 kJ

Hesss law if a reaction is carried out in a
series of steps, DH for the reaction will be
equal to the sum of the enthalpy change for the
individual steps.