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CHEM120 Midterm #2 Review November 10, 2010

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CHEM120 Midterm #2 Review

November 10, 2010

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- Marie Leung, SOS CHEM120 Coordinator/Tutor
- A little about me...
- Also a CHEM120L TA =)
- 4A Biomedical Sciences
- Glee Addict!

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- Chapter 7: Thermochemistry
- introduction to energy systems
- heats of reaction
- pressure-volume work
- first law of thermodynamics
- enthalpy, ∆H & Hess’s Law

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Outline of Session

- Chapter 8: Electrons in Atoms
- electromagnetic radiation
- introduction to quantum theory
- quantum numbers and electron orbitals
- electron configurations

- Question and Answer Period

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- Introduction to Energy Systems
- system vs surroundings
- types of systems:
- open system
- closed system
- isolated system

- types of energy:
- kinetic
- thermal
- potential

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- Heat
- energy that is transferred between a system and its surroundings, as a result of a temperature difference
- quantity of heat, q (in joules):
- m= mass of substance (in grams)
- c = specific heat capacity (in J/g•°C)
- ∆t = change in temperature (°C)

q = mc∆t

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- Heat
- energy that is transferred between a system and its surroundings, as a result of a temperature difference
- quantity of heat, q (in joules)
- exothermic reaction: qrxn < 0
- endothermic reaction: qrxn > 0

q = mc∆t

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- Enthalpy, ∆H
- measure of total energy of system
- measured in kJ or kJ/mol (depending on situation)
- q = quantity of heat (in joules)
- n = moles

∆H = q/n

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- Heat
ex. 1: Given 8.27 g of H2O (specific heat = 4.18 J/g•°C), how much heat is required to raise the temperature from 25°C to 99°C?

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- Heat & Law of Conservation of Energy
- energy cannot be added to or taken away from the universe, but is simply transferred between a system and its surroundings

qsystem + qsurroundings = 0

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- Heat & Law of Conservation of Energy
ex. 2: A 1.22-kg piece of iron at 126.5°C is dropped into 981 g of water at 22.1°C. The temperature rises to 34.4°C. Determine the specific heat of iron, in J/g•°C.

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- Heat & Calorimetry
ex. 3: The combustion of 1.010g sucrose (MC12H22O11 = 342.3g), in a bomb calorimeter causes the temperature to rise from 24.92°C to 28.33°C. The heat capacity of the calorimeter assembly is 4.90 kJ/°C.

a. what is the heat of combustion of sucrose?

b. how much energy is present in one teaspoon (i.e. 4.8g) of sucrose?

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- Pressure-Volume Work
- work involved in the expansion or compression of gases
Let’s think about a few scenarios...

- work involved in the expansion or compression of gases
- constant volume (an isochoric process)
w = -Pext x (0) = 0 = NO WORK!

- constant pressure
- isobaric expansion (∆V is positive) -Pext x (+V) = negative work
- isobaric compression (∆V is negative)
-Pext x (-V) = positive work

w = -Pext x ∆V

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- Pressure-Volume Work
ex. 4: How much work, in joules, is involved when 0.225 mol N2 (at a constant temperature of 23°C) is allowed to expand 1.50 L against a Pext of 0.750atm?

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- First Law of Thermodynamics
- states the relationship between heat (q), work (w) and changes in internal energy (∆U)
- in an isolated system, ∆U = 0, and thus, the energy of an isolated system is constant
- sign conventions:
- +q, +w: energy entering system (i.e. heat absorbed by system, or work done on system)
- -q, -w: energy leaving system (i.e. heat released by system, or work done by system)

∆U = q+ w

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- First Law of Thermodynamics
- ex. 5: In compressing a gas, 355 J of work is done on the system, while 185 J of heat is released from the system. Find ∆U.
- sign conventions:

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- Enthalpy, ∆H
- we know that:
- under constant temperature and pressure:
- therefore:

∆U = q+ w

w = -P∆V

qP = ∆H

∆U = ∆H- P∆V

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- Enthalpy, ∆H
- ex. 6: For which of the following combustion reactions is ΔU = ΔH?
A. CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)

B. C2H5OH(l) + 3 O2(g) → 2 CO2(g) + 3 H2O(l)

C. C4H9OH(l) + 6 O2(g) → 4 CO2(g) + 5 H2O(l)

D. none of the above

- ex. 6: For which of the following combustion reactions is ΔU = ΔH?

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- Hess’s Law & Heats of Formation
- Guidelines:
- 1. When reaction is multiplied or divided, multiply or divide ∆H by the same value.
- 2. The sign for ∆H changes when reaction is reversed.
- 3. When the reactions are summed together, the ∆H can be determined by summing together the ∆H of each individual reaction.

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- Hess’s Law & Heats of Formation
- ex. 7: Find C2H4 (g) + H2 (g) C2H6 (g)
C2H4 (g) + 3 O2 (g) 2 CO2 (g) + 2 H2O (l)

∆H = -1411 kJ

C2H6 (g) + 7/2 O2 (g) 2 CO2 (g) + 3 H2O (l)

∆H = -1560 kJ

H2 (g) + ½ O2 (g) H2O (l)

∆H = -285.8 kJ

- ex. 7: Find C2H4 (g) + H2 (g) C2H6 (g)

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- Intro to Electromagnetic Radiation:
- c = speed of light ≈ 3 x 108 m/s
- ν = frequency (in s-1, or Hz)
- λ = wavelength (in m)

c = λν

higher frequency shorter wavelength

lower frequency longer wavelength

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Lawrence Berkeley National Laboratory

http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html

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- Quantum Theory
- Planck’s Equation
- E = energy (in J)
- h = Planck’s constant, 6.62607 x 10-34 J•s
- note the trends:
- shorter wavelength = higher frequency = higher energy
- longer wavelength = lower frequency = lower energy

E = hν = hc/λ

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HIGHEST ENERGY

LOWEST ENERGY

LOWEST FREQUENCY

HIGHEST FREQUENCY

LONGEST WAVELENGTH

SHORTEST WAVELENGTH

...going back to the electromagnetic spectrum:

- Electromagnetic Spectrum
- Ex. 8: Which of the following has the highest energy?
- A. red light
- B. microwaves
- C. ultraviolet radiation
- D. radiowaves

- Brief Overview of Quantum Mechanics
- Heisenberg Uncertainty Principle:
- we cannot know the exact position and momentum of an electron at the same time
- that is, if we know one variable, we do not know the other

- Quantum Numbers and Electron Orbitals
- 1. principal quantum number, n
- shell number
- must be positive, nonzero integral value
- n = 1, 2, 3, 4...
- i.e. “the neighbourhood”

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- Quantum Numbers and Electron Orbitals
- 2. orbital angular momentum quantum number, ι
- may be zero or a positive integer
- must not be larger than n-1
- ι = 0, 1, 2, 3... (n-1)
- corresponds to subshells:
- s: ι =0
- p: ι =1
- d: ι =2
- f: ι =3

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- Quantum Numbers and Electron Orbitals
- 3. magnetic quantum number, mι
- may be negative, zero or a positive integer
- ranges from -ι to +ι
- refers to number of orbitals
- e.g. if ι =1 (i.e. p subshell), mι = -1, 0, 1
- thus, there are three p orbitals (and 2 electrons in each one - total 6 e-)
- i.e. “the house”

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- Quantum Numbers and Electron Orbitals
- 4. electron spin number, ms
- either+1/2 or -1/2
- two electrons per orbital - spin in opposite directions

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- Quantum Numbers and Electron Orbitals
- ex. 9: Which of the following sets of quantum numbers are allowed?
- a. n = 3, ι = 2, mι = -1
- b. n = 1, ι = 2, mι = 0
- c. n = 4, ι = 4, mι = 3
- d. n = 1, ι = 0, mι = 0
- e. n = 2, ι = 1, mι = -1

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- Quantum Numbers and Electron Orbitals
- wavefunction, Ψ
- how electron behaves in orbital
- electron density, Ψ2
- probability of finding electrons at one point at
- distance r from nucleus

- probability of finding electrons at all points distance
- r from nucleus

- Quantum Numbers and Electron Orbitals
- the ORBITRON....

http://winter.group.shef.ac.uk/orbitron/

Orbital Diagram

2s

Dr. Richard Bader, McMaster University

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Wavefunction (atomic orbital)

Radial Probability Distribution

Dr. Richard Oakley, University of Waterloo

http://www.science.uwaterloo.ca/~oakley/chem120/notes/chapter_08.htm

http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_IV/Energiezustand.htm

Take home message: s-orbitals Ψ, Ψ2 nonzero at r = 0!

Orbital Diagram

2p

Dr. Richard Bader, McMaster University

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Wavefunction (atomic orbital)

Radial Probability Distribution

Dr. Richard Oakley, University of Waterloo

http://www.science.uwaterloo.ca/~oakley/chem120/notes/chapter_08.htm

http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_IV/Energiezustand.htm

Orbital Diagram

3d

Dr. Richard Bader, McMaster University

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Wavefunction (atomic orbital)

Radial Probability Distribution

Dr. Richard Oakley, University of Waterloo

http://www.science.uwaterloo.ca/~oakley/chem120/notes/chapter_08.htm

http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_IV/Energiezustand.htm

Orbital Diagram

4f

Dr. Richard Bader, McMaster University

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Wavefunction (atomic orbital)

Dr. Richard Oakley, University of Waterloo

http://www.science.uwaterloo.ca/~oakley/chem120/notes/chapter_08.htm

- Electron Configurations
- 1. Electrons fill orbitals in a way that minimizes the energy of the atom
- the aufbau principle
- i.e. lowest energy levels are filled first

- Electron Configurations
- 2. No two electrons in an atom may have the same four quantum numbers
- the Pauli exclusion principle
- n, ι and mι determine the electron orbital
- electrons that share the first three quantum numbers belong to the same shell, subshell and orbital

- Electron Configurations
- 3. Within orbitals of identical energy, electrons will first fill them singly before pairing up
- Hund’s Rule
- stability is associated with half filled or fully filled orbitals

- Electron Configurations
- ex 10. Determine the elements denoted by the following electron configurations:
- a.
- b. 1s22s22p63s1

- Electron Configurations
- ex 11. Draw electron configurations for each of the following elements:
- a. potassium
- b. copper

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- Further Questions?
- Marie (mariejasmineleung@gmail.com)
- For more information on Waterloo Students Offering Support, visit http://www.waterloosos.com/

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