Equilibrium and Radioactivity

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Equilibrium and Radioactivity

• From there to here, from here to there, funny
  things are everywhere
• --TSG 1957

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The rate of a reaction

• Expressed in mol/sec or M/s

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N2 3H2?2NH3

• If 2.40 moles of NH3 are produced each second,
  what is the rate of use of N2 and H2?

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N2 3H2?2NH3

• If 2.40 moles of NH3 are produced each second,
  what is the rate of use of N2 and H2?
• 2.40 mol NH3/s x 1 N2/2 NH3
• 1.20 mol N2/s
• 2.40 mol NH3/s x 3 H2/2 NH3
• 3.60 mol H2/s

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How can you speed up a reaction?
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How can you speed up a reaction?

• --Heat it up.
• --Crush, grind or powder a solid reactant.
• --Increase pressure of a gaseous reactant
• --Increase concentrations of aqueous reactants
• --Add a catalyst (if known)
• (Stir or shake to bring reactants together.)

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How would you speed up

• Hydrochloric acid acts on tin metal to form
  hydrogen gas and aqueous tin (II) chloride

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How would you speed up

• Hydrochloric acid acts on tin metal to form
  hydrogen gas and aqueous tin (II) chloride
• Increase concentration of HCl
• Powder the tin
• Heat the reactants
• Stir or shake
• (I dont know of a catalystits pretty fast
  already)

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Reversible reactions.

• AKA all reactions
• All reactions work in reverse, at least a little
  bit.

should be written as
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Write the reverse reaction

• 2NaHCO3 (s) ?Na2CO3 (s) H2O (g)
• CaCO3 (s) ?CaO (s) CO2 (g)
• H2 (g) Cl2 (g) ?2HCl (g)
• N2 (g) 3H2 (g) ?2NH3 (g)

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H2 I2 2HI
1 mole H2 and 1 mole I2 (1L)
If you start with 1 mole H2 and 1 mole I2 in a 1L
flask
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H2 I2 2HI
1 mole H2 and 1 mole I2 (1L)
.8 mole H2 .8 mole I2 and .4 mole HI (1L)
it will proceed forwards. Some of the reactants
will form products.
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H2 I2 2HI
2 mole HI (1L)
If you start with 2 moles HI in a 1L flask
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H2 I2 2HI
2 mole HI (1L)
.8 mole H2 .8 mole I2 and .4 mole HI (1L)
it will proceed in reverse. Some of the
products will form reactants
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H2 I2 2HI
1 mole H2 and 1 mole I2 (1L)
2 mole HI (1L)
.8 mole H2 .8 mole I2 and .4 mole HI (1L)
Did you notice?
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H2 I2 2HI
1 mole H2 and 1 mole I2 (1L)
2 mole HI (1L)
.8 mole H2 .8 mole I2 and .4 mole HI (1L)
You get the same final concentrations
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Starting with reactants
Rate of reaction (mol/s)
Time (s)
The forward reaction starts out fast, then slows
as reactants are used up
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Starting with reactants
Rate of reaction (mol/s)
Time (s)
The reverse reaction starts out at 0 mol/s, then
speeds up as products are produced
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Starting with reactants
Rate of reaction (mol/s)
Time (s)
Did you notice?
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Starting with reactants
Rate of reaction (mol/s)
Time (s)
The forward and reverse reactions reach the same
rate. Concentrations will stabilize
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Eventually

• reactants make products just as fast as products
  make reactants.

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Eventually

• reactants make products just as fast as products
  make reactants.
• Its inevitable.

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Eventually

• reactants make products just as fast as products
  make reactants.
• Its inevitable.
• Its dynamic equilibrium

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That's EQUILIBRIUM!
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Try it.

• N2 3H2 2NH3
• Describe the rate of the forward reaction if you
  start with nitrogen and hydrogen.
• What is the rate of the reverse reaction?
• What happens to each rate?
• Why?
• Eventually

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The equilibrium constant expression

• For aA bB?? cC dD
• (if all substances are gasses or aqueous)
• The expression
• Cc Dd
• Aa Bb is a constant (K) at a given
  temperature

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Please note

• Products on top
• Coefficients become exponents
• Brackets mean molarity
• Concentrations are multiplied
• Solid and liquid substances are not included
• then this ratio is a constant!

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For example

• For H2(g) I2 (g)??2HI (g)
• The equilibrium constant expression is
• K HI2 (.4M)2 .25
• H2I2 (.8M)(.8M)

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Write the equilibrium constant expression for

1. 4NH3(g)5O2(g)??4NO(g)6H2O(g)
2. CO (g) 2H2 (g) ??CH3OH (g)
3. NH3(g)H2O (l) ?? NH4 (aq) OH-(aq)

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Rookie mistakes

• --putting reactants on top
• --using coefficients inside the brackets
• --adding instead of multiplying concentrations
• --multiplying by coefficients, instead of raising
  to the power
• --including liquids and solids.
• Avoid these errors!

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What is the value of K?

• 4NH3(g)5O2(g)??4NO(g)6H2O(g)
• .050 M .30 M .20 M .40 M
• 2) CO (g) 2H2 (g) ??CH3OH (g)
• .20 M .20 M .030 M
• 3) NH3(g)H2O (l) ?? NH4 (aq) OH-(aq)
• .10 M 55.5 M .0013 M .0013 M

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What is the unknown concentration?

• 4NH3(g)5O2(g)??4NO(g)6H2O(g)
• .060 M .40 M .15 M ? M
• 2) CO (g) 2H2 (g) ??CH3OH (g)
• ? M .25 M .070 M
• 3) NH3(g)H2O (l) ?? NH4 (aq) OH-(aq)
• ? M 55.5 M .0019 M .00030M

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Le Chateliers Principle

• If a system in equilibrium is subjected to a
  stress, the system will shift in the direction
  that will relieve that stress

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Application of LeChateliers principle

• Shift right
• --forward reaction is faster,
• --more of all products are formed
• --all reactants are used
• Shift left
• --reverse reaction is faster,
• --more of all reactants are formed
• --all products are used

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Application of LeChateliers principle

• An aqueous or gas substance in the reaction
  addedshift away to use it up
• Increasing pressureshift toward side with fewer
  moles of gas to relieve pressure
• Increasing temperatureshift in the endothermic
  direction to absorb heat

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N2(g) 3H2(g) 2NH3(g) D Which way would
the equilibrium shift if you

1. Add N2(g)
2. Add H2(g)
3. Add NH3(g)
4. Increase P (compress)
5. Increase T
6. Add a catalyst
7. Remove N2(g)

• 7. Remove H2(g)
• 8. Remove NH3(g)
• 9. Decrease P (allow to expand)
• 10. Decrease T
• 11. Increase pressure by adding He (g)

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N2(g) 3H2(g) 2NH3(g) D Which way would
the equilibrium shift if you

1. Add N2(g)
2. Add H2(g)
3. Add NH3(g)
4. Increase P (compress)
5. Increase T
6. Add a catalyst
7. Remove N2(g)

• 7. Remove H2(g)
• 8. Remove NH3(g)
• 9. Decrease P (allow to expand)
• 10. Decrease T
• 11. Increase pressure by adding He (g)

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N2(g) 3H2(g) 2NH3(g) D Why?
Forward reaction speeds up

1. Add N2(g)
2. Add H2(g)
3. Add NH3(g)
4. Increase P (compress)
5. Increase T
6. Add a catalyst
7. Remove N2(g)

• 7. Remove H2(g)
• 8. Remove NH3(g)
• 9. Decrease P (allow to expand)
• 10. Decrease T
• 11. Increase pressure by adding He (g)

Reverse reaction slows down
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How would you shift this reaction to the left?

• HCOOH (aq) D??HCOO- (aq) H (aq)
• (formic (heat) (formate (hydrogen
• acid) ion)
  ion)

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Why do reactions proceed at all?
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Why do reactions proceed at all?

• To go to a more stable, lower energy state.
• 1) If DH is (-), reaction gives off heat. (DHlt0)
• OR
• 2) an advantage in gaining entropy, S. (DSgt0)
• OR BOTH!

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Enthalpy and Entropy

• DH
• Endo- or exothermic
• Energy is stored in/released from chemical bonds
• Measured in kJ/mol

• DS
• Gains or loses entropy
• A system becomes more or less disordered
  (sltlltaqltltg)
• Measured in J/ mol k

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2H2 O2?2H2O
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2H2 O2?2H2O

• DH is very negativeit gives up a lot of heat.
• 2H2 O2?2H2O D

Releasing heat is an advantage for a reaction
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2H2 O2?2H2O

• DS is also negativeit loses entropy as 3 moles
  of gasses form only 2 moles.
• This is a disadvantage, its worse at higher
  temperatures. Over 5000oC, hydrogen gas wont
  even burn.

The advantage for entropy depends on temperature
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What is DH, DS and DG?

• D CaCO3 (s) ?CaO (s) CO2 (g)
• H2 (g) Cl2 (g) ?2HCl (g) D
• N2 (g) 3H2 (g) ?2NH3 (g) D

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• What happens at a higher temperature?

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at a higher temperature

• 1) Particles move faster.
• 2) There are more collisions.
• 3) Those collisions have more energy.

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To react, reactants must collide with enough
energy, the activation energy.
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Cool, medium, warm
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Notice

1. The bell-shaped distributions
2. The average speed is higher at higher To
3. The speeds spread out more at higher To

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What is fast enough to react?

• More collisions will have enough energy to react
  at higher temperatures

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What if this is fast enough?
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What if this is fast enough?
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To react, reactants must collide with enough
energy, the activation energy.
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Catalysis

• A catalyst speeds up a reaction
• This is done by lowering the energy barrier, Ea
• When the barrier is lower, more collisions are
  fast enough

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Nuclear Chemistry--
--as opposed the the unclear chemistry you have
studied
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Nuclear Chemistry

• --breaks the rules that one atom cannot be
  converted to another.
• Chemistry the dance of the electrons
• nuclear reactions change the nuclei of atoms
• --charge and mass are still conserved.

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Nuclide Notation

• A nuclide is a nucleus or atom of a specific
  isotope of an element

K
39
19

• Potassium-39.
• -- has 19 protons (atomic number 19), making it
  potassium, and 20 neutrons (making a mass number
  of 39)

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How many p, n, e- in each?What is the mass
number and atomic number?
Cl-
36
I-
131
H
3
17
53
1
Sr2
90
Th
228
Fe3
59
38
90
26
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How many p, n, e- in each?What is the mass
number and atomic number?
undergoes a b decay
Cl-
36
I-
131
H
3
17
53
1
Sr2
90
Th
228
Fe3
59
38
90
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undergoes an a decay
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Natural decays

• athe loss of a particle from a nuclide
• --The a particle is composed of 2p and 2n, the
  4He nucleus
• --decreases the mass by 4 and the atomic number
  by 2
• bemission of an electron (b particle) from the
  nucleus by the conversion of a n ? p e-
• --the electron is the b particle
• --increases the atomic number by 1, does not
  affect mass

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Write the reaction

• Argon-39 undergoes a b decay
• Thorium-228 undergoes an a decay
• An a decay forms lead-204
• A b decay forms nitrogen-14
• A natural decay forms Sc-45 from Ca-45
• A natural decay forms Ac-227 from Pa-231

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Stable?
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Nuclear reactions

• Many nuclear reactions involve colliding nuclei
  or smaller particles at some significant fraction
  of the speed of light,
• --find the missing particle by balancing mass and
  charge.

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Fission vs Fusion

• Fissionbreaking up large nuclei
• --natural radioactive decay of large atoms
• --used for nuclear power
• Fusioncombining small nuclei
• --occurs naturally in stars
• --prospects for nuclear energyno radioactive
  byproducts
• Both are transmutationsone nuclide is converted
  into another

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Consider the relationships

• Half life
• Original amount
• Final amount
• Time elapsed

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Consider the relationships

• AA0(1/2)
• A is the amount of the sample remaining
• A0 is the original amount in the sample
• t is the time that has passed, and
• t 1/2 is the half-life of the nuclide

t/t1/2
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Please notice

• AA0(1/2)
• A / A0 the fraction remaining and
• t / t 1/2the number of half-lifes that have
  passed

t/t1/2
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Try it.

• Hydrogen-3 has a half life of 12.3 years. If you
  start with a 20 g sample of H-3
• --how much is left after 12.3 years?
• --how much is left after 24.6 years?
• --how much is left after 30.2 years?

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Try it.

• Br-82 has a half life of 35.3 hours. If you
  start with a 6.5 mg sample of Br-82
• --how much is left after 4 days?
• --how long will it take to reach .75 mg?

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Try it.

• Br-82 has a half life of 35.3 hours. If you
  start with a 6.5 mg sample of Br-82
• --how much is left after 4 days?
• --how long will it take to reach .75 mg?

How do you solve for an exponent?
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Use a log function

• log (A/A0) log(1/2)
• log (A/A0) log(1/2)
• log (A/A0)
• log(1/2)

t/t1/2
t/t1/2
t/t1/2
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Try it.

• Br-82 has a half life of 35.3 hours. If you
  start with a 6.5 mg sample of Br-82
• --how much is left after 4 days?
• --how long will it take to reach .75 mg?

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Try it.

• If you start with 1.38 mg of U-234 and t1/22.44
  x 105 yrs for its decay
• --how much is left after 20,000 years?
• --how long will it take to reach 0.40 mg?

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Try it.

• A .350 mg sample of K-42 decays to only .066 mg
  in 29.7 hours.
• --what is the half life?
• --how much was left after 20.0 hours?
• --how long will it take to reach .010 mg?

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The uses of radioactivity
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The uses of radioactivity

• Medicinetracers, radiation therapy
• History/geologyradioisotope dating
• Nuclear energy
• Nuclear weapons

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The uses of radioactivity

• Medicine
• Tracers
• I-131, S-35, F-18, P-32
• Radiation therapy
• I-131, Lu-177, Y-90, Sr-89

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The uses of radioactivity

• History/geologyradioisotope dating
• C-14, U-238, Sm-147, K-40

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The uses of radioactivity

• Nuclear Energy
• Nuclear reactions give off a large amount of
  energy
• This energy is often converted to electricity
• A nuclear reactor contains the reactants so the
  by-products (usually neutrons) carry out the
  chain reaction

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Pressurized water reactor
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Boiling water reactor
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Heavy water reactor
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Gas-cooled reactor
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Hydride salt reactor
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Pebble bed modular reactor
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NERVA