Equilibrium and Radioactivity

From there to here, from here to there, funny things are everywhere

--TSG 1957

The rate of a reaction

• Expressed in mol/sec or M/s

N2 + 3H22NH3

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

N2 + 3H22NH3

• 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

How can you speed up a reaction?

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.)

How would you speed up…

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

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 don’t know of a catalyst—it’s pretty fast already)

Reversible reactions.

• AKA “all reactions”

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

should be written as

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)

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…

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.

H2 +I2 2HI

2 mole HI

(1L)

If you start with 2 moles HI in a 1L flask…

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

H2 +I2 2HI

1 mole H2

and 1 mole I2

(1L)

2 mole HI

(1L)

Did you notice?

.8 mole H2 .8 mole I2

and .4 mole HI

(1L)

H2 +I2 2HI

1 mole H2

and 1 mole I2

(1L)

2 mole HI

(1L)

You get the same final concentrations

.8 mole H2 .8 mole I2

and .4 mole HI

(1L)

Starting with reactants…

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 60

The forward reaction starts out fast, then slows as reactants are used up

Rat

e of

rea

ctio

n (m

ol/s

)

Time (s)

Starting with reactants…

The reverse reaction starts out at 0 mol/s, then speeds up as products are produced

0

0.005

0.01

0.015

0.02

0.025

0 20 40 60

Rat

e of

rea

ctio

n (m

ol/s

)

Time (s)

Starting with reactants…

Did you notice?

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 10 20 30

Rat

e of

rea

ctio

n (m

ol/s

)

Time (s)

Starting with reactants…

The forward and reverse reactions reach the same rate. Concentrations will stabilize

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 10 20 30

Rat

e of

rea

ctio

n (m

ol/s

)

Time (s)

Eventually…

…reactants make products just as fast as products make reactants.

Eventually…

…reactants make products just as fast as products make reactants.

• It’s inevitable.

Eventually…

…reactants make products just as fast as products make reactants.

• It’s inevitable.

• It’s dynamic equilibrium

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…

The equilibrium constant expression

• For aA +bB cC + dD

(if all substances are gasses or aqueous)

• The expression

[C]c [D]d

[A]a [B]b is a constant (K) at a given temperature

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!

For example

• For: H2(g) +I2 (g)2HI (g)

• The equilibrium constant expression is:

• K= [HI]2 = (.4M)2 = .25

[H2][I2] (.8M)(.8M)

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)

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!

What is the value of K?

1) 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

What is the unknown concentration?

1) 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

Le Chatelier’s Principle

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

Application of LeChatelier’s 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

Application of LeChatelier’s principle

• An aqueous or gas substance in the reaction added—shift away to use it up

• Increasing pressure—shift toward side with fewer moles of gas to relieve pressure

• Increasing temperature—shift in the endothermic direction to absorb heat

N2(g) + 3H2(g) 2NH3(g) + 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)

N2(g) + 3H2(g) 2NH3(g) + 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)

N2(g) + 3H2(g) 2NH3(g) + Why?

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)

Forward reaction

speeds up

Reverse reaction

slows down

How would you shift this reaction to the left?

HCOOH (aq)+ HCOO- (aq) + H+ (aq)

(formic (heat) (formate (hydrogen

acid) ion) ion)

Why do reactions proceed at all?

Why do reactions proceed at all?

• To go to a more stable, lower energy state.

1) If H is (-), reaction gives off heat. (H<0)

OR

2) an advantage in gaining entropy, S. (S>0)

OR BOTH!

Enthalpy and Entropy

H

• Endo- or exothermic

• Energy is stored in/released from chemical bonds

• Measured in kJ/mol

S

• Gains or loses entropy

• A system becomes more or less disordered (s<l<aq<<g)

• Measured in J/ mol k

2H2 +O22H2O…

2H2 +O22H2O…

• H is very negative—it gives up a lot of heat.

2H2 +O22H2O +

Releasing heat is an advantage for a reaction

2H2 +O22H2O…

• S is also negative—it loses entropy as 3 moles of gasses form only 2 moles.

This is a disadvantage, it’s worse at higher temperatures. Over 5000oC, hydrogen gas won’t even burn.

The advantage for entropy depends on temperature

What is H, S and G?

• + CaCO3 (s) CaO (s) +CO2 (g)

• H2 (g) +Cl2 (g) 2HCl (g) +

• N2 (g) + 3H2 (g) 2NH3 (g) +

• What happens at a higher temperature?

…at a higher temperature…

1) Particles move faster.

2) There are more collisions.

3) Those collisions have more energy.

To react, reactants must collide with enough energy, the activation energy.

Cool, medium, warm

Notice:

1) The bell-shaped distributions

2) The average speed is higher at higher To

3) The speeds spread out more at higher To

What is “fast enough” to react?

More collisions will have enough energy to react at higher temperatures

What if this is “fast enough”?

What if this is “fast enough”?

To react, reactants must collide with enough energy, the activation energy.

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”

Nuclear Chemistry--

--as opposed the the unclear chemistry you have studied

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.

Nuclide Notation

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

K39

19

• Potassium-39.

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

How many p, n, e- in each?What is the mass number and

atomic number?

Cl-36

17

Sr+290

38

I-131

53

Th228

90

H3

1

Fe+359

26

How many p, n, e- in each?What is the mass number and

atomic number?

Cl-36

17

Sr+290

38

I-131

53

Th228

90

H3

1

Fe+359

26

undergoes a decay

undergoes an decay

Natural decays

• —the loss of particle from a nuclide--The particle is composed of 2p and 2n,

the 4He nucleus--decreases the mass by 4 and the atomic

number by 2• —emission of an electron ( particle) from the

nucleus by the conversion of a n p + e---the electron is the particle--increases the atomic number by 1, does

not affect mass

Write the reaction

• Argon-39 undergoes a decay

• Thorium-228 undergoes an decay

• An decay forms lead-204

• A decay forms nitrogen-14

• A natural decay forms Sc-45 from Ca-45

• A natural decay forms Ac-227 from Pa-231

Stable?

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.

Fission vs Fusion• Fission=breaking up large nuclei—

--natural radioactive decay of large atoms --used for nuclear power

• Fusion=combining small nuclei --occurs naturally in stars --prospects for nuclear energy—no radioactive byproducts

Both are transmutations—one nuclide is converted into another

Consider the relationships

• Half life

• Original amount

• Final amount

• Time elapsed

Consider the relationships

A=A0(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

Please notice

A=A0(1/2)

A / A0 = the fraction remaining and

t / t 1/2=the number of half-lifes that have passed

t/t1/2

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?

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?

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?

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

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?

Try it.

• If you start with 1.38 mg of U-234 and t1/2=2.44 x 105 yrs for its decay:

--how much is left after 20,000 years?

--how long will it take to reach 0.40 mg?

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?

The uses of radioactivity

The uses of radioactivity

• Medicine—tracers, radiation therapy

• History/geology—radioisotope dating

• Nuclear energy

• Nuclear weapons

The uses of radioactivity

• Medicine—

Tracers:

I-131, S-35, F-18, P-32

Radiation therapy

I-131, Lu-177, Y-90, Sr-89

The uses of radioactivity

• History/geology—radioisotope dating

• C-14, U-238, Sm-147, K-40

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

Pressurized water reactor

Boiling water reactor

Heavy water reactor

Gas-cooled reactor

Hydride salt reactor

Pebble bed modular reactor

NERVA