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Collision Theory

Reversible Chemical Reactions

BIOB111

CHEMISTRY & BIOCHEMISTRY

Session 4

Key concepts: session 4From this session you are expected to develop an understanding of the following concepts:

Concept 1: Processes that occur during a chemical reaction

Concept 2: Collisions to begin chemical reactions

Concept 3: Changing the rate of a chemical reaction

Concept 4: Energy transfer in chemical reactions

Concept 5: Activation energy

Concept 6: Endothermic reactions

Concept 7: Exothermic reactions

Concept 8: Equilibrium reactions

Concept 9: Stresses on equilibrium reactions

These concepts are covered in the Conceptual multiple choice questions of tutorial 4

Session OverviewPart 1: Molecular collisions

• Chemical equations represent chemical reactions

• Collisions between molecules drive chemical reactions

Part 2: Interpreting chemical reactions

• Chemical reaction rate

• Energy transfer in chemical reactions

• Exothermic vs endothermic reactions

Part 3: Chemical equilibrium

• Chemical equilibrium

• Re-establishing chemical equilibrium

Part 1: Molecular collisions

• Chemical equations represent chemical reactions

• Collisions between molecules drive chemical reactions

Progression through a chemical reaction:

– Start- step 1: The chemical bonds holding the reactant molecules together are broken• Chemical bond breakage requires an energy input

• Example below: Chemical bonds broken within methane and oxygen

– Middle- step 2: Once the chemical bonds have been broken, the atoms rearrange to adopt new positions

• Example below: Carbon, hydrogen and oxygen atoms rearrange

– End- step 3: After atom rearrangement, new chemical bonds form between the atoms creating the products• Chemical bond formation releases energy

• Example below: New chemical bonds are formed to produce carbon dioxide and water

Chemical equations represent chemical reactions

Chemical reaction:

Reactant 1 Reactant 2 Product 1Product 2

+ +H

H

HH

H H

H H

C C

OO

O OO O

O

O

Reactant 1:Methane Reactant 2:

Oxygen Product 1:Carbon dioxide

Product 2: water


Start- step 1:

Chemical bond breakage in reactants

+H

H

HH C

OO

O O

Reactant 1:Methane Reactant 2:

Oxygen

Covalent bond broken• Bond

breakage requires energy


Middle- step 2:

Atom rearrangement

+H

H

HH C

OO

O O


End- step 3:

Chemical bond formation in products

C

O O

H H

O

Product 1:Carbon dioxide

Product 2: Water

H

O

H

Newly formed covalent bond• Bond formation

releases energy Product 2: Water


1(CH4) 2(O2)+ 1(CO2) 2(H2O)+CH4 2O2+ 2H2OCO2 + Simplified

representation


Collisions between molecules drive chemical reactions

• Collisions between different molecules drive chemical reactions– Different reactant molecules must

collide to form products

http://phet.colorado.edu/en/simulation/legacy/reactions-and-rates

• Most collisions do not result in a

chemical reaction, as the molecules just

bounce off each other

– Only effective collisions allow the

chemical reaction to begin


• Only effective collisions result in a chemical reaction

• An effective collision requires:

NO2 + CO → NO + CO2


– 1) Convenient orientation of molecules at the time of collision

– 2) The energy of the Collision must meet the activation energy

• The collision between molecules must have sufficient energy to break specific chemical

bonds within the reactants

– The energy of a collision depends on the speed of reactant molecules and on the angle of their

approach

• Activation Energy: The minimum amount of energy from the collision between two

reactant molecules that will allow the chemical reaction to begin

N

O O C ON

O OC O

Effective collision

• High energy collision, which meets the activation energy• Collision has a convenient orientation with the carbon

(from CO) and the oxygen (from NO2) colliding



NO

O

C ON

O

OC O


Unsuccessfulcollision

• Collision has an inconvenient orientation with the carbon (from CO) and the nitrogen (from NO2) colliding


N

O O C ON

O OC O

• Collision has a convenient orientation with thecarbon (from CO) and the oxygen (from NO2) colliding

• Low energy collision, which does not meet the activation energy


Unsuccessfulcollision


When reactant molecules (above) collide, what factors

determine whether a chemical reaction will occur?

G

NO + O3 NO2 + O2

When reactant molecules (above) collide, what factorsdetermine whether a chemical reaction will occur? • For the chemical reaction to take place, the energy of the

collision (between the reactant molecules) must be equal to or greater than the activation energy– Collision energy ≥ activation energy:

Collision energy allows specific chemical bonds within the reactants to be broken

Atoms rearranged

Products formed (new chemical bonds formed)

• The angle that NO and O3 collide must be convenient – Oxygen must collide with nitrogen, to allow an extra oxygen to bond to nitrogen (after detaching from O3)

NO + O3 NO2 + O2

Attempt Socrative questions: 1 to 4

Google Socrative and go to the student login

Room name:

City name followed by 1 or 2 (e.g. PERTH1)

1 for 1st session of the week and 2 for 2nd session of the week

Part 1: Molecular collisions• Chemical equations represent chemical reactions

– In a chemical reaction, the reactants on the left hand side are

converted into the products on the right hand side of the equation,

with the arrow representing the progression of the chemical reaction• CH4 + 2O2 → CO2 + 2H2O

– No atoms are created or destroyed in a chemical reaction, only rearranged to form new substances (products)

• Collisions between molecules drive chemical reactions– Collisions between reactant molecules provide the energy required to

begin the chemical reaction

– For a collision to allow a chemical reaction to begin, the collision must:• Have a collision energy equal to or greater than the activation energy

– Required to break some of the chemical bonds that exist within the reactants

• Have a convenient orientation between the colliding reactants, which allows specific chemical bonds to be broken to start the chemical reaction



• Energy transfer in chemical reactions


Reaction Rate: The rate at which reactants are converted

into products in a chemical reaction in a given time period

– Tracking how often the chemical reaction occurs

NO2 + CO NO + CO2

Reactants Products

Chemical reaction rate


How can the rate of a chemical reaction be determined?

• 2 different ways:

– Determine how much product is being formed

in a given period of time

– Determine how much reactant is being used up (consumed)

in a given period of time


Establishing the rate of a chemical reaction

by tracking the amount of product being created

2H2O2 → 2H2O + O2Hydrogen peroxide

(liquid)Water(liquid)

Oxygen(gas)

• Evidence that the chemical reaction has taken place is the creation of the

oxygen gas (product)

– For example, if 600 mL of oxygen is produced in 7 minutes

– Reaction rate = 85.7 mL of oxygen produced per minute (or 1.43 mL per second)

Chemical reaction rate =

Change in concentration

(amount) of product or reactant

Time


Establishing the rate of a chemical reaction

by tracking the amount of reactant being used up

2C2H5OH + 3O2 → 3H2O + CO2Ethanol(liquid)

Water vapour

(gas)

Oxygen(gas)

• Evidence that the chemical reaction has taken place is the decrease in the

amount of ethanol present (reactant)

– For example, if 200 mL of ethanol is used up (combusted/burnt) in 70 minutes

– Reaction rate = 2.9 mL of ethanol consumed per minute (or 0.05 mL per second)

Chemical reaction rate =

Change in concentration

(amount) of product or reactant

Time

Carbon dioxide

(gas)

Two main factors affect the rate of a chemical reaction:


N

O O C ON

O OC O

Effective collision

• Collision which meets the activation energy• Collision has a convenient orientation with the carbon

(from CO) and the oxygen (from NO2) colliding

– The speed of the collisions between the reactant molecules

• The higher the speed of the reactant molecules,

the larger the collision energy

– High collision energies are likely to meet the activation energy

– How often collisions occur between the reactant molecules

The factors below have affect one or both of:

• The number of collisions between reactant molecules

• The energy of the collisions between reactant molecules


Catalysts– Catalysts lower the activation energy

• Energy needed from the molecular collisions to begin the chemical reaction decreases

– Catalysts are not consumed in the reaction • Catalysts can be reused in future chemical

reactions

Amount (concentration) of

reactant molecules present– Reaction rate increases as concentration

increases• Increased rate of collisions between

molecules

Temperature – Reaction rate increases as temperature

increases• Increased rate of collisions

• The energy of the molecular collisions increases, as the reactant molecules are moving more quickly

Physical state of the reactant molecules– Chemical reactions occur faster between

reactants in the same physical state• Gas-gas interaction are the fastest

– Allows for highest rate of molecular collisions


Reactant Concentration

– Increasing the concentration of one or more types of reactant molecules:• Increases the amount

of collisions between reactant molecules

• Effective collisions occurs more frequently, which increases the reaction rate

Amount (concentration) of

reactant molecules present– Reaction rate increases as concentration

increases• Increased rate of collisions between

molecules


Low reactant concentration High reactant concentration


• Normal body temperature: 36.5 and 37.4ᵒC– Increasing the body temperature causes:

• An increase in the rate of the biochemical reactions that occur in the body

• An increase in both the breathing and heart rate

• Hyperthermia:

Core body temperature above 41ᵒC– Rate of biochemical reaction rate increases

• Hypothermia:

Core body temperature below 36ᵒC – Rate of biochemical reaction rate decreases


Temperature – Reaction rate increases as temperature

increases• Increased rate of collisions

• The energy of the molecular collisions increases, as the reactant molecules are moving more quickly

Temperature

– High temperatures increase the rate of the chemical reaction

• Molecules move faster & collide more frequently

• The reaction rate doubles for every 10ᵒC increase in temperature

– Low temperature decrease the rate of the chemical reaction

• Molecules move more slowly & collide less frequently


N

O O C ON

O OC O

• High energy collision, which meets the activation energy• Collision has a convenient orientation with the carbon (from CO)

and the oxygen (from NO2) colliding


High temperature: 40°CEffective collision


N

O O C ON

O OC O

• Collision has a convenient orientation with the carbon (from CO) and the oxygen (from NO2) colliding

• Low energy collision, which does not meet the activation energy


Low temperature: 5°CUnsuccessful

collision


Catalyst: A substance that increases the reaction rate without being consumed in the chemical reaction

– A specific catalyst lowers the activation energy of a specific chemical reaction

• Due to the lower activation energy, more molecular collisions between reactants will be successful

– Increases the reaction rateStoker 2014, Figure 9-10 p251

Catalysts– Catalysts lower the activation energy

• Energy needed from the molecular collisions to begin the chemical reaction decreases

– Catalysts are not consumed in the reaction • Catalysts can be reused in future chemical

reactions


• Activation energy required for the above

reaction to proceed is

90 units of energy– Activation energy with catalyst present is

70 energy units

• Lower activation energy due to the presence

of the catalyst

NO + O3 NO2 + O2

C1 C2 C3

Activationenergy

Energy units

100

0

50

Collisions

1 effective collision

2 unsuccessful collisions

C1 C2 C3

Lower activation

energyEnergy units

100

0

50

Collisions

2 effective collisions

1 unsuccessful collision

No catalyst

Catalyst present

3 different molecular collisions

occur between NO + O3:

– C1: 100 units of energy from collision



Enzymes are the catalysts of the human body:

• Enzymes allow chemical reactions in the body to occur quickly enough to keep us alive– All enzymes are proteins

• Specific enzymes decrease the amount of energy required to begin specific chemical reactions – Decrease the activation energy

Timberlake 2014, Figure 3, p.737


Progression through a chemical reaction:

– Start- step 1: The chemical bonds holding the reactants together are broken• Chemical bond breakage requires an energy input

• Example below: Chemical bonds broken within methane and oxygen

– Middle- step 2: Once the chemical bonds have been broken, the atoms rearrange to adopt new positions

• Example below: Carbon, hydrogen and oxygen atoms rearrange

– End- step 3: After atom rearrangement, new chemical bonds form between the atoms creating the products

• Chemical bond formation releases energy

• Example below: New chemical bonds are formed to produce carbon dioxide and water

Energy transfer in chemical reactions

• Chemical reactions include breaking of old chemical bonds (in the reactants) & the formation of new chemical bonds (in the products)

• Overall, a chemical reaction can either release or absorb energy, depending on the reaction

Energy transfer

in chemical reactionsActivation Energy: The minimum amount of energy from the collision between two reactant molecules that will allow the chemical reaction to begin

A chemical reaction with a high

activation energy:

– A large amount of energy input

is needed to begin the chemical

reaction

• Few collisions between

reactant molecules meet the

activation energy = the

chemical reaction proceeds at

a slow rate

High Activation

energyEnergy units

200

0

100

Collisions

Few effective collisions

Many unsuccessful

collisions

• Chemical reaction with a high activation energy of 150 energy units

– Most collisions will be unsuccessful,

as the energy of the molecular

collisions will frequently be below the

activation energy

• Few chemical reactions take place

Activation Energy:

The minimum amount of energy from the collision between two reactant molecules that will allow the chemical reaction to begin

A chemical reaction with a low

activation energy:

– A small amount of energy input

is needed to begin the chemical

reaction

• A large amount of collisions

between reactant molecules

meet the activation energy =

the chemical reaction proceeds

at a fast rate

Low Activation

energy

Energy units

200

0

100

Collisions

Many effective collisions

Few unsuccessful collisions

• Chemical reaction with a low activation energy of 50 energy units

– Most collisions will be effective

(successful), as the energy of the

collision will frequently be above the

activation energy

• Many chemical reactions take place

Energy transfer

in chemical reactions

High Activation

energyEnergy units

200

0

100

Collisions

Few effective collisions

Many unsuccessful

collisions

Low Activation

energy

Energy units

200

0

100

Collisions

Many effective collisions

Few unsuccessful collisions

High activation energy chemical reaction Low activation energy chemical reaction

Few effective collisions = few chemical reactions

Many effective collisions = Many chemical reactions

Energy transfer in chemical reactions

Exothermic vs endothermic reactionshttps://www.freeimages.com/photo/blue-flame-1402795

https://www.freeimages.com/photo/leaf-detail-1153686

Exothermic reaction Endothermic reaction

Wax candle burning (combustion reaction)

Photosynthesis (makes glucose)

Exothermic reactions release energy

Endothermic reactionsabsorb (require) energy

2C22H46(wax) + 67O2 → 44CO2 + 46H2O + energy 6CO2 + 6H2O + energy → C6H12O6(glucose) + 6O2

Exothermic vs endothermic reactions

Endothermic

chemical reactions

• Overall, energy is absorbedby the reaction

• High amount of energy needed to start the reaction (high activation energy) = low rate of reaction (occurs slowly)– Energy seen on the reactant

side of the reaction (energy consumed)

Exothermic

chemical reactions

• Overall, energy is releasedby the reaction

• Low amount of energy needed to start the reaction (low activation energy) = high rate of reaction (occurs readily)– Energy seen on the product

side of the reaction (energy produced)


Exothermic Reaction

• Exothermic reactions release energy (often in the form of heat)

• The products of an exothermic reaction contain less energy than the reactants

• Example: – 3H2 +N2 → 2NH3 + 22.0 kcal energy

Stoker 2014, Figure 9.7, p248


Endothermic Reaction

• Endothermic reactions absorb energy

• The products of an endothermic reaction contain more energy than the reactants

• Example: – H2O + 137 kcal energy → 2H2 + O2

Stoker 2014, Figure 9.7, p248

Is a chemical reaction with a high or low

activation energy more likely to take place? Why?

For a chemical reaction with a high activation energy, will

the reactants be converted into products readily or slowly?

Explain.

For a chemical reaction with a low activation energy, is more

energy released or consumed overall by the reaction?

Explain.

Key concept: chemical reactions, activation energy

Attempt Socrative questions: 5 to 9


Room name:





– The chemical reaction rate is the speed that reactants are

converted into products

• Chemical reaction rate can be determined by:

– Tracking the number of products created in a specific time period

– Tracking the number of reactants used up in a specific time period

– The rate of a chemical reaction is largely determined by:

• The number of collisions between the reactant molecules

• The speed of the collisions between the reactant molecules

– Other factors that affect chemical reaction rate:

• Temperature

• Amount (concentration) of reactant molecules

• Presence or absence of a catalyst

• Physical state (solid, liquid or gas) of the reactant molecules


• Energy transfer in chemical reactions– To begin a chemical reaction, an energy input is required to break some of the

existing chemical bonds present in the reactants

• The energy input is the activation energy

– After atom rearrangement, new chemical bonds are formed in the products, which releases energy

• The activation energy is the minimum amount of energy from the collision between two reactant molecules that will allow the chemical reaction to begin

• If a molecular collision exceeds (or is equal to) the activation energy, the chemical reaction begins

• If a molecular collision is lower than the activation energy, no chemical reaction occurs

– Chemical reactions with a high activation energy, require a large energy input

• Few molecular collisions meet the activation energy, resulting in a low reaction rate

– Chemical reactions with a low activation energy, require a small energy input

• Many molecular collisions meet the activation energy, resulting in a high reaction rate



– Exothermic reactions are those that overall release energy

• Energy is one of the products

• Exothermic reactions have low activation energies and high reaction rates

• Example:

– Combustion reactions: burning a wax candle

– Endothermic reactions are those that overall consume energy

• Energy is one of the reactants

• Endothermic reactions have high activation energies and low reaction

rates

• Example:

– Photosynthesis: where energy is consume to make the energy rich glucose


• Reversible vs non-reversible chemical reactions


• Re-establishing chemical equilibrium

• Biologically relevant reversible reaction

Reversible vs non-reversible chemical reactions

Reversible chemical reactions can proceed in both the forward and reverse directions

– Shown by a double arrowN2 + 3H2 2NH3

CH4 + 2O2 CO2 + 2H2O

Non-reversible chemical reactions proceed in the forward direction only

– Shown by a single arrow

Chemical equilibrium:

A chemical equilibrium is achieved when the forward and reverse reactions occur at the same rate

N2 + 3H2 2NH3

N N H H

H H

H H

NH H

H

NH H

H

Chemical equilibrium

• Once a chemical equilibrium is established:– The rate of the forward reaction =

the rate of the reverse reaction

– The concentrations (amounts) of reactants & products do not change• As quickly as the products are made via the

forward reaction, other product molecules are converted back into reactants via the reverse reaction

• A chemical equilibrium is dynamic– Both forward and reverse reactions are

occurring at the same time• Neither reaction stops during a chemical

equilibrium

N2 + 3H2 2NH3

Reverse reaction:

2NH3 N2 + 3H2

Ammonia (2NH3) used to make nitrogen and hydrogen

• Amount of ammonia decreases

• Amount of nitrogen and hydrogen increases

Forward reaction:

N2 + 3H2 2NH3

Nitrogen and hydrogen used to make ammonia (2NH3)

• Amount of nitrogen and hydrogen decreases

• Amount of ammonia increases

Reversible chemical reaction at equilibrium

The amount of ammonia, hydrogen and nitrogen created = the amount of ammonia, hydrogen and nitrogen consumed

N2 + 3H2 2NH3

Reversible chemical reaction at equilibrium

The amount of ammonia, hydrogen and nitrogen created = the amount of ammonia, hydrogen and nitrogen consumed

• Once a chemical equilibrium is established:

– The rate of the forward reaction =

the rate of the reverse reaction

– The concentrations (amounts) of N2 , H2 (reactants) and NH3

(product) do not change

• As quickly as the NH3 molecules are made via the forward reaction,

other NH3 molecules are broken down into N2 and H2 molecules via the

reverse reaction

• Equilibrium is not permanent

for a reversible chemical

reaction

– Equilibrium can be lost due to a stress

– Examples of stresses:

• Change in the amount of one or more

of the reactant or product molecules

• Change in temperature

Re-establishing chemical equilibrium

• Once a stress is applied to a chemical

reaction at equilibrium:

– According to Le Châtelier’s Principle:

the chemical reaction adjusts to remove

the stress in order to re-establish

equilibrium

• Ways that a chemical reaction can adjust to a

stress:

– Increase the rate of the forward reaction

– Increase the rate of the backward reaction



• The above chemical reaction is at equilibrium until a

stress pushes the reaction out of equilibrium

– Stress applied: adding more NH3 (product)

N2 + 3H2 2NH3

– Remove the added NH3 (product) by increasing the rate of the reverse reaction• More NH3 (product) will be broken down into the N2 + 3H2 reactants

• Once enough of the added NH3 has been broken down via the reverse reaction, the rates of the forward and reverse reactions will return to the same rate and equilibrium will be re-established

• What is the best way for the chemical reaction to remove the

stress and re-establish equilibrium?




– Stress applied is the adding more H2 (reactant)

N2 + 3H2 2NH3

– Remove the added H2 (reactant) by increasing the rate of the forward reaction• More H2 (reactant) (and N2) and will be converted into the NH3 product

• Once enough of the added H2 has been converted to NH3 via the forward reaction, the rates of the forward and reverse reactions will return to the same rate and equilibrium will be re-established






– Stress applied is the removal of N2 (reactants)

N2 + 3H2 2NH3

– Increase the amount of N2 by increasing the rate of the reverse reaction• More N2 (reactant) will be created, by breaking down the NH3 product into the N2 and H2

reactants

• Once enough of the NH3 has been broken down into N2 and H2 via the reverse reaction, the rates of the forward and reverse reactions will return to the same rate and equilibrium will be re-established



Biologically relevant reversible reaction• The haemoglobin (Hb) protein in our blood can bind to

either oxygen or carbon monoxide (CO) in the reversible chemical reaction shown below

CO

CO

CO

Haemoglobin

O2CO

CO

Oxygen molecule

Carbon monoxide compound

Hb(O2)4 + 4CO ⇋ Hb(CO)4 + 4O2

O2

O2

O2

O2

CO

CO CO

CO

O2O2

O2O2

• The chemical bonds that attach haemoglobin to CO are 300 times stronger than

between haemoglobin and O2

– The reversible reaction favours the right-hand side, meaning more haemoglobin bind CO than O2

• Once haemoglobin binds CO, it is not available to bind to O2

• Hb(CO)4 is even more red than haemoglobin with oxygen bound – Can show as a red flushed face

Biologically relevant reversible reaction• The haemoglobin (Hb) protein in our blood can bind to

either oxygen or carbon monoxide (CO) in the reversible chemical reaction shown below

CO

CO

CO

Haemoglobin

O2CO

CO

Oxygen molecule

Carbon monoxide compound

Hb(O2)4 + 4CO ⇋ Hb(CO)4 + 4O2

O2

O2

O2

O2

CO

CO CO

CO

O2O2

O2O2

• To treat carbon monoxide poisoning, the reversible reaction must be shifted to the left to allow haemoglobin to bind to oxygen– Increasing the O2 will shift the reversible reaction to the left,

to use up the excess oxygen• Oxygen will bind to haemoglobin instead of carbon monoxide

– CO can be exhaled

With reference to the rate of the

forward and reverse chemical reactions,

what is a chemical equilibrium?

What may disrupt a chemical equilibrium?

Why would the factor you have identified

disrupt the chemical equilibrium?

In the above reaction, would the addition of more product (NH3)

increase the rate of the forward or reverse reaction? Why?

Key concept: equilibrium, forward and reverse reactions

N2 + 3H2 2NH3

Attempt Socrative questions: 10 and 11


Room name:




• Reversible vs non-reversible chemical reactions

– Reversible reactions can proceed in either the forward or reverse direction

• Shown by a double-headed arrow

– Non-reversible reactions can proceed in only the forward direction

• Shown by a single-headed arrow


– Chemical equilibrium occurs when the rate of the forwards and reverse reactions are equal (in a reversible reaction)

• Both the forward and the reverse reactions are occurring at equilibrium

– Once equilibrium is established, the concentration (amount) of the reactants and products does not change


• Re-establishing chemical equilibrium– Equilibrium is not permanent and chemical reactions can be pushed out of

equilibrium by stresses such as:• Change to the amount of a specific reactant or product molecule

• Change in temperature

– According to Le Châtelier’s Principle, the chemical reaction adjusts to remove the stress in order to re-establish equilibrium by either:• Increasing the rate of the forward reaction

• Increasing the rate of the backward reaction

– The reversible reaction attempts to return to equilibrium by accelerating either the forward or the reverse reaction, to remove the added stress

• Biologically relevant reversible reaction– Haemoglobin binds to either oxygen or carbon monoxide in a reversible reaction

– By adding extra oxygen molecules, the haemoglobin is forced to attach to oxygen in preference to carbon monoxide

Readings & Resources• Stoker, HS 2014, General, Organic and Biological Chemistry, 7th edn,

Brooks/Cole, Cengage Learning, Belmont, CA.

• Stoker, HS 2004, General, Organic and Biological Chemistry, 3rd edn, Houghton Mifflin, Boston, MA.

• Timberlake, KC 2013, General, organic, and biological chemistry: structures of life, 4th edn, Pearson, Boston, MA.

• Alberts, B, Johnson, A, Lewis, J, Raff, M, Roberts, K & Walter P 2008, Molecular biology of the cell, 5th edn, Garland Science, New York.

• Berg, JM, Tymoczko, JL & Stryer, L 2012, Biochemistry, 7th edn, W.H. Freeman, New York.

• Dominiczak, MH 2007, Flesh and bones of metabolism, Elsevier Mosby, Edinburgh.

• Tortora, GJ & Derrickson, B 2014, Principles of Anatomy and Physiology, 14th edn, John Wiley & Sons, Hoboken, NJ.

• Tortora, GJ & Grabowski, SR 2003, Principles of Anatomy and Physiology, 10th edn, John Wiley & Sons, New York, NY.