Líf í AlheimiKennari: Ágúst Kvaran

F01 29.1.2013

Lecture plan - chemistry

· Atoms - chemical bond· Carbon chemical bond· Atoms and molecules in space;Information derived from spectroscopy· Molecules in the universe;Existance and formation· Interactions between light and matter;photochemistry, photoionization, photofragmentation· Thermochemistry in the universe· Biochemistry

The atomic model

Atoms are made of nuclei, which consist protons(p+) and neutrons(n), and electrons( e−).The diameter of an atom is on the scale of 0.1nm ' 1 angstrom. The simplest atom is theHydrogen atom, 1 e− and 1 p+.Niels Bohr's atomic model suggests that the electron has a wave property. Waves have afunction, Ψ and so the electron should also have its function. By taking the square of Ψone gets the probability distribution. If the electron has this wave property it will have aprobability distribution around the nucleus and therefore di�erent probabilities of �ndingthe electron.If two waves are out of phase they will cancel each other out. Out of phase orbits aretherefore not possible because if there is no wave there is no electron. If the waves are onthe other hand in phase, they get bigger and form a standing wave, �giving� the electron anorbit.

(a) Electron's wave function and prob. distribution

(b) Waves out of phase, deconstructiveinterference

(c) Waves in phase creating a standingwave

Wave properties of electrons

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By expanding this model to atoms bigger than hydrogen, a standing wave forms for eachorbit. In between the waves they cancel due to deconstructive interference. This explainswhy only certain orbits are allowed and others not, making the orbits quantized.

(a) Standing waves in an extendedatomic model

(b) Allowed/Quantized orbits

Extended atomic model

The energies of orbits are

E = −Rn2

where n take positive integer values and n = 1 represents the closest orbit. The criteria forquantum energy levels are the standing waves.

Energies of orbits

But how to consider all this in three dimensions? By looking at the probability distributionof the electron the 2D orbit is approximately where the maximum probability of �nding thee− is. But in theory, the e− could be essentially everywhere because of the prob. distribution.Now, by extending this distribution around the nucleus the orbit is acquired from all themaxima of the distributions. This creates a so called probability space and the probabilityof �nding the e− is the same on the space's boundary. The s orbitals form a sphericalprobability space.By searching for points with the same probabilities, Ψ2(r, θ), one gets the p, d and f orbitals.These orbitals however don't form a spherical space. They form a sort of �balloon-ee� orbitals.These orbitals are the basis of the periodic table.One familiar with the Pauli exclusion principle knows that two electrons can not occupy thesame quantum state. Each orbital can therefore only contain two electrons, with spins upand down.

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(a) Maxima of prob. distribution form-ing s orbitals

(b) Points of same probability formingp orbitals

Forming the orbitals

(a) Shapes of the orbitals

(b) Spins of electrons

Orbitals and spins

Screening

The electrons �want� to be in the lowest energy state.

H : 1s1 ground stateH∗ :> 1s1 excited stateC : 1s2 2s2 2p2 ground stateC∗ : 1s2 2s2 2p1 3s1 exapmlary excited state

The valence electrons are the highest energy electrons. Inner/core electrons have lower energyand are closer to the core. Valence e− can �go everywhere� and are usually outside the coree−. s→ p→ d; e− moves further away from core e− and distorts the energy diagram of thehydrogen atom. Elements are grouped in the periodic table by valence electrons.

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Relationship between atoms and valence electron orbitals

Molecules

Lets take the bonding of two hydrogen atoms as an example. It is possible to either add orsubtract the wave functions and then take the square to �nd the probability distribution ofthe electrons. The two atom orbitals become two molecular orbitals.

2(Ψ21s)⇒

{(Ψ1s −Ψ1s)

2

(Ψ1s + Ψ1s)2

(a) Net repulsion forces: antibonding (b) Net attraction forces: bonding(Chemicalbond)

Molecular orbits by subtracting/adding wave functions

By adding the wave functions the system becomes more stable to make a molecule(lowerenergy tendencies). The molecular energies(orbitals) become quantized.

A∗, AB∗ → High energy electron con�guration - excited statesA, AB → Low energy electron con�gurations - ground states

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Líf í AlheimiKennari: Ágúst Kvaran

F02 31.1.2013

Chemical bonds

Lets look at the four elements associated with life in the universe

H, C, N, O

Notation of H2 chemical bonding

Carbon has four valence electrons. It is impossible to distinguish between electrons. Thecore electrons are not needed for consideration, only valence electrons are important. Theconventional energy diagram gets distorted a bit, creating four sp3 orbitals instead of one sand three p. Because electrons repel each other, the valence electrons try to be as far fromeach other as possible.

(a) Carbon and its valence e− (b) Energy diagram for carbon

Carbon valence electron placement and energies

Nitrogen has three valence e− and therefore one paired sp3 orbital and three unpaired.Oxygen has two valence e− and two unpaired sp3 orbitals. By combining carbon, nitrogenand oxygen with hydrogen one gets: CH4 - methane, NH4 - ammoniak and H2O - water.

Valence electrons

H 1O 2N 3C 4

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(a) Methane (b) Ammoniak (c) Water

Molecules made from H, C, N and O

Here an emphasis will be on carbon chemistry, because of its importance for life on earth.Also, energies of the atoms will be related to the periodic table.

In the universe there are mostly atoms in the 1st and 2nd line of the periodic table.

H ∼ 75 %He ∼ 25 %rest < 1 %

Most of the �rest� part are elements in the 2nd line of the periodic table.

As mentioned before, carbon has four valence electrons. This fact is a very important andinteresting one, especially on hybridization(forming the 4xsp2 orbitals).In chemistry, hybridization is the concept of mixing atomic orbitals to form new hybridorbitals suitable for the qualitative description of atomic bonding properties. Hybridisedorbitals are very useful in the explanation of the shape of molecular orbitals for molecules.It is an integral part of valence bond theory.Valence electrons in molecules will try to be as far away from each other as possible. As aresult a maximum angle will be between them.In chemistry, pi bonds (π bonds) are covalent chemical bonds where two lobes of one involvedatomic orbital overlap two lobes of the other involved atomic orbital. Pi bonds are usuallyweaker than sigma bonds. From the perspective of quantum mechanics, this bond's weaknessis explained by signi�cantly less overlap between the component p-orbitals due to theirparallel orientation. (2p orbitals with unpaired electrons form a molecular orbital.)

Two p-orbitals forming aπ bond

Max angle of CH4 andhybridization

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(a) Angle (b) Molecule(c) Simple schematic

Angle and hybridization of C2H4

(a) Orbitals

(b) Schematic

Angle and hybridization of C2H2

More examples

Lazy, but convenient notation

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Di�erent isomers

Chirality

A chiral molecule is a type of molecule that has a non-superposable mirror image. The featurethat is most often the cause of chirality in molecules is the presence of an asymmetric carbonatom. The term chiral in general is used to describe an object that is not superposable onits mirror image. Achiral (not chiral) objects are objects that are identical to their mirrorimage. Human hands are perhaps the most universally recognized example of chirality.Chrial isomers/chirality - left/right hand molecules. Only di�er in terms of symmetry butcan have completely di�erent properties. Amino acids have chiral isomers, for exampletryptophane(basic unit in proteins/enzymes)

Chirality

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Tryptophane

Carbon containing molecules have a very large variety in structure because of carbon's ��ex-ibility�. Carbon-chemistry: organic- and bio-chemistry. Adenine is a good example. Itis a building block of DNA, along with bla, ble and blu. Carbon also plays a big role inBio-compounds and macromolecules in life.

Adenine

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Líf í AlheimiKennari: Ágúst Kvaran

F03 5.2.2013

Forces, potentials and energies

Atoms have an attraction force acting between them. It grows stronger and stronger as theatoms get closer to each other.

F = −dUdr

When the electron clouds start overlapping, the huge repulsion force starts to have e�ect.

Net force with respect to atomic distance

Instead of the regular energy levels of a single atom, molecular energy levels are not reallylevels, but form potential wells at each level. With rising energy the energy levels becomedenser.

Molecular potential wells at energy levels

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The molecule vibrates inside the potential well, it is restricted within the potential. Theparticles are moving and have a wave property. From this quantum energy levels are deri-ved(similar to orbital quantum energy levels). Standing waves are nescessary to form quant-um energy levels. Out of phase waves will only canel each other out. Faster vibrations higherin potential well.

Vibrations within potential well

Vibrations within potential well

Spacing between rotational levels get bigger and bigger with increasing energy levels. Fasterrotations with rising energy levels.

Rotational energy levels

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Molecules form and get �more stable�, i.e. they have lower energy levels than atoms. Asmentioned earlier, molecular energy levels are not levels, but potentials. The bottom of thosepotential wells is approximately the energy level. Each potential curve has vibrational levelsand vibrational levels have rotational levels. This gets more and more complex with risingenergy.

Energy levels: Atomic, molecular, vibrational, rotational

Di�erent types of light(radiation) excite di�erent energy levels.

Blue/ultraviolet E(n); molecule gets excitedInfrared E(v); vibrations get excited

Microwaves E(J); excite rotations

Each factor has its characteristic parameters. These parameters are acquired from excitationof di�erent energies and compared with databases to determine molecules. This is whatspectroscopy is all about.

Characteristic parametersAtoms RA

Molecules RAB, δAB

Vibrations CAB

Rotations BAB

Absorbtion and emission

A beam of light from a distant object passes through numerous intervening gas clouds ingalaxies and intergalactic space. These clouds subtract speci�c colors from the beam. Theresulting absorbtion spectrum is used to determine the distances and chemical compositionof the invisible clouds. If there are for example three clouds, it will not be able to determinefrom which cloud the absorbtion lines belong.

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Examplary absorbtion spectrum

For emission it is di�erent. Molecules are in excited states due to vibrational/rotational/electronicenergy and go down an energy level or many energy levels, emitting energy while doing so.Electronic level emission (En) emits ultraviolet light (λ ∼ nm), vibrational (Ev)emit infraredlight (λ ∼ µm) and rotational (EJ) emits microwaves (λ ∼ cm).

Molecular clouds in space absorb light(ultraviolet photons) from light sources and can thenemit themselves visible light(optical photons).

At �rst, prisms were used to deviate light to some sort of a screen which revealed thespectrum. Today electronic devices are used for this.

Lets look at the hydrogen atom. Emission lines are at di�erent wavelengths depending onthe energy transition. The same goes for the absorbtion lines.

Hydrogen emission lines

Hydrogen absorbtion lines

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Carbon monoxide, CO, is a key molecule. It is seen alot from clouds in space. The emissionlines are plotted versus frequency. The bigger the molecule is, the spectrum becomes morecomplex. Here are a few examples, all in the microwave spectra, that is, rotational emissionlines.

CO emission spectrum (microwave)

More complex spectra

Problems with detection

i) Cloud problem mentioned aboveii) Absorbtion/Emission:If we have a rotational molecule and an electromagnetic(EM) wave → only absorbtion iffrequency of EM waves is the same as rotational frequency. Also, the molecule has to bepolar. Hence, EM wave, made of Electric �eld, grabs pole of molecule and starts to rotateit. Same goes for vibrations.

Absorbtion if frequencies are the same

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However, H2 is nonpolar and doesn't absorb according to this.H-detection?H nonpolar → no absorbtion due to rotational or vibrational excitationsAbsorbtion in the vacuum UV region / a�ected by the atmosphere. i.e. molecules in at-mosphere absorb and therefore distort measurements from space. Better to measure spectrafrom space.

The solution to the hydrogen problem is that the proton and the electron are spinning. TheH atom has an excited state where spins are in the same direction. It jumps to the groundstate which has antiparallel spins and emits a photon. This can be detected because ofabundances of H and solves the space detection problem.

Hydrogen emission

If we look again at the CO spectrum. Are qualatative and quantitative analysis possible?The peak heights for the same compound di�er. That is because number of molecules indi�erent quantum energy levels is di�erent. This distribution of molecules gives the spectrum.This spectrum is temperature dependent and the distributions become di�erent with varyingtemperatures. These kind of measurements are used to determine the temperature. A good�t of measured vs. calculated values gives the temperature after comparing with databases.The kinetic energy is in contrast with the temperature.

Determine temperature

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Comparing spectra with di�erent temperatures

Large temperature variations in space: giant molecular clouds(GMC). Hot molecular cloudsare in the vicinity of stars/light energy. Cold molecular clouds are far away from stars/lightenergy.

(a) Hot MC (b) Cold MC

(c) How cold MC work

Giant molecular clouds

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Líf í AlheimiKennari: Ágúst Kvaran

F04 7.2.2013

In space, if 2 atoms collide they will not stick together and form a molecule. They willcollide and bounce away from each other. The atoms need to go down in energy to make amolecule. Their energy consists of potential energy and kinetic energy

Etot = Epot + Ekin

The atoms need to lose energy in order to �go down� into the molecular potential energywell, as described before. How is this achieved?A third body is needed. While colliding the atoms durint their collision, it jumps away withmore energy and the atoms lose energy and get trapped in the potential well. This thirdbody can be another atom or something else, a solid particle (crystal/dust particle).

(a) High energy atoms(b) Collision with a third body

(c) Molecule formed (d) How molecules form

Atomic collisions

This third body can be a surface(dust particle ∼ µm), where the atoms get stuck on surface,di�use on surface, combine and give away energy to the dust. They then go away as amolecule. Therefore the dust acts as a catalyst for molecular formation. This dust is app-roximately 1% of compounds in interstellar medium (ISM) and is typically of the order of0.1−1µm. This dust is like a cold cloud, it has solid states compounds with carbonaceous(C)or silicate(Si) core. These are normally cold particles so other atoms can di�use and combineon its surface.

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Dust surface

This is not the only way for molecules to form in space. Two molecules can collide and formby transferring energy to rotational/vibrational energy. Two colliding molecules can alsolose energy as photon in order to form a molecule.

Reactions in intersellar medium

This can be summarized in a pretty simple way:

atom + atom −→CM(s) Molecule

butatom + molecule −→ molecules

molecule + molecule −→ molecules

Two examples of reactions are

Exchange reaction: A + H3CB −→ ACH3 + BAddition reaction: H2C−−CH2 + AB −→ H2AC−CH2B

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There have been 12 di�erent atoms detected in space in molecular clouds. The most commonare: H, C, N and O (�CHON�).Lets now look at the molecular di�erence in GMC, ISM and Earth's surface.Collisions between particle needed for reactions:Collision frequency:

A+B/ZAB

A+ A/ZAA

(no. of collisions per sec per volume unit)ZAA ∝ size/d2A

ZAA ∝ velocity A = v(T,mA)ZAB ∝ [A][B]ZAA ∝ [A]2

T, mA const. : Z ′AA = [A]2

Above, d is the diameter of the atom. [A] is the concentration of A, and Z is numberof collisions per second per volume. The collision frequence parameters are size, speed,temperature and mass.

GMC ISM Earth/surfaceTemperature [K] 102 10− 20 300

Molec. density [A = molec./cm3] 106 1 1019

Collision freq. [Z ′AA = A2] 1012 1 1038

Rate ∝ ZAB, Rate ∝ f ⇒ Rate ∝ fZAB

f: High enough energy to break bonds and form new ones. Number of molecules with enoughenergy to exceed activation energy.

Probability of collision

The moving atom, A, will hit the stationary atom, B, if A's center is within a circle withB's diameter as radius(see �g). A's center needs to be within the cross section

σ = d2π

Rdotted = Dblue

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For ions this is a bit di�erent.A moving particle containing charge creates an electric �eld.The attraction force is, F ∝ 1/r2.A and B start attracting each other. Atoms with charge tend to deviate from their straightline of movement to collide with neutral atoms. This increases collision frequency drastically,and the collision cross section greatly increases, σ >> d2π.f: energy barrier

Ionized collisions

Thermal equilibrium → fewer particles with high energy (Boltzmann distribution).Higher temperature increases energy of particles→ more more can overcome energy barrier.

(a) Without catalyst (b) With catalyst

Energy barriers, Ea: activation energy

Dust can help in breaking of bonds. Molecule(AB) attaches to dust and gets split intoatoms A and B. Another molecule arrives and bonds with A and B, then leaves the dust.

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Dust acts as a catalyst

The dust decreases the energy barrier/activation energy → catalysis e�ect. This makesthe dust particles important, key to forming molecules. This catalysis e�ect increases f .

Dust surface reaction

Radicals

Atom/molecular fragments with unpaired electrons. They are reactive because e− want topair, i.e. reactivity determined by electron pairing. Unpaired electrons enhance ractivity.Radicals therefore tend to pair. The energy barrier is very small.

Low energy barrier for radical reactions

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Líf í AlheimiKennari: Ágúst Kvaran

F05 7.2.2013

Cosmic rays

Ions and radicals?Created by radiation:

-Cosmic rays; p+ 84%, He2+/α 14%, cores 2%. Cosmic rays are made of particles. Cos-mic rays can also dissociate molecules.

-Electromagnetic waves from stars Waves carry energy

Ions:radiation + AB −→ AB+ + e�

hν+AB −→ AB+ + e�

p+ + AB −→ AB+ + e�

He2+ + AB −→ AB+ + e�

.

.

.Radicals:

radiation + AB −→ A + Bhν+AB −→ A + Bp+ + AB −→ A + BHe2+ + AB −→ A + B

→ Energy can be transferred to molecules(excite molecules)→ Electrons can go away, leaving the molecule as an ion: Photoionization.Ionization energy di�er from various atoms/molecules.

(a) Ionization energy. Middle column:energy needed, right column: max λ

(b) Bond energies, 102 nm ∼ UV

Ionization and bond energies

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Electron-ion and electron-molecule reactions

C2H2 being radiated→ dissociate→ form big molecules... life?This is considered a possible reason for the creation of big organic molecules in space.

Radiation of C2H2

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Laser experiment

Ground state of C2H2 is inert and linear.Excited state(valence e− in higher energy orbitals) behaves much di�erently. It dissociatesand forms radicals.

(a) Radicals from C2H2

(b) Excitement of ground state of C2H2

C2H2

Radiation excites molecules→ dissociates → forms radicals

Ionized fractions with high enough energy form organic molecules. These fractions/radicalsformed from dissociated C2H2 because of cosmic rays.

Hydrocarbon reactions

H+

3 hot stu� today!

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Líf í AlheimiKennari: Ágúst Kvaran

F06 7.2.2013

Entropy and free energy

The entropy, Stotal of the Universe increases, i.e. ∆Stotal > 0 for an isolated system. Letslook at the Universe as our isolated system. Is a system is an isolated system, it will reacha maximum in entropy. Stot(max) is not nescessarily possible in the Universe. Entropy as awhole in the universe is increasing.If S ↑, some changes/evolutions are occuring within the system.Equilibrium: change/evolutions do not occur.

Entropy in the Universe as an isolated system. The path can be a reaction, evolution of agalaxy etc. (NOT time)

Forming a solar system resulsts in a negative entropy change ∆Ssolar system < 0. Otherentropy change has to be bigger for a positive total entropy change

→ ∆Stot = ∆Ssolar system + ∆Sother > 0.

Other examples can be where two liquids form a crystal in an isolated system:

∆Sreaction < 0, ∆Sother > 0, → ∆Stotal = ∆Sreaction + ∆Sother > 0.

or the creation of life, where molecules are gathered to form bigger things, whether it issmall, or a human being:

∆Slife < 0, ∆Sother > 0, → ∆Stotal = ∆Slife + ∆Sother > 0.

G is the free energy and is proportional to the entropy in the following way:

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∆G ∝ −∆S

The free energy, ∆G is the maximum work that can be extracted from a reaction(100 %e�ciency)

Entropy and Free energy of an isolated system

Equilibrium/Inequilibrium in the universe?

In space and interstellar medium the chemistry is slow. To measure whether a system is inequilibrium or not, chemists use an equilibrium constant. This constant is calculated by theratio of chemical concentration of the products and the reagents from a process:

A + B ↽−−−⇀ C + D

[C][D]

[A][B]= K

Measurements imply that there is inequilibrium in the Universe.

Particles with high energy become less frequent → Boltzmann distribution.By passing the energy barrier and increasing concentration on right side, until there areequal numbers of molecules above the energy barrier on each side results in equilibrium(See�g). In equilibrium, the free energy is equal to zero, ∆G = 0, but in inequilibrium, it isnegative, ∆G < 0.

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System in equilibrium

(a) Equilibrium (b) Inequilibrium in ISM

HNC −→ HCN

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Equilibrium vs. inequilibrium

Work from reaction

The �rst law of thermodynamics:

∆U = internal energy = w + q

There is an instance where the work can be used again to get the reagents(by adding someheat). That is a state of equilibrium between system and surroundings.

wmax + qmin ⇒ ∆G = wreversible

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Líf í AlheimiKennari: Ágúst Kvaran

F06 7.2.2013

Inequilibrium is the driving force for things to happen.

In the human body a lot of chemical reactions occur. Lets look more closely at carbo-hydrates. They are broken down to smaller units, glucose. The glucose is an �energy storage�which is stored in the cytoplasm.

Glucose : C6H12O6

Glucose + oxygen −→ products + Energy

Glucose comes from the cytoplasm and oxygen from the air. The products are water, whichleaves as urea and sweat, and carbon dioxide, which goes through breathing. The energy isfor keeping the body temperature and for the body to perform actions.

Reagent energy is higher than the products'

Irreversable process

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Reversable process - get much more work

Glycogen is a macromolecule of glucose. ADP/ATP is important for energy storing.The net process of glucose is

C6H12O6 + 6O2 −→ 6CO2 + 6H2O; ∆G = −2870 kJ (per mol/glucose)36ADP + 36Pi −→ 36ATP + 36H2O; ∆G = +1080 kJ

Net negative ∆G

∆G > 0 is unfavourable. In the ATP process, something with a higher |∆G| and a negative∆G is needed to make the overall process negative. That is achieved with the glucose process.ADP take energy and store it in ATP. Enzymes help with reaction steps

S + E −−⇀↽−− SE −→ P + E

Biopolymers are macromolecules

DNA is a double helix, sort of like a wound up zipper. The DNA bases are Cytosine andThymine (small units) and Adenine and Guanine (bigger units). The possible combinationsof those are A−T and G−C. They are combined by Hydrogen bonds and are ��at� molecules.

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DNA

RNA is a single stream of molecules, while DNA are double streams. The fundamentaldi�erence between DNA and RNA is that RNA have Uracil while DNA have Thymine.

DNA & RNA

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DNA & RNA

With the help of enzymes, RNA is made from information from DNA. RNA string is likeone half of the DNA double helix.

DNA is �opened� and RNA pieces are formed in the gap

RNA has hidden information on how to make proteins. mRNA attaches to ribosome(a�factory�) and produces enzymes/proteins with tRNA(small units with 3 bases).

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Protein construction

RNA amino acids

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Protein synthesis

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