Preparatory Problems Final

8/12/2019 Preparatory Problems Final

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38thInternational Chemistry Olympiad * Preparatory Problems

Problem 1: A brief history of life in the universe

Chemistry is the language of life. Life is based on atoms, molecules and complex

chemical reactions inoling atoms and molecules. It is only natural then to as! "here

atoms came from. #ccording to a "idely accepted model, the unierse began about $%

billion years ago in a big bang and has been expanding eer since. &he history of the

unierse as a "hole can be ie"ed in terms of a series of condensations from

elementary to complex particles as the unierse cooled. Of course, life as "e !no" it

today is a special phenomenon that ta!es place at moderate temperatures of the 'arth.

Light elements, mostly hydrogen and helium, "ere formed during the first seeral

minutes after the big bang in the rapidly expanding and, therefore, rapidly cooling earlyunierse. (tars are special ob)ects in space, because temperature drop is reersed

during star formation. (tars are important in chemistry, because heay elements

essential for life are made inside stars, "here the temperature exceeds tens of millions

of degrees.

&he temperature of the expanding unierse can be estimated simply using

T+ $$ - t$-

"here Tis the aerage temperature of the unierse in /elin 0/1 and tis time 0age of

the unierse1 in seconds. #ns"er $2$ through $2 "ith one significant figure. 4ound off

if you "ant.

$2$. 'stimate the temperature of the unierse "hen it "as $ second old at "hich time

the temperature "as too high for fusion of protons and neutrons into helium nuclei

to occur.

$2. 'stimate the temperature of the unierse "hen it "as about 3 minutes old and the

nuclear synthesis of helium "as nearly complete.

$23. 'stimate the age of the unierse "hen the temperature "as about 3, / and the

first neutral atoms "ere formed by the combination of hydrogen and helium nuclei

"ith electrons.

$25. &he first stable molecules in the unierse "ere possible only after the temperature

of the expanding unierse became sufficiently lo" 0approximately $, /1 to allo"

$


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atoms in molecules to remain bonded. 'stimate the age of the unierse "hen the

temperature "as about $, /.

$2%. 'stimate the aerage temperature of the unierse "hen the unierse "as about

3 million years old and the first stars and galaxies "ere born.

$2. 'stimate the temperature of the unierse presently and note that it is roughly the

same as the cosmic micro"ae bac!ground measurement 03 /1.

$26. Order the follo"ing !ey condensations logically, consistent "ith the fact that oer

77 of atoms in the expanding unierse are hydrogen or helium.

a 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1

a. 9uar!s : proton, neutron

b. $$5cells : human being

c. ;, C,


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Problem 2: Hydrogen in outer space

;ydrogen is the most abundant element in the unierse constituting about 6% of its

elemental mass. &he rest is mostly helium "ith small amounts of other elements.

;ydrogen is not only abundant. It is the building bloc! of all other elements.

;ydrogen is abundant in stars such as the sun. &hus the Bil!y ay galaxy,

consisting of oer $ billion stars, is rich in hydrogen. &he distance bet"een stars is

seeral light years on the aerage. ;ydrogen is also the ma)or constituent of the

interstellar space. &here are about $ billion galaxies in the unierse. &he empty

space bet"een galaxies is ast. ?or example, the Bil!y ay galaxy is separated from

its nearest neighbor, the #ndromeda galaxy, by million light years. ;ydrogen again isthe primary constituent of the intergalactic space een though the number density is

much less than in the interstellar space. &he aerage density of matter in the

intergalactic space, "here the current temperature is the cosmic bac!ground energy of

.6 /, is about $ atom-m3.

2$. Calculate the aerage speed, 08RT-M1$-, of a hydrogen atom in the intergalactic

space.

2. Calculate the olume of a collision cylinder s"ept out by a hydrogen atom in one

second by multiplying the cross2sectional area, d, by its aerage relatie speed

"here d is the diameter of a hydrogen atom 0$ x $ 28 cm1. Bultiply the aerage

speed by s9uare root of to get the aerage relatie speed. Bolecules "hose

centers are "ithin the cylinder "ould undergo collision.

23. Calculate the number of collisions per second experienced by a hydrogen atom by

multiplying the aboe olume by the number density. ;o" many years does it ta!e

for a hydrogen atom to meet another atom in the intergalactic spaceD

25. Calculate the mean free path of hydrogen in the intergalactic space. is the

aerage distance traeled by a particle bet"een collisions.

;ydrogen atoms are relatiely abundant in interstellar regions "ithin a galaxy, there

being about $ atom per cm3. &he estimated temperature is about 5 /.

2%. Calculate the aerage speed of hydrogen atom in the interstellar space.

3


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2. Calculate the mean free path 01 of hydrogen in the interstellar space.

26. hat do these results imply regarding the probability of chemical reactions in

spaceD

5


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Problem 3: Spectroscopy of interstellar molecules

#toms in interstellar space seldom meet. hen they do 0most li!ely on ice surfaces1,

they produce radicals and molecules. &hese species, some of "hich presumably

played a role in the origin of life, hae been identified through the use of different

spectroscopic methods. #bsorption spectra of interstellar species can be obsered by

using the bac!ground radiation as the energy of excitation. 'mission spectra from

excited species hae also been obsered. (imple diatomic fragments such as C; and

C< "ere identified in interstellar space oer years ago.

32$. &he bac!ground electromagnetic radiation in the interstellar space has acharacteristic energy distribution related to the temperature of a blac!body source.

#ccording to ienEs la", the "aelength 01 corresponding to the maximum light

intensity emitted from a blac!body at temperature Tis gien by T+ .7 x $23m

/. LetEs consider a region near a star "here the temperature is $ /. hat is the

energy in )oule of a photon corresponding to the pea! emission from a blac!body

at $ /D

hen molecules "ith non2>ero dipole moments rotate, electromagnetic radiation can

be absorbed or emitted. &he spectroscopy related to molecular rotation is called

micro"ae spectroscopy, because the electromagnetic radiation inoled is in the

micro"ae region. &he rotational energy leel of a diatomic molecule is gien by EJ+

J0J=$1h-8I"here Jis the rotational 9uantum number, his the Planc! constant, I is

the moment of inertia, R. &he 9uantum number Jis an integer increasing from and

the reduced mass is gien by m$m-0m$=m1 for diatomic molecules 0m$and mare

masses of the t"o atoms of the molecule1. Ris the distance bet"een the t"o bonded

atoms 0bond length1.

32. Carbon monoxide is the second most abundant interstellar molecule after the

hydrogen molecule. hat is the rotational transition 0change of J 9uantum

number1 "ith the minimum transition energyD hat is the minimum transition

energy of the $C$O rotation in )ouleD &he bond length of CO is $$3 pm. Compare

the transition energy of CO "ith the radiation energy in problem 32$. hat does

the result implyD &he distribution of molecules in different energy leels is related

to the bac!ground temperature, "hich affects the absorption and emission spectra.

%


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?igure 32$. Oscillogram for the lo"est rotational transition of $C$O at $$%,6

B;>. &he upper cure "as ta!en at the temperature of li9uid air, the lo"er at

the temperature of dry ice. 04eference O. 4. Filliam, C. B. Gohnson and .

Fordy. Phys. Rev.ol. 68 0$7%1 p.$5.1

323. &he e9uation for the rotational energy leel is applicable to the rotation of the

hydrogen molecule. ;o"eer, it has no dipole moment so that the transition of J

+ $ by radiation is not allo"ed. Instead a ery "ea! radiatie transition of J+ is

obsered. Calculate the temperature of interstellar space "here the photon energy

at the maximum intensity is the same as the transition energy of the hydrogen

molecule 0$;1 bet"een J+ and . &he ;2; bond length is 65 pm.


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Problem : !deal gas la" at the core of the sun

Life on 'arth has been made possible by the energy from the sun. &he sun is a typical

star belonging to a group of hydrogen2burning 0nuclear fusion, not oxidation1 stars

called main se9uence stars. &he core of the sun is 3 hydrogen 0$;1 and 5 helium

05;e1 by mass. @nder the high temperature and pressure inside the sun, atoms lose all

their electrons and the nuclear structure of a neutral atom becomes irreleant. &he ast

space inside atoms that "as aailable only for electrons in a neutral atom becomes

e9ually aailable for protons, helium nuclei, and electrons. (uch a state is called

plasma. #t the core of the sun, the estimated density is $%8 g-cm3 and pressure .% x

$$$

atm.

52$. Calculate the total number of moles of protons, helium nuclei, and electrons

combined per cm3at the core of the sun.

52. Calculate the percentage of space occupied by particles in hydrogen gas at 3 /

and $ atm, in li9uid hydrogen, and in the plasma at the core of the sun. &he

density of li9uid hydrogen is .7 g-cm3. &he radius of a nuclear particle can be

estimated from r + 0$.5 x $2$3cm10mass number1$-3. #ssume that the olume of a

hydrogen molecule is t"ice that of a hydrogen atom, and the hydrogen atom is a

sphere "ith the Hohr radius 0.%3 x $28 cm1. 'stimate your ans"er to $ significant

figure.

523. @sing the ideal gas la", estimate the temperature at the core of the sun and

compare your result "ith the temperature re9uired for the fusion of hydrogen into

helium 0$.% x $6/1.

6


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Problem #: Atmosphere of the planets

&he solar system "as born about 5. billion years ago out of an interstellar gas cloud,

"hich is mostly hydrogen and helium "ith small amounts of other gases and dust.

%2$. &he age of the solar system can be estimated by determining the mass ratio

bet"een Pb2 and @238 in lunar roc!s. rite the oerall nuclear reaction for

the decay of @238 into Pb2.

%2. &he half2life for the oerall reaction is goerned by the first alpha2decay of @238 0238

92 @

234

90 &h =

4

2 ;e1, "hich is the slo"est of all reactions inoled. &he half2life for this reaction is 5.%$ x $7yr. 'stimate the mass ratio of Pb2 and @238

in lunar roc!s that led to the estimation of the age of the solar system.

'lemental hydrogen and helium are rare on 'arth, because they escaped from the

early 'arth. 'scape elocity is the minimum elocity of a particle or ob)ect 0 e.g., a gas

molecule or a roc!et1 needed to become free from the graitational attraction of a

planet. 'scape elocity of an ob)ect "ith mass m from the 'arth can be determined by

e9uating minus the graitational potential energy, 2GMm-R, to the !inetic energy,

0$-1mv, of the ob)ect.


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&he chemical composition of the atmosphere of a planet depends on the temperature

of the planetEs atmosphere 0"hich in turn depends on the distance from the sun,

internal temperature, etc.1, tectonic actiity, and the existence of life.

#s the sun generated heat, light, and solar "ind through nuclear fusion of

hydrogen to helium, the primitie inner planets 0Bercury, Jenus, 'arth, and Bars1 lost

most of their gaseous matter 0hydrogen, helium, methane, nitrogen, "ater, carbon

monoxide, etc.1. #s the heay elements such as iron and nic!el "ere concentrated at

the core through graity and radioactie decay produced heat, internal temperature of

the planets increased. &rapped gases, such as carbon dioxide and "ater, then

migrated to the surface. &he subse9uent escape of gases from the planet "ith a gienescape elocity into space depends on the speed distribution. &he greater the

proportion of gas molecules "ith speed exceeding the escape elocity, the more li!ely

the gas is to escape oer time.

%2%. Circle the planet name "here the atmospheric pressure and composition are

consistent "ith the gien data. 'xplain.

#erage surface temperature and radius of the planet are as follo"s

Jenus 63 /A ,% !m 'arth 88 /A ,368 !m Bars $8 /A 3,373 !m

Gupiter $% /A 6$,5 !m Pluto 5 /A $,$ !m

pressure 0in atm1 composition 01 planet

a. K $ ;081A ;e0$61 0Jenus, 'arth, Bars, Gupiter, Pluto1

b. 7 CO07.51A


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Problem $: %iscovery of the noble gases

Bolecules such as ;,


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2%. Calculate the molecular "eight of nitrogen one "ould get from the density

measurement of the nitrogen prepared by the second method.

2. &o 4ayleighEs surprise, the densities obtained by the t"o methods differed by a

thousandth part N a difference small but reproducible. Jerify the difference from

your ans"ers in 23 and 2%.

26. &o magnify this discrepancy, 4ayleigh used pure oxygen instead of air in the

ammonia method. ;o" "ould this change the discrepancyD

28.


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xenon sun

$3


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Problem &: Solubility of salts

&he solubility of metals and their salts played an important role in 'arths history

changing the shape of the 'arths surface. ?urthermore, solubility "as instrumental in

changing the 'arths atmosphere. &he atmosphere of the primitie 'arth "as rich in

carbon dioxide. (urface temperature of the early 'arth "as maintained aboe the

boiling point of "ater due to continued bombardment by asteroids. hen the 'arth

cooled, it rained and a primitie ocean "as formed. #s metals and their salts dissoled

the ocean became al!aline and a large amount of carbon dioxide from the air dissoled

in the ocean. &he COpart of most carbonate minerals is deried from this primitie

atmosphere.#s life arose about 3.8 billion years ago and photosynthetic bacteria eoled about

3 billion years ago, molecular oxygen "as produced as a by2product of photosynthesis.

#s oxygen reacted "ith the metal ions in the ocean, metal oxides "ith lo" solubility

"ere deposited on the ocean floor "hich later became dry land through plate tectonic

motion. Iron and aluminum ores "ere, and still are, of particular importance as ra"

materials in human ciili>ation.

Lets consider a solubility problem using siler halides. Kspalues for #gCl and #gHr are

$.8$2$and 3.3$2$3, respectiely.

62$. 'xcess #gCl "as added to deioni>ed "ater. Calculate the concentration of Cl 2 in

e9uilibrium "ith solid #gCl. 4epeat the calculation for Hr2assuming that #gHr "as

added instead of #gCl.

62. #ssume that .$ L of $.$23B #g=solution is added to a Cl 2solution of the

same olume and concentration. hat is the concentration of Cl2 in the solution

once e9uilibrium has been establishedD hat percentage of the total chloride is in

solutionD

623. #ssume that .$ L of $.$23 B #g=solution is added to a Hr2solution of the

same olume and concentration. hat is the concentration of Hr2 in the solution

once e9uilibrium has been establishedD hat percentage of the total bromide is in

solutionD

$5


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625. 'xperimental erification of the ans"ers in 62 and 623 is difficult, because the

exact olume and concentration of the solutions are un!no"n. 4epeat the

calculations in 62 and 623 assuming that the concentration of the #g=solution is

$.$$23 B.


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Problem ': Physical methods for determination of Avogadro(s number

#ogadros number is a fundamental constant in chemistry. ;o"eer, an accurate

determination of this alue too! a long time. #ogadro 0$662$8%1 himself did not

!no" #ogadros number as it is !no"n today. #t about the time of his death,

#ogadros number determined from gas properties, such as diffusion coefficient and

iscosity, approached % x $. #ogadros number as "e !no" it today 0. x $31

became aailable only in the early th century. Lets consider three separate

approaches.

82$. #t thermal e9uilibrium, the probability of finding a molecule "ith a mass mat heighth is proportional to the Holt>mann factor, exp02E0h1-kBT1, "here E0h1 is the

graitational potential energy 0mgh, "here gis 7.8$ m-s1 and kBis the Holt>mann

constant. &hus, the number density at hfollo"s QbarometricQ distribution

( )

=

Tkhhmg

h

h

B

oexp)(

)(

0

0a1 (pherical particles of diameter .% Rm and density $.$ g-cm 3are suspended in

"ater 0density $. g-cm31 at SC. Calculate the effectie mass m of the particles

corrected for buoyancy.

0b1


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?igure 82$. Lattice structure of sodium chloride

In the roc!2salt structure one finds a face2centered cubic array of anions and the same

array of cations. &he t"o arrays interpenetrate each other. # unit cell contains 5 anions

08 centered at the apexes are each shared by 8 unit cells thus giing $ anion, and

positioned at the face centers are each shared by unit cells giing 3 anions1. # unit

cell also contains 5 cations.

823. In a celebrated oil drop experiment, Billi!an determined in $7$3 that the basic unit

of electric charge is $.%73 x $2$7coulombs. Calculate #ogadros number from this

alue and ?araday, "hich is electric charge per e9uialent 0$ ?araday + 7,57

coulomb as used by Billi!an1.

$6


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Problem ): An electrochemical method for determination of Avogadro*s

number

Hy definition, #ogadros number is the number of atoms in exactly $ g of carbon2$.

#ogadros number recommended by CO# 0Committee on ata for (cience and

&echnology1 in is .$5$%0$1$3 mol2$, "here the number in parenthesis

represents one standard deiation in the last t"o digits.

#ogadros number can be determined electrolytically. Current and time are

measured in order to obtain the number of electrons passing through the

electrochemical cell from T + IUt 0charge + current x time1. Copper electrodes "ere

used for electrolysis of .% B ;(O5. uring electrolysis, copper is lost from the anodeas the copper atoms are conerted to copper ions. &he copper ions pass through the

solution. #t the surface of the cathode, hydrogen gas is liberated through reduction of

hydrogen ions in the acidic solution. 'xperimental results are as follo"s

decrease in anode mass .3%%5 g

constant current .$ #

time of electrolysis $8 s


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Problem 1+: ,nthalpy- entropy- and stability

#ll chemical changes in liing and non2liing systems obey la"s of thermodynamics.

&he e9uilibrium constant of a gien reaction is determined by changes in Fibbs free

energy, "hich is in turn determined by enthalpy change, entropy change, and the

temperature.

$2$. ?ill in the blan!s 0a2f1 "ith all that apply from the follo"ing

e9uilibrium constant, Ke9

entropy change, VS

enthalpy change, VHfree energy change, VG

a. strongly temperature2dependent 0 1

b. closely related to bond strength 0 1

c. measure of change in randomness 0 1

d. related to the 9uantity of reactants and products 0 1

e. measure of spontaneity of a reaction 0 1

f. measure of heat released or absorbed 0 1

&he follo"ing e9uilibrium exists in the apor phase dissociation of molecular addition

compounds of donor molecules, , and boron compounds, H3.

H30g1 W 0g1 = H30g1

Kp + XYXH3Y-XUH3Y

$2. issociation constants 0Kp1 at $SC of the molecular addition compounds

Be3


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$25. hich is more critical in determining the oerall stability of these addition

compounds at $SC, enthalpy term 0VH1 or entropy term 0TVS1D

$2%. #t "hat temperature does Be3


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Problem 11: .e"is acids and bases

#cids and bases are essential for life. #mino acids hae both acidic and basic groups.

ation change "hen the boron halide forms an adduct "ith

a base such as pyridine 0C%;%


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H?3 HCl3 HHr3

VH$0!cal-mol1 2 .6 2 8.6 2 $.%

VH0!cal-mol1 2 %. 2 3.8 2 3.

Calculate VH3for the follo"ing reactions. o they agree "ith your prediction in

$$25D

H30li9.1 = C%;%


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Problem 12: Solubility euilibrium in a buffer solution

Hiochemical reactions ta!e place in buffered a9ueous enironments. ?or example, the

p; of the blood is maintained around 6.5 by the buffering action of carbonate,

phosphate, and proteins. Bany chemical reactions in the laboratory are also carried out

in buffer solutions. In this problem, letEs consider the solubility e9uilibrium in a buffer

solution.

$2$. ;( gas occupying 55 mL at (&P can be dissoled in $ mL of "ater at % oC.

Calculate the molar concentration of ;( in "ater saturated "ith ;(. #ssume that

there is no olume change in "ater upon dissolution of ;(.

$2. #ssume that e9uilibrium is established after a .$ B ?eClsolution is saturated

"ith ;( by continuously bubbling ;( into the solution.

Ksp0?e(1 + X?e=YX(2Y + 8. x $2$7at %oC 0$1

?or acid dissociation of ;(,

K$+ X;=YX;(2Y-X;(Y + 7.% x $28 01

K + X;=YX(2Y-X;(2Y + $.3 x $2$5 031

?or self ioni>ation of "ater,

K" + X;=YXO;2Y + $ x $2$5 051

In the solution, the positie charge is balanced by the negatie charge

X;=Y = X?e=Y + XCl2Y = XO;2Y = X;(2Y = X(2Y 0%1

Cross out terms that are negligibly small in the charge balance e9uation, 0%1,

in order to determine X;=Y and X?e=Y. ould you increase or decrease the p; of the

solution to precipitate more ?e(D ;o" does the increase of $ in p; affect the

concentration of ?e= ionD

$23. ;o" "ould you ad)ust the final p; of the solution saturated "ith ; ( to reduce

the concentration of ?e=from .$ B to $. x $28BD

3


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$25. Mou "ant to use acetic acid 0;O#c1-sodium acetate 0


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Hr01 = ;0g1 = ;O01 : HrN0aq1 = ;3O=0aq1.

(iler ions are added until #gHr precipitates at the cathode and X#g =Y reaches .

B. &he cell oltage is then measured to be $.6$ J. Calculate VES for the galanic cell.

$32. 'stimate the solubility of bromine in the form of Hr0aq1 in "ater at %SC.


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Problem 1: 5easuring the o6one level in air

O>one both helps protect and leads to damage of life forms. #s the oxygen leel in the

'arthEs atmosphere built up significantly about billions years ago during "hich time

the, o>one leel in the upper atmosphere also increased. &his o>one layer effectiely

bloc!ed ultraiolet radiation and made life on land possible. &oday, the o>one layer

appears to be depleting 2 deeloping a large hole 2 thus, the fate of this layer is of great

concern. On the other hand, o>one is a health ha>ard in our immediate enironment at

ground leel. It is a !ey constituent of photochemical smog.

# simple method for measuring the concentration of o>one in the ground2leel

atmosphere is as follo"s. #ir is bubbled through an acidic a9ueous solution containingiodide and the atmospheric o>one oxidi>es iodide to triiodide ia the follo"ing

unbalanced reaction

O30g1 = I[0a91 : I320a91 = O0g1 0$1

#t the end of the sampling period, the triiodide concentration is determined "ith a @JN

Jis spectrophotometer at %5 nm.

#ir "as bubbled for 3. min into $ mL of an a9ueous solution containing excess

of /I under the follo"ing atmospheric conditions pressure + 6% torr, temperature +

78 /, flo" rate + % mL min2$. &he absorbance of the resulting I32 solution "as

measured in a $.$2cm cell by using a spectrophotometer e9uipped "ith a photocell.

&he photocell resistance is inersely proportional to the light intensity. 4esistance

alues for the blan! and the sample solution "ere $.$ !and $7.5 !, respectiely.

&he molar absorption coefficient of the I32solution "as determined to be .5 x $%B2$

Ucm2$. In arious useful units, the uniersal gas constant is 4 + 8.3$556 G U / 2$U mol2$

+ .8%65 L U atm U /2$U mol2$+ .336 L U torr U /2$U mol2$+ $.786 cal U /2$U mol2$

$52$. Halance e9uation 0$1.

$52. ra" the Le"is structure for o>one.

$523. Calculate the number of moles of o>one in the sampled air.

$525. #ssuming that the gases behae ideally under the conditions used, calculate the

concentration in!!"of o>one present in the sampled air.

6


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Problem 1#: .ifesaving chemistry of the airbag

Certain chemical reactions can protect people from serious in)ury or death. &he

follo"ing chemical reactions used to be utili>ed to rapidly produce large amounts of

nitrogen gas inside an automobile airbag

ide similarD

$%25. rite a balanced e9uation for the reaction of sodium a>ide "ith sulfuric acid to

form hydra>oic acid 0;ide reacts "ith $ mL of 3 B sulfuric acid, ho" many

grams of hydra>oic acid are producedD

8


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Problem 1$: 0atalysts for the synthesis of ammonia

&he synthesis of ammonia is a prime example of ho" chemistry can be used to

improe human life. 'en though primitie liing systems had been \fixing] nitrogen to

ma!e compounds of nitrogen for hundreds of millions of years, human beings learned

to prepare ammonia only about $ years ago.

#mmonia is a source of nitrogen atom re9uired for all amino acids and is essential

in the production of fertili>er. #mino groups can be easily transformed into nitro groups

found commonly in explosies such as &ed "ithout proper conditions

or use of catalyst. In the early th century, ;aber2Hosch method "as deeloped for

ammonia synthesis using high pressure and temperature, "hich is still employed in

todayEs chemical industry. ;aber 0$7$81 and Hosch 0$73$1 "ere a"arded the e in chemistry for these contributions.

$2$. ?irst, let us see if the reaction is feasible from a thermodynamic standpoint.

Calculate the standard entropy change of the system in the follo"ing reaction


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$23. @sing the alue of VHfoyou selected aboe, calculate the entropy change at %oC

of the system and the surroundings combined.

$25. 4eaction rate is another important consideration. &he rate determining step of the

reaction, ation is the bond energy of the

nitrogen molecule 075 !G mole2$1 and that the # factor of the rate determining step

is $$3 sec2$, calculate the rate constant of atomi>ation at 8oC using the

#rrhenius rate la". Calculate the rate constant at the same temperature "hen the

actiation energy is lo"ered by half "ith a catalyst.

&he amount of catalyst used by the chemical industry is enormous. Bore than $ tons

of catalyst are used in a factory "here $ tons of ammonia can be produced daily. In

addition to the ?e catalyst that has been used since ;aber and Hosch, a 4u catalyst is

used in ammonia synthesis. Betal complex binding "ith elemental nitrogen and

hydrogen is also studied as homogeneous catalyst for ammonia synthesis in solution.

$2%. 4eactions bet"een reactants and undissoled metal catalyst can occur at the

metal surface so that the catalyst surface area affects the catalysis rate. Calculate

the mole number of nitrogen molecules adsorbed on $ !g of ?e catalyst. #ssume

that the catalyst is composed of $ m3cube 0ery fine po"der1 and that all six

faces of the cube are aailable for nitrogen adsorption. &he density of ?e is 6.8

g-cm3and the adsorption area for a nitrogen molecule is .$ nm.

$2. If a soluble, homogeneous catalyst "ith B of % g-mole is synthesi>ed for

nitrogen molecule binding, ho" many nitrogen molecules bind to $ !g of catalystD

#ssume one catalyst molecule binds one nitrogen molecule. Compare the result

"ith the number of nitrogen molecules adsorbed on the ?e surface in Problem $2

.

$26. hile ammonia is synthesi>ed under high pressure and temperature in the

chemical industry, natural ammonia is synthesi>ed from atmospheric nitrogen, .8

atm. 'n>ymes for ammonia synthesis in nature called nitrogenases are proteins

"ith cofactors that contain ?e or Bo. &he ammonia synthesis reaction by

nitrogenases is an electron transfer reaction


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#P and inorganic phosphate, and releases an energy of 3.% !G-mole. Calculate

the energy re9uired to synthesi>e $ mole of ammonia using nitrogenase. #t least

5 !G of energy is used for the synthesis of $ mole of ammonia in the chemical

industry these days.

3$


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Problem 1&: 7rom sand to semiconductors

Chemistry enables life. Chemistry also enriches life. ?or thousands of years, human

beings hae been putting sand to good use. Flass "as made from sand. Lenses "ere

made from glass and "ere used to ma!e telescopes, microscopes, eyeglasses, and

glass"are for chemical experiments.

Bore recently, sand became a starting material for semiconductors. One of the

most abundant elements in the 'arths crust is silicon, "hich is found in compounds

containing (i2O bonds. (ilica 0(iO1 is present in abundance at the earthEs surface.

?igure $62$. _2cristobalite, one structure of silica.

$62$. ;o" many (i and O atoms exist in the unit cell of _2cristobaliteD

$62. (uggest the hybridi>ed orbital of (i for this structure and guess the bond angle of

O2(i2O.

(iOis ery unreactie, yet it reacts "ith ;?. &he reaction "ith ;? may be used to etch

glass or in semiconductor manufacturing

(iO0s1 = ;?0a91 : A0a91 = ;=0a91 = ;O0l1

$623. ra" the molecular structure of A.

(ilicon can be obtained by heating silica and co!e 0a form of carbon1 at 3SC in an

electric arc furnace.

3


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$625. rite a balanced e9uation for the reaction of (iO "ith carbon. In this case,

assume that only one !ind of gas is formed "hose Le"is structure should sho"

formal charges.

$62%. (!etch the molecular orbitals of the gas formed from the reaction aboe.

&o obtain ultrapure silicon, crude silicon is treated either "ith Cl gas to gie \/or "ith

;Cl gas to gie \0.

$62. rite a balanced e9uation for the reaction of (i "ith Cl.

$626. Predict the molecular structure of \/.

$628. Is the product \0 from the follo"ing reaction 0$1 polar or notD ra" the 32

dimensional structure of 0and s!etch the direction of its dipole moment, if any

(i0s1 = 3;Cl0g1 : \00g1 = ;0g1 0$1

&he reerse reaction of 0$1 is spontaneous at $oC, depositing ultrapure silicon. &he

final purification of the silicon ta!es place by a melting process called >one refining.

&his process depends on the fact that the impurities are more soluble in the li9uid

phase than in the solid phase 0?igure $621. &he >one refining procedure can be

repeated until the desired leel of purity 0less than .$ ppb impurity1 is obtained.

33


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?igure $62. `one refining of silicon

$627. ;o" many atoms per gram in the silicon "afer hae been replaced by impurity

atoms "hen the impurity leel is .$ ppbD

Li!e all semiconductors, high2purity silicon fails to conduct electrical current until a

minimum electrical oltage is applied, but at higher oltages it conducts moderately

"ell. (emiconducting properties of silicon can be improed significantly by doping.

oping is the addition of a minor amount of a different element.

$62$. hen a small number of boron atoms replace silicon atoms in solid silicon, "hat

is the charge carrierD hat is the name for this type of doped2semiconductorD

$62$$. ra" a band diagram that can explain conductiity improement upon

replacement of some silicon atoms "ith boron atoms. (ho" in your dra"ing the

band gap change after doping.

35


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Problem 1': Self8assembly

@seful and essential structures can be made by self2assembly. In fact, life2forms "ere

first made possible by the self2assembly of cell membranes about 5 billion years ago.

(elf2assembly is a fundamental principle that generates structural organi>ation on all

scales from molecules to galaxies. (elf2assembly is defined as reersible processes in

"hich pre2existing parts or disordered components of a pre2existing system form stable

structures of "ell2defined patterns.

(ome transition metal complexes can participate in the self2assembly. ?or

example, a


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?igure $82$. &he molecular structure for #=and the pac!ing structure of #0ClO51;O.

$825. hat is the driing force for such assemblyD 0;int Its ionic compound,

#0ClO51;O, is found to float on the surface of "ater although its density is

greater than $..1

Betal complexes of &C


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$82. Point out the bond0s1 0among a2e1 "hich might be shortened "hen &C


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Problem 1): Stereochemistry 9rganic synthesis ; 1e2aoiding insect.

?igure 32$. aily maximum and minimum temperatures and glycerol content

in the free>e2aoiding larae of the goldenrod gall moth. &he structure of

glycerol is gien on the right. 04eference /.H. (torey and G.B. (tory $788

Physiol. 4e. 861

32$. hat is the "eight percent of glycerol in the insect if it could aoid free>ing at N

oC due to glycerol concentration aloneD #ssume the insect behaes as an ideal

solution. hat "ould be the osmotic pressure at this glycerol concentrationD

Comment on the resulting alues. &he free>ing point depression constant for "ater

is Kf+$.8oC-0mol-!g1.

55


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32. hat is the actual fraction of glycerol in the insectEs "et "eight in GanuaryD

hat "ould be the free>ing point of "ater in the insect in Ganuary considering the

amount of glycerol aloneD

323. In addition to free>ing point depressants, \antifree>e proteins] are !no"n to act to

aoid free>ing in animals including cold2"ater fish and many insects. &he

colligatie free>ing point depression due to antifree>e proteins is 9uite small.

'xperiments suggest that antifree>e proteins inhibit the gro"th of small ice

particles. If some threonine or aspartate side chains composing the protein are

chemically modified, the antifree>e actiity disappears. hat !ind of interactions

bet"een antifree>e proteins and ice particles are probably responsible for theantifree>e actiityD

Protein backbone

Side chains

5%


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Problem 2: >he human body

&he human body consists of cells, "hich in turn consist of atoms. #bout t"o thirds of

body "eight is "ater, "hich means that about t"o thirds of cell mass is "ater.

52$. # human body "eighing !g consists of about $ 0 1 atoms. Consider the

aerage atomic "eight of the three atoms in a "ater molecule. ?or your o"n

information, consider the aerage atomic "eight of atoms in other molecules such

as proteins, fats, and carbohydrates.

52. # human body consists of about $ trillion 0$$5

1 cells. #ssume that all humancells are cubic and identical in si>e. 'stimate the si>e of an aerage human cell

0length of the edge of the cube1 in one significant figure.

523. #ssume that all atoms in a cell are uniformly distributed. 'stimate the distance

bet"een t"o atomic nuclei in a cell.

525. 'stimate the distance bet"een the centers of mass of t"o "ater molecules in

pure "ater.

52%. 'stimate the aerage distance bet"een atomic nuclei in pure "ater. Compare

your result "ith ans"ers in 523 and 525.

5


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Problem 2#: Hemoglobin

#nother important class of compounds in the human body is proteins. Bany proteins

carry out catalytic functions. ;emoglobin, on the other hand, transports oxygen from

the lung to remote parts of the body.

%2$. &he molecular "eight of hemoglobin is about 6, g-mol. &he aerage amount

of hemoglobin in erythrocytes in $ mL of blood is $% grams. &he concentration of

hemoglobin in blood is 0 1 B.

%2. 'stimate the aerage distance bet"een t"o oxygen molecules in the air "ebreathe. #ssume frigid air at oC in "hich $ of air is oxygen.

%23. ;enryEs la" is "ritten

solubility + k;x partial pressure 0k; ;enryEs constant1

;enryEs constant for oxygen is $.3 x $ 23 mol L2$ atm2$. 'stimate the aerage

distance bet"een t"o oxygen molecules in "ater in e9uilibrium "ith air.

%25. # hemoglobin molecule can bind up to four oxygen molecules. 'stimate the

aerage distance bet"een t"o oxygen molecules in blood "hen all of the

hemoglobin is saturated "ith oxygen. Compare your result "ith ans"ers in %2

and %23 and note ho" efficiently hemoglobin concentrates and transports oxygen

to tissues "here the partial pressure of oxygen is lo".

%2%. &here are about 0 1 amino acids in hemoglobin. 'stimate using aerage

molecular "eight of amino acids and chec! against literature alues.

%2. &here are about 0 1 different !inds of amino acids in hemoglobin.

%26. &rypsin hydroly>es peptide bonds at the carboxyl group of arginine and lysine.

Consider, for example, the follo"ing peptide.

;3


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;3


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Problem 2$: 5ass spectrometry of hemoglobin

2$. If you lied in the $7th century, "hat method "ould you use to determine the

molecular "eight of hemoglobinD 'xplain.

Hrea!throughs in molecular "eight determinations of biopolymers such as proteins

"ere recogni>ed "ith the e in chemistry a"arded to ?enn for

deeloping electrospray ioni>ation mass spectrometry 0'(I B(1 and to &ana!a for

pioneering "or! leading to matrix2assisted laser desorption-ioni>ation time2of2flight

mass spectrometry 0B#LI2&O? B(1. In B#LI2&O? B(, proteins are embedded in a

crystal of @J2absorbing matrix molecules and desorbed-ioni>ed upon irradiation "ith a@J laser pulse. (ingly charged protonated protein ion, XB=;Y=, is produced as a ma)or

species from a protein "ith mass B.

2. Consider hemoglobin "ith a 6,535 a molecular "eight. #fter desorption-

ioni>ation, the XB=;Y= ion is accelerated by . !J. Calculate the energy of the

protein ion in )oule. 0coulomb x olt + )oule10e + $.$8 x $2$7coulomb1

23. &he accelerated protein ion is then allo"ed to trael $. m in an eacuated

flight tube to a detector. #ll electrical energy is conerted to !inetic energy 0mv-1.

If the flight time of the protein ion "as determined to be $.3$7 x $ 25s, "hat is the

molecular "eight of hemoglobin calculated from the flight time measurementD

hat is the mass accuracy in ppmD

25. &he flight tube is maintained under a high acuum at % oC. hat is the residual

pressure in the flight tube at "hich the mean free path of air molecules is the same

as the length of the flight tubeD (ee Problem for definition of mean free path.

#ssume that all air molecules are spheres "ith a diameter of angstroms.

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Problem 2&: Post8translational modification

ymes are not the reerse of each

other.

62$. Considering the functional groups of side chains existing in amino acids, "hat

!ind of functionality is suitable for generating more diersity o"ing to methylation

and demethylationD


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625. &"o steps ma!e up the proposed mechanism for demethylation. &he en>yme

uses ?# as a cofactor for the first step. Propose plausible mechanisms for

demethylation.

yme, amino acid residues including side chains hae eoled to proide space for

the transition state 0&(1 of the chemical transformation to exist "ith conformational and

electrostatic match. &hus, the binding affinity of this &( to the en>yme is expected to be

ery high 0if one can calculate1, stabili>ing the energy of the transition state through an

en>yme2&( complex. &his lo"ers the actiation energy of the reaction and creates rate

acceleration. If one can calculate the binding constant o"ing to the complex formation,

one could readily deduce ho" efficient the en>yme is by calculating kcat-kuncat.Ban2made en>ymes are holy grails for some chemists, because they can gie

insight about the behaior of natural en>ymes and can be used as useful synthetic and

therapeutic tools. Catalytic antibodies can be one of these !inds of artificial en>ymes.

#ntibodies hae antigen2binding sites, in "hich the target antigen binds "ith high

affinity 0K + $272$2$$B1 and "ith great specificity. &hese properties can be exploited

as actie sites in artificial en>ymes. #ntigen2binding sites may sere to specifically

recogni>e substrates and perform certain chemical reactions.

(ince these catalytic antibodies need to accommodate transition state 0&(1

structures in chemical transformations, an antigen that triggers the production of the

catalytic antibody must be designed and synthesi>ed )ust li!e the &( structure.

;o"eer, chemists cannot prepare a transition state structure because it is transient.

Instead, one can synthesi>e a stable compound that resembles the structure of the

transition state. &his ne"ly designed compound is called a transition state analogue

0&(#1. Once a &(# is made, it can be in)ected into mice to generate antibodies. &he

half2life of the &(# should be longer than "ee!s at physiological conditions to obtain

an ade9uate immune response. #fter generating as many antibodies as possible, the

most tightly binding and specific antibodies are selected as candidates for antibody

catalysts.

82$. If one of the selected antibodies has K+ $2$3B against the &(#, comparing

"ith normal antibody 0K+ $2B1 ho" much stabili>ation energy can the &(# gain

from the binding to this specific antibodyD

82. Let us assume that the &(# can be considered as the real transition state 0&(1.

&hen, ho" much rate enhancement "ill be obtained "hen "e "ill use this catalytic

%


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antibody for the intended chemical transformationD escribe this enhancement by

kcat-kuncat.

Bost scientists are interested in the specific hydrolysis of the pathogenic proteins or

peptides such as _2amyloid as the intended chemical reaction by catalytic antibodies.

#ssuming that the follo"ing reaction is the intended reaction by catalytic antibody, &(

of the hydrolysis of the amide bond should be considered to ma!e a plausible &(#.

ation or step2reaction

polymeri>ation. # fe" examples of step2reaction polymeri>ation are proided belo".

72. ra" the repeating unit in each polymer product.

;OOCCOO;

=

;.rue or false

32$. ;ydrogen is the most abundant element at the core of the sun.

32. ;ydrogen is the only element in the periodic table that can exist "ithout a

neutron. &his suggests that a neutron is essential for binding positiely charged

protons in the nucleus.

323. &he number of neutrons for heay nuclei exceeds the number of protons,

because the electrostatic repulsion bet"een protons is long2range "hereas the

strong nuclear force among the protons and the neutrons is short2range.

325. ;elium is the second2most abundant element in the unierse. &he molar ratio

bet"een hydrogen nuclei 0proton1 and helium nuclei 02particle1 is about 3 to $.

32%. ;elium "as first made in the interior of the first star in the history of the

unierse.

32. &he mass of an 2particle + x 0proton mass = neutron mass1.

326.


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Problem 31: 5olecular "eight determination of carbon dioide from

density measurements

!ntroduction

#ogadroEs principle 0$8$$1 is fundamental. ?or example, molecular "eight

determinations from gas densities are based on this principle. Canni>>aro sho"ed in

$8%8 that molecular "eights determined from gas density measurements can be used

to determine atomic "eight. ?or example, the molecular "eight of nitric oxide, nitrous

oxide, and nitrogen dioxide relatie to that of hydrogen gas, "hich Canni>>aro defined

to be , is 3, 55, and 5, respectiely. ?rom a large body of such data, one coulddeduce the atomic "eight of different elements.

Fas density measurements led to another ma)or brea!through in the $7th century.

4ayleigh and 4amsay discoered argon "hile determining the density of nitrogen gas

0see Problem 1. (oon a ne" group "as added to help complete the periodic table.

#ogadroEs principle is exemplified in the follo"ing experiment "hich inoles

determining the molecular "eight of carbon dioxide from density measurements. &his

experiment also uses the ideal gas la".

5aterials

dry ice, "ater

Apparatus

Halance "ith at least .$ g accuracy, t"o % mL flas!s "ith sidearm, rubber tubing,

rubber stopper, aluminum foil, cylinder, thermometer, barometer

,perimental %esign

3$2$. eise t"o separate procedures for determining the density of carbon dioxide at

room temperature and atmospheric pressure using dry ice as the source of carbon

dioxide.

3$2. Indicate possible sources of error and suggest "ays to minimi>e these errors.

3$23. Calculate the molecular "eight of carbon dioxide 0i1 from its density relatie to

that of air and 0ii1 using the ideal gas la".

%6


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Procedure A

$. 4ecord the ambient temperature 0T1 and atmospheric pressure 0!1.

. eigh a flas!. 4ecord %$.

%$+ %0flas!1 = %0air1 0$1

3. Place crushed dry ice at the bottom of the flas! and allo" time for sublimation to

occur. #fter a "hile, ma!e sure that there is no solid dry ice remaining and

measure the temperature inside the flas!. ait until temperature is e9uali>ed "ith

the openings loosely coered "ith aluminum foil to let carbon dioxide at room

temperature and atmospheric pressure fill the flas!, "ipe out condensed "ater on

the outer surface of the flas!, and "eigh. 4ecord .%+ %0flas!1 = %0CO1 01

5. (eal the opening of the side arm "ith a rubber stopper. ?ill the flas! to the rim "ith

"ater and measure olume of the "ater "ith a graduated cylinder. &his is the

olume of carbon dioxide in the flas! 0V1. Calculate the "eight of air, %0air1,

occupying this olume under the experimental conditions. #ssume that 68 of air

is nitrogen, $ oxygen, and $ argon. # mole of air "eighs 7. g. Calculate

%0flas!1 from 0$1 and %0air1. &hen calculate %0CO1 from 01 and %0flas!1.

%. etermine the molecular "eight of carbon dioxide from %0CO1 and %0air1.

M%0CO1 + 07.1X%0CO1-%0air1Y

. #lso determine the molecular "eight of carbon dioxide using the ideal gas la".

!V+ X%0CO1-M%0CO1YRT

Procedure /

$. Connect t"o flas!s through their side arm "ith one piece of rubber tube. 'leate

one flas! and place a sufficient amount of crushed dry ice at the bottom of this

flas!. (eal the opening of this eleated flas! "ith a rubber stopper and let carbon

dioxide gas oerflo" through its side arm, and fill the receiing 0lo"er1 flas!.

. Once a sufficient amount of carbon dioxide has oerflo"ed, "eigh the receiing

flas! filled "ith carbon dioxide after coering its openings "ith aluminum foil. &he

adantage of this procedure is that carbon dioxide in the receiing flas! is at room

temperature and atmospheric pressure.

3. etermine the olume, V, and "eight of the flas! as in Procedure #.

5. 4epeat until consistent "eight of carbon dioxide in the flas! is obtained.

%. etermine the molecular "eight of carbon dioxide as aboe.

%8


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Problem 32: %etermination of molecular "eight by free6ing point

depression

!ntroduction

#ccurate measurement of gas density "as used for the determination of molecular

"eight of gaseous compounds in the $7th century. ?or li9uid and solid compounds,

ho"eer, colligatie properties had to be used. ;ere, free>ing point depression "ill be

used to demonstrate ho" $7th century chemists estimated the molecular "eight of an

un!no"n compound and determined the molecular formula from a gien empirical

formula. ?ree>ing point depression also can be used to test #rrheniusEs theory ofelectrolytic dissociation.

5aterials

ice, sodium chloride, un!no"n compound # 0glucose1, un!no"n compound H 0sucrose1

Apparatus

thermometer or digital temperature sensor 0.$SC accuracy1, bea!er, test tube, "ire

Procedure

$. Bix enough sodium chloride "ith ice and "ater in a bea!er to bring the

temperature of the ice "ater do"n to about 28 ^ 2$SC. #dd more ice and salt as

necessary to maintain this temperature range.

. #dd seeral milliliters of "ater to the test tube 0^3 cm in diameter1. Place a

thermometer or digital temperature sensor and a "ire bent at one end to form a

ring to facilitate mixing. &hen immerse the lo"er half of the test tube assembly into

the ice bath and monitor the temperature change for about $ min "hile igorously

agitating the "ater "ith the "ire. &he temperature "ill drop sharply to a point of

super2cooling and increase slightly to the free>ing point, "here the temperature

"ill remain steady. Calibrate the thermometer or the temperature sensor to SC at

the free>ing point of "ater.

3. Prepare $. and . molal solution of sodium chloride in "ater. etermine the

free>ing point of these solutions follo"ing the procedure aboe. @sing the three

data points 0origin from >ero point calibration, $. and . molal concentration1,

construct a cure sho"ing free>ing point s. molal concentration. etermine

%7


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free>ing point constant, K&, of "ater from the slope and the anEt ;off ' factor for

sodium chloride.

2 VTf+ Kfm '

5. issole g of un!no"n compound in 8 g of "ater. #lso dissole g of

un!no"n compound H in 8 g of "ater. etermine the free>ing point depression of

these solutions and calculate molality.

%. ?rom the calculated molality and the number of grams of the compound in $, g

of solent, calculate the molecular "eight of both compounds.

. 'lemental analysis sho"ed that the compounds are simple carbohydrates. &he"eight percentages of C, ;, and O 0by difference1 for both compounds "ere

similar "ithin experimental error 0C 5^5, ; ^6, O %$^%51. (uggest

molecular formulas for compounds # and H.


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Problem 33: 5olecular "eight determination of polymer by titration

!ntroduction

Polycaprolactone 0PCL1 is a biodegradable polyester "ith a lo" melting point 0^SC1

typically prepared by ring opening polymeri>ation 04OP1 of 2caprolactone 02CL1 using

a catalyst such as tin0II1 2ethylhexanoate 0stannous octanoate1.

:

:

80aprolactone

Sn :202

PCL is fully biodegradable. ?urthermore its lo" melting point ma!es PCL a useful

component of a composite biodegradable material. ?or example, PCL mixed "ith

starch is used to ma!e cheap biodegradable trash bags.

PCL is degraded by hydrolysis of its ester lin!ages under physiological conditions

and, therefore, has also receied a great deal of attention for use as an implantable

biomaterial. PCL has been approed in certain countries for use in the human body,

and may be potentially used in drug deliery, sutures, adhesion barriers and scaffolds

for tissue repair. (o far, a ariety of drugs hae been encapsulated "ithin PCL beads

for controlled release and targeted drug deliery.

4ecently, it has been reported that the 4OP of 2CL can proceed "ith a heat in the

presence of natural amino acids. &herefore, the biocompatibility and in io safety of

PCL thus2obtained could be satisfying for medical and pharmaceutical purposes.

;.< COO;

+

O

O

Ala'i'e Capr#la"#'e

In this experiment, four 4OP reactions "ill be carried out for different time interals to

prepare polymer samples "ith arying molecular "eights. (ince the degree of

polymeri>ation 0P1 of these samples is relatiely lo" and each polymer molecule

$


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contains an end2group suitable for simple acid2base titration, the aerage molecular

"eight of the polymers can be determined by end2group analysis. # main problem in

such an approach for molecular "eight determination is finding a solent for the

polymer that is compatible "ith the titration. ?ortunately, an appropriate solent system

is aailable for PCL. PCL can be titrated "ith /O; in isopropyl alcohol-$,52dioxane

solent 0v-v+$-51 using $ phenolphthalein solution in pyridine as an indicator. &he

aerage molecular "eight, Bn, of the polymer can be calculated as follo"s from the

sample "eight and the number of moles of the end group

M(+ "eight of polymer sample in g - number of moles from end group analysis

&he degree of polymeri>ation at specific reaction time can be obtained from Mn for each

polymer sample.

P + Mt-B,

MtA molecular "eight at time t

MA molecular "eight of one monomeric unit

5aterials

0R a(d S )#des re&er t# r'sk a(d sa&ety !hrases r the )hem')as.1

L2alanine,

2caprolactone 0( 325-%1,

/O; 04 23%, ( 23-36-3725%1,

&etrahydrofuran 0&;?, 4 $$2$723-36, ( $272331,

methanol 04 $$23-5-%237-3-5-%, ( 62$23-3625%1,

isopropyl alcohol 04 $$2326, ( 62$25-%21,

$,52dioxane 04 $$2$723-36252, ( 72$23-36251,

$ phenolphthalein solution in pyridine 04 $$2-$-, ( 281

Apparatus

Halance "ith at least .$ g accuracy, four % mL flas!, four % mL bea!er, test tubes,

% mL burrette, Pasteur pipette, oil bath, and hot plate stirrer, acuum oen, mg2scale

balance


63/77


Procedure 1: =eat ring8opening polymeri6ation

$. In each of four % mL $2nec! round bottom flas!s 04H?1, mix .$3g L2alanine 0$.%

mmol1 and %.$3 g 2caprolactone 05% mmol1 and stir the mixture at $SC in an oil

bath. Connect the flas!s to nitrogen line to release any pressure deeloped during

the heating.

. #fter $, %, $, and 5 h, remoe one of the flas!s from the bath and cool it do"n to

room temperature. issole the mixture in % mL tetrahydrofuran 0&;?1 and

precipitate the polymer product by pouring the solution into 8 mL methanol-; O

0v-v+5-$1 solution.

3. ?ilter the precipitated polymer products and dry in a acuum oen for seeralhours. Beasure the "eight of dried polymer products.

Procedure 2: >itration "ith @H

$. Prepare a standardi>ed solution of /O; 0about .8 B1 in isopropyl alcohol-$,52

dioxane 0v-v+$-51.

. issole each polymer sample obtained aboe in %. mL of isopropyl alcohol-$,52

dioxane 0v-v+$-51. #dd 5 drops of $ phenolphthalein-pyridine solution to $. mL

ali9uot of each polymer solution and titrate "ith the standardi>ed /O; solution.

4epeat this titration.

3. Calculate the aerage experimental molecular "eight alue 0g-mol1 from the

aerage olume of the titrant.

5. 4epeat steps and 3 for other polymer samples.

uestions

#ssume that $ conersion of monomer is obtained after 5 h, and all the amino

acid 0alanine1 is incorporated into the polymer.

332$. hat is the structure of the resulting compound if alanine attac!s the

caprolactoneD #nd explain the meaning of titration "ith /O;.

332. #t times of $, %, $, and 5 h, calculate yields, mol of /O; used in titration, the

number of polymer chain, aerage experimental molecular "eight alue 0g-mol1 of

polymer 0Mn1, and degree of polymeri>ation.

3


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Procedure : Preparation of a chromatographic column

Prepare a chromatographic column by placing a small plug of glass "ool 0or cotton1 at

the constriction of a 2mL Pasteur pipet. (ilica gel 05%-6 mesh1 slurried in ethyl acetate

is added to the pipet to produce 52% cm of pac!ed gel in the column.

Procedure #: 0olumn chromatography and uantitation

$. &ransfer a 52L ali9uot of un!no"n li9uid to the column.

. 4inse the "alls of the column "ith a fe" drops of an eluent selected from &able $,

pass the eluent through the column and collect the eluate in a $2mL olumetricflas! containing 23 drops of triethylamine.

3. Pass a second eluent through the column selected from &able $, and collect the

eluate in a separate $2mL olumetric flas! containing 325 drops of concentrated

;Cl. # small band of impurity may be left behind at the top of the column.

5. ilute the first fraction in its purple, basic form to olume "ith the first eluent.

%. ilute the second fraction in its acidic, red form to olume "ith the second eluent.

. ?ind the concentration of each sample, and thus the amount 0mg1 of each dye in

the un!no"n from the calibration cure for each dye.

>able 381B Possible eluent systems

'luent


68/77


uestions

352$. hat are the concentrations in ppm of #4 and HCF in your sampleD

352.


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Problem 3#: Synthesis of C8dimethylaminopropiophenone hydrochloride

!ntroduction

Pro>ac is a famous antidepressant, also !no"n as the \happy drug] as it can help

alleiate depression. &he actie ingredient in Pro>ac is fluoxetine. ?luoxetine is

prepared from _2dimethylaminopropiophenone in a four step se9uence.

O

e and shape of each spots1

0(ho" calculations1

6


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&est 4eagent &est result

Obsered expected

$1 /BnO50HaeyerEs test1

1 ;Cl, `nCl0LucasEs test1

31 ?eCl30?erric chloride solution1

51 #g


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75/77


Problem 3$: ,n6yme ?inetics by catalase

!ntroduction

Catalysis is a central concept in chemistry and biology, essential in life and industrial

processes. 'n>ymes are catalysts for biochemical reactions. In this experiment, the

Bichaelis2Benten !inetics of hydrogen peroxide decomposition 0;O;O = O1

by catalase in potato )uice "ill be inestigated. Catalase is "ell !no"n for its extremely

high reaction rate. One catalase molecule can decompose 5 million hydrogen

peroxide molecules in one second. (uch a high rate is needed to scaenge reactie

oxygen species and protect cellular components in the oxidatie enironment. &hefigure belo" sho"s a 32dimensional structure of catalase from E. )#'determined by 2

ray crystallography.

&he number of moles of the eoled oxygen gas can be determined from its olume

measured using a buret or from the pressure change in an enclosed reaction essel.

4eaction rate can be expressed as the number of moles of oxygen per unit time.

#n en>yme 0'1 combines "ith a substrate 0(1 and produces an en>yme2substrate

complex 0'(1 "ith a rate constant k$. '( could be decomposed bac! to ' and ( "ith a

rate constant kor concerted to a product 0P1 "ith a rate constant k3. &he steady state

condition for '( can be determined by e9uating the follo"ing rate e9uations.

dX'(Y-dt+ k$0X'Ytot 2 X'(Y1X(Y , "here X'Ytot+ X'Y = X'(Y

2dX'(Y-dt+ kX'(Y = k3X'(Y

X(Y0X'Ytot2 X'(Y1-X'(Y + 0k= k31-k$

0k= k31-k$ is defined as the Bichaelis2Benten constant, KB.

(oling the last e9uation for X'(Y, one getsX'(Y + X'YtotX(Y-0KB=X(Y1.

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Let v be the initial rate for the eolution of oxygen v+ k3X'(Y

If the en>yme is present only as '(, v"ill approach a maximum alue, Vmax+ k3X'Ytot

?rom these relations, one gets the Bichaelis2Benten e9uation.

v+ VmaxX(Y-0KB= X(Y1

Obiously, KB is the alue of X(Y "hen v+ Vmax-. &a!ing the inerse of the Bichaelis2

Benten e9uation one gets the celebrated Line"eaer2Hur! e9uation 0see ?igure1,

"hich is one of the most fre9uently used e9uations in chemistry.

$-v+0KB-Vmax10$-X(Y1 = $-Vmax

5aterials

hydrogen peroxide 04 35, ( 823-3725%1, fresh potato, catalase

Apparatus

blender, ice bath, boiling "ater bath

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Preparatory Problems Final

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