CHEMISTRY
Paper I

Inme Allowed Three Hours IIMaximum' Marks 300 1
INSTRUCTIONS
Each qilestion is printed both in Hindi and in
English.
Answers must be written in the 'medium
specified in'the Admission Certificate iS$ued,
to you, whichmzist be stated clearly on the
cover ofthe answer-book in the space pr:ovided
for the purpose. No marks will be given for
r
the answers written in.a medium o.ther than­
that' specified in "the Admission Certificate.
Candidates should attempt Questions no. 1
and 5 which are c6'mpulsory, and any three
of the· rem.aining questions selecting at .least one question from each Secti?n;
The number marks' carried by each question is indicated the end of the
question.

Symbols and notations carry usual
r meanlngs, unless otherwise indicated. Coordinate diagrams, wherever required, may be, pl9#ed on-the itself. .
Assume suitable da.tci if considered necessary and indicate the same clearly.

rarR 3/jd.wt moo rrr I

SECTION A

1. Show that the function
W N
satisfies the Schrodinger equation for a
particle in a one-dimensional box with a
potential functionV(x) equal to zero for
o5 x 5 L and
What values may the quantum number n
take? What are the allowed energy levels?
Why is it important that the wavefunction be ..
normalized Calculate the normalization
constant, N. 15
J 2sin e de 21 ,(.e,Sin2 29

the following;information
.
A B C D kJ

ilHo for each of the following reactions: 15

C+D A B


2C 2D 2A 2B


A E C-DTN-l-DIA 2
IContd.]

r


q)fH If! N Sin(
o x L a:fR Vex) W2T, if, q)UT cit -"Bw
q:q i2: 4 (941 n l1RT CfiT B eft t
7.ffi" W CfiT
t1ll1lr4Jrpd 'RlffiiCh, CfiT tIT{Cf)(1""i
Jsin20dO Sin220)]
.IJiI'iChIU
A C+D LHD -'10·0 kJ
C+D E LHo 15·0 kJ

tt trRGfi<1'"i
C+D A+B
2C 2D 2A+ 2B
A E
3 lContd.]
State the van der Waals equation of state and justify briefly the appearance of the parameters a and b in the equation. Given that for Xe,
a bar dm6 mol-2, b =5·16 x· dm3 mol-1
... .
determine by 1molofXein a container . of volume,20 dm3 at 300 K. How does
. ­
the pressure compare with ,thatpr.edicted by the perfect gas law Explain. 0·083 bar dm3 mol-1K-1) 15
The nicotine-water system exhibits two critical solution temperatures.. What is the effect of external pressure on the system
2. Draw and label an energy level diagram for molecular· orbitals up to a*·2p. Use the diagram to explain why

The:bondJength of Li2 is much that ofB2,


Bi isparamagnetic, but C2 is


NO+ iSHmore stable tow:ards dissociation into its atoms than NO, whereas co+ is less stahle than CO.
C-DTN-L-DIA 4 [Contd.]

3iE4f4T Cilcti q)f cti?;R am: .G 3ih= b SPI2-=i it -mft ,Xe
a 4-191-bar dm6
b 5·16 x dm3 mort
300K 20dm3 t Xe 1 mol mr (1J II q;r mRur ih1 .Ch1 WRTll GJGf (Cfld-=il
.
15 bar "dm3 morl
m-cit I CflIT >MTCf 15
2. cr* 2p 3lTfTrqq; "fffi: 31fug 31R, I tfil{oTf ,31fug 'qrr •
Liq,1 Bc€t
2 2


C2
NO+ 'q<qlUjm • I 20
[,Contd.]
According to the kinetic model of gases, the pressure and volume of a gas are related through the root mean·square molecular speed,
c v2 by
Pv n Mc2
, 3
M rriNA is the molecule's mass, and n is-the -number of moles of gas present.
According to the 'equi·partition of classical mechanics, the average energy per molecule for three-dimensional transitional
3
motion is 2 kBT, where kB IS the
Boltzmann's constant. Use this and the above equation to derive ideal gas law.
Show that the root mean square molecular speed is" given,by
•
c
Calculate c 02 at room (298 K).
Calculate the'ratio of fOF He to that for 02 at 298 K. 8:314 J mol-I)
C-DTN-L-DIA 6 [Contd.l

ilm lil'S(1 M ..am: 3illld"'l qrf V 2
I 2
pV 3 n c
M C1iT n ih:r it MilJiH, I I

l;=jidir 7Tfu ifi. furo: >rffr kBT kB Hlfni<:fi I ihr it

c
I
"ffltr', .(298 1R CfiT I
298K He c'ctr 02 c 'ttRCfi(1'1 I 8;314 J 25

C-DTN-L-DIA 7
...·a
".

:Using.theKelvin e<:Iuation.cal<;ulatePsl P at 25°C,
where P a js the ·vapour pressure for a very small
droplet of water of I:adius r 1 x and P is
that of bulk water.
Given for at:this'temperature,
y-=71·97 x =0·9970 x 103 kg
and R 15
3. The energy· levels .of the electron 'in".a hydrogen
atom -are given-by
. -RH ...
where RH js the Rydberg constan.t and_ n is -the
principal quantum
'Draw a clearly
showing the 'first three energy levels of the
electron and all the quantum states
belonging"to each energy level.
(H5 Give the the:first three
energy levels; giVing the allowed l andml
values,and -the orbital Suggest a
relates ,the..
of an energy leyel,.to .its principaJ .·quantum . .....
number.
8 [Contd.] .

.. ;CliT 25°C tR P Cf)f
x 10-3 m q,l Ch1 -am p iK1 ft1Q: qr&f I fq) ffil1 y 71·97 x 10-3 p 0:9970 x l03'kg m-3
mol-I.
3. q{qluJ -rnr
n2, n ... •
n
Ii q:c(j2J1
H

w.T11-, (fR m 31R
. .. .

31it&
ml·llRT am:
'Wll1 m
mB "
Ch1 q;r arcRT
tit.6q/ m21 I

.. _._[Contd .J





C-DTN-L-OIA
The wavefunction of an electron In a hydrog'en 18 orbital is given by

WIs(r) oc e
where is the radiar distance ,from the nucleus, and ao 52·9 pm is 'the Bohr radius.
Write down an expreSSIOn for the radial
2
distribution funcfion Wand explain why this function has different-physjcal
...
interpretation to W2. Sketch V and ,41t 112•
Find the most 'probable radius at which the electron will fourid. Justify the statement "the hydrogen atom has a diameter of approximately orie A". 30
-CsCl in a cubic structure and has a CI-at each corner and a Cs+ at the centre of the unit celL Use the ionic radii of CS+ (169 pm) and (181 pm) to predict the lattice constant a -and compare this value with the value of ,a. calculated from the observed of CsCl, 3·97 x 103 kg m-3 (Cs Cl

CaJculate, the packing efficiency In the

primitive' unit cell. 30
[Contd.]

•.



C-DTN-L-DIA
Is cnT (i{II41fH
IDU
-rJao
jf oc e
r am ao 52·9 I
fCH1{Uj lfi(1'i· jI2 fc;ro: cz4'StCb cp:rr Chl{0l *fen Cf){1rt. cnr. lj/2 Hm
2
I 3lk 4n w'cnr
I
"CR I q{GIUj cnr
(1JIWT A 'QJ2R CfiT 30
CsCl it 3fu: 1R lR L Cs+ (169 pm) 31R CI­(181 pm) cfiT CfiT, a fc;ro:
3-97 x 103 kg m-3 (Cs 132-9, Cl
a l=fR ¥AT

Q}*ictl .q Cf)T
I 30

JContd 4. One mole of'CaC03 washeated)n an open 'vessel

at 1 bar pressure to 1QOO K when it decomposed into CaD and CO2 Calculate the work done
. during the decomposition, assuming that CO2 may
. ..
as an ideal gas. 15 0·083 bar" d:in3 mol-1
The vapour"pressure, of a liquid vanes with temperature, according to "the Clausius -Clapeyr0J:l equation,
din p
dT where R 8·314 J is the gas constant and is the' standard enthalpy change vaporization. Show by integration that this equation can be used to';predict the vapour pressure, at one temperature, T2, from a known vapour pressure, at another temperature, TI .

in P2
. PI RTT2
I
What' assumption have you made about the temperature"dependence of
Use the above formula to predict the saturation vapour pressure at 298 K from its value at 373 K. Take LUI 40·65 kJ mol-I. 25
C-DTN-L-DIA 12 [Contd.]
1 bar 1000 K TJlf F:f>lrr 1'fC1T, ifq Cffl, CaO CO2 I 3i,Q£f2'i CiiT l1R
CO2 ih1 I ,CR =0-083 bar.dm3 mol-1 15

d lnp_ :RT2
K-1 mol-1 ihr' RlfdiCfl
qItq;f &iT qlliq-i' tTftcffi;r q)T 9TUl ,ffitf, I
aR" 1R CfT&l c=nTr, T2, qpq CfiT
iff '8Cfictl I In
<tt JITtf . R 3TItR' cpn
373 K 1R llR 298 K
40,65 kJ 25

[Con.td.J
Ci) Write down the Hamiltonian for the
hydrogen molecule ion, H;.
For a trial wavefunction of the fonn
caVa cb"'b
where is the normalized orbital on
atom i and the ci are coefficients, show that
the normalization constant is N 2Sr1
where S Bab Sba is the overlap integral.
Assume that the ci's are all equal and that
identical normalized hydrogen-like
wavefunctions are
By expanding-the probability density,
qualitatively confirm that
2Sr1l2 Vb)
represents the wavefunction for a bonding
orbital of H;. 20

C-OTN-L-DIA 14
..

3lUJ

cb'Vb
qVHUJi,1R 31R f&i
1::rrrct PilH9iCfl N S Sab.= Sba I 'l1R ri am,
etr T.flR'

lMlC4dl fqfdl{
qrr .H{C4 0 1 CiiUff I 20
15 [Contd.]

SECTION·B

5. Draw the shape of orbitals. On the basis ·of Crysta1:Field Theory explain orbitals in'octahedral and tetrahedral fields. The splitting pattern is different in octahedral and tetrahedraL fields. Why? 15

Discuss the role of sodium and, pQtassium 1n biological processes. Both alkali metals belong to the,same,group; even though their functiop IS opposite to each other. Why? 15

Write BET; equation' and define the terms used, therein. 15


Distinguish ,between homogeneous, and heterogeneous catalysis. 15


6. Complex fonnation is an acid-base 'reaction. 'Explain with suitable example.
Draw the cis and trafts structures of complex ,diamminedichloroplatinum(II). Which form of the ,complex is used in the treatment -of cancer,
Write on cytochromes: 20
C-DTN-L-DIA 16 (Contd.l


5. q)a.m. ett CfiT m I 3lftlR lR, if; fCtQl2Fi qi) 3UiLfit1Chflr am I 15
03) Q¢h1il 11 m

"
CfliT 15
ffJ1nlq 00 m ate: etr 1JRmtIT I 15
am: I 15
6. (D -M{iFi mm
1
etf, fin:r 31R ?frr fi{oq,FilaTI I d qij R -Ciif 41(1 ..
R040ft I 20
C-DTN-L-DIA 17 [Contd.]
.­
Borazine IS a ·close analogue of benzene. Explain on the basis of preparation, molecular structure and reactions of borazine.
(ii)T}iscuss magnetic and spectral' of, lanthanides. 20
Write' phase rule equation and defihe the terInS used therein.'How many phases, components and degrees' of freedom are in the following system


20

7. Give "the IUPAC names of the following­complexes 10
C12
!S[OsCIsN]
Cl3
What is EDTA Give,its molecular structure, total. number of donor atoms available in,it; and dentate character. Draw
..
the molecu1ar structure of Zn-EDTA
10
C-DTN-L-DIA 18 [Contd.]



Reg efiT r fCi(iI!i, fi{i'Fil 3lp:m I

tR 20
ett -qftcqm 31R'{"q(15tctl Ch1


20
7. 10
[CoCI(NH3)S]. C12
K2[QsClSN] [Fe(CNCH3)6] Br2
[Co(H20)z(NH3)4l.CI3
EDTA CFIT 'a4cl<S:tl ¥f 3lR (dentate) I ,:cfiT I 10
"

I C-DTN-L-DIA [Contd .J 1
Give brief account .on inter halogen
and discuss molecular structure·

of IF7' 10
,Localized accumulation of.alumfnhim iIi the·
brain is resppnsible for Alzheimer's disease.
10
Derive an expression for the rate constant of
a first order reaction, .10
Show:that the half-life period of. a first order
reaction IS independent of initial
concentration, 10
8. Give electronic on
the basis of this explain lanthanide contraction. 20·
Why doescai'bonmonoxideJorm metal' carbonyls
Give synthesis of metal carbonyls and discuss cr
and 1t bonding in case ofFe(CO)5' 20
Discuss shape, hybridization, number of unpaired
electrons, magnetic moment and their magnetic
behaviour in the following 20
Ni(CO)4

Oii)
·[FeCF) 6


C-DTN-L-DIA 20
...


m fqq{OI 3ffi. IF7 'Ch1 311fUqq; li. 10
if q1T
irT 3iHGI4r mor Cf<IT 10
G1:. it
I 10
cnTfZ Ch1 mm I 10
8. q)f
If'l c€t I 20
Cfi149i mg 3fu: Fe(CQ)5 41qR I 20
7t
fiCf){OI, ett 31R C4qi?R If'l 20




C-DTN-L-DIA 21
..
..

-.....

J/(iJCb JlR 3tk 3tUJff if EJrlT I 3m mr 1lnZll1 ffflt JfR f3ttl(fjJ Jffi'& Mal 3tk 1lJ&l1l C/5T -as rR 3i&n Piflce WR mx:rr J!RT
fJJf&e· I CR" 3fffiRid 1lJ&l1l 31frlRdJ
3RT kbm 11TU/1f 71 ffRt-7TT! rR: cmt 3ic5
;:reff mflJ) I
J1R l 3tk 5 3fRc:J74 1m J/c4Cb W7s l!l5 JlR g9Oid5>< 8R 3ff( cf)!JJe I Rc4Cb JlR fffi! Had 3kP JlH 3Rf 1f J fiJ;dlM{ fflJf/;<J 3T2f 3Fl12rr PtUte g I 3fTffl, .JfffF 3fIClftl/Cb
....,.
IC-DTN-L-DIAI
19.urfifi 300 1

JfR-S«td5 lR 3l1c1R!Jd c5rf3:re
.. 311CJfl4d5 m-rtr C5T FJ'Ff"
afJf3te om JPfdJ) .Cb7&te I


Note-: English version of the Instructions is printed on
the -front cover of this question paper,