civils mains 2013 CHEMISTRY Paper I

Time allowed: Three Hours

Maximum Marks: 250

Question Paper Specific Instructions
Please read each ofthe following instructions carefully before attempting questions:
There are EIGHT questions divided in two SECTIONS and printed both in HINDI and in ENGLISH.
Candidate has to attempt FIVE questions in all.
Questions no. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted choosing at least ONE from each section. The number of marks carried by a question /part is indicated against it.
Answers must be written in the medium authorized in the Admission Certificate which must be stated clearly on the cover of this Question-cum-Answer Booklet in the space provided. No marks will be given for answers written in a medium other than the authorized one.
Coordinate diagrams whenever required shall be drawn in the space provided for answering the question itself
Unless otherwise mentioned, symbols and notations carry their usual standard meanings.
Assume suitable data, if considered necessary, and indicate the same clearly.
Attempts ofquestions shall be counted in chronological order. Unless struck off, attempt ofa question shall be counted even ifattempted partly. Any page or portion of the page left blank in the answer book must be clearly struck off.

SECTION A

Q1. A particle of mass m is confined in a one-dimensional box of length L. The wavefunctions of the particle are given by

<img src='./qimages/91-1a.jpg'>

n is the quantum number, and 0 L is the distance along the length of the box.

Sketch the wavefunctions for the states with n n 2 and 3.
Describe what is meant by the Born interpretation,
<img src='./qimages/91-1a2.jpg'>
Sketch the probability of finding the particle within the box for the states with n n 2 and n 3.
What is the average momentum of a particle in a box? 10

How is entropy defined thermodynamically?
What role does l1S play in determining the direction of
spontaneous change?
At 25°C, the enthalpy change of the graphite diamond phase transition is 1·8961 kJ morl and the entropy change is 3.2552 J mol-I. Which is the spontaneous direction at 25°C? Which direction is favoured by a rise in temperature? 10

Determine expressions for the critical constants of a Van der Waals gas, defined by the expression
<img src='./qimages/91-1c.jpg'>
where the symbols have their usual meanings. 10

(d)Calculate the number of phases, components and degrees of freedom in the following systems: 10
H20 H20
CaC03 CaO CO2
2Hz O2 HzO
HzO HzO H20
NH4CI NH3 HCI
(e)The molar enthalpy of formation of oxygen atoms is 246·5 kJ mol-1. What is the longest wavelength photon which could dissociate O2? 10
2. Compare the molecules OF, OF- and discussing molecular orbitals, bond orders, bond lengths, bond energies, and paramagnetism. 15
Which of the following pairs is expected to have the larger bond angle and why? 10
H20andNHs
SF2 and BeF2
BFs and BFi
PHs andNHs
NH3 andNF3

The molecular speeds are distributed according to the Maxwell
distribution,

<img src='./qimages/91-2b1.jpg'>

Sketch for He and for N2.
Show that rev) is normalized, i.e.
<img src='./qimages/91-2b2.jpg'>
(iii)Show that the most probable molecular speed vmp,is given by
<img src='./qimages/91-2b3.jpg'>
The surface tension of water at 20°C IS 72·75 x 10-3 Nm-1 . A 33·24 vol% solution of ethanol has y 33·24 x 10-3 Nm-1 at the same temperature. Given p 0·9614 x 103 kg m-3 for the solution and 0·9982 x 103 kg m-3 for water. How much less will alcohol solution rise in the same capillary tube?

3. The basic Schrodinger equation for a hydrogenic (l-electron) atom is
<img src='./qimages/91-3a.jpg'>
Explain what the terms in this equation mean. 5
u is the reduced mass ofthe electron-nucleus pair. For hydrogen, how does it compare with me, the mass of the electron? 5
Evaluate the average electron-nucleus separation for the ground state of a hydrogenic atom:
<img src='./qimages/91-3a2.jpg'>
given that
<img src='./qimages/91-3a3.jpg'>
and the wavefunction is given by
<img src='./qimages/91-3a4.jpg'>
where Z is the nuclear charge and a0 src='/qimages/91-3a5.jpg'> 52·9 pm
is the Bohr radius. 10
Why is this different from the most probable radius(ao/Z)? 5
Potassium crystallizes as a body centred cubic lattice having unit cell length a 520 pm. 5x3=15

(i)What is the distance between nearest neighbours 5
(ii)What is the expected density of crystalline K metal 5
(Given: At. wt. ofK 39·1)
(iii)What is the ionic radius ofK+

What are the electrode reactions for charging and discharging of the Cd Ni alkaline battery? What are the advantages of choosing Cd and Ni for the cell 10

Q4. NOz gas is a paramagnetic brown gas at room temperature. When a sample of the gas is cooled below its molecular weight increases, and it loses its paramagnetism and colour. 5x3=15
Using electron dot structure, write an equation which accounts
for these observations. 5
Based on these observations, predict whether the reaction taking place is endothermic or exothermic. 5
Use the following data for the pressures of NOz and its product at equilibrium to calculate the equilibrium constant for the reaction at 298 K PNOz 46 mm Hg, p (product) 23 mm Hg
(i)What is an ideal solution?5
Show that the entropy of mixing of two liquids to form an ideal solution of mole fractions xA and xB is
<img src='./qimages/91-4b2.jpg'>

where n nA nB is the total amount of solution resulting from
nA moles ofliquid A and nB moles ofliquid B. 10

What mole fractions give the maximum entropy of mixing? 5

Construct a trial LCAO MO wavefunction for the Hz molecule. 5
The trial VB wavefunction used by Heitler and London to
describe the Hz molecule III terms of hydrogen-like
wavefunctions is
<img src='./qimages/91-4c2.jpg'>
Compare with the wavefunction you wrote in and comment on the differences, if any. 15

5. Show that in the adiabatic reversible expansion of a gas
<img src='./qimages/91-5a.jpg'>
where
Il Joule Thomson Coefficient
Cp =Molar specmc heat at constant pressure.

Below 18·5°C triethylamine is miscible with water in any proportion. What is the temperature known as
What is the molecular mechanism for the existence of such a
temperature? 10
DeltaG298 is found to be -77·8 kJ, for the following reaction
1/2 Oz HzO 2H+ 20H-
Calculate E298 for the following half-reaction
1/2
(Given: 1 Faraday 96,500 10

The mechanism of a chemical reaction A B can be written as follows:
<img src='./qimages/91-5d.jpg'>
(i)Write expressions and d interms 0f and the rate constants.
(ii)Assuming a steady state approximation for express the rate
constant for the fonnation of the product B'in tenns of [AJ and
the rate constants.
(iii)Under what conditions does the reaction become first order and second order? 10
How many types of absorption are there on solid adsorbents Prove that, for chemisorption, the amount of the adsorbed phase m is equal to AP where P is equal to the pressure of the adsorbent, A l+KP and K are some constants of the system. 10

6. R3SiCI, RzSiClz, RSiCI3, methyl) are used for making silicon polymers. Explain the roles ofthese compounds in the synthesis. 10
Explain why
(i)The complex [CuCl4]z- exists, but does not.
IS more stable than whereas is more stable than
Copper metal dissolves in HCN with evolution of hydrogen gas, but it does not dissolve in sulphuric acid.
The stability constant of is higher than that of
[Cu(NH3)J NHz CHz CHz NHz).
(i)What is the co-operative effect of haemoglobin during oxygen transport
(ii)Describe the metal site of Cytochrome C and its function. 20

Q7. A solution of a dye has its maximum wavelength light absorption at 453 nm and maximum fluorescence emission at 508 nm. The quantum efficiency of fluorescence is 40%. What percentage of absorbed light is emitted as fluorescence? 15
The absorption spectra of lanthanide ions are sharper than those of ions of the first transition series. Explain. 10
What are the differences between the triple point and boiling point? Illustrate with the help of the phase diagram ofwater. 10
Calculate the half-life ofNZ0 5 at 25°C and the fraction decomposed after 104 given that the rate constant of its decomposition IS k 6·93 x 10-5 s-l. 15

Q8. Does the complex have isomeric forms? If so, draw their structures and identify the type(s) of isomerization.
Write the chemical (IUPAC) name of the complexes.
Do the isomers have identical physical properties and chemical reactivities? 15
Calculate the values of tJ.G, tJ.S and tJ.H for the reversible condensation of 36 g of water at DOC to ice at DOC. The latent heat of melting of ice at O°C is equal to 335 Jg-1. 15
Explain why the eutectic point of a solution between solid A and solid B Is invariant.
Calculate the standard potential EO of the reaction
<img src='./qimages/91-8d.jpg'>
<img src='./qimages/91-8d1.jpg'>