Indian Institute of Technology Kharagpur (IIT-K) 2008 M.Sc Chemistry Physical -1 mid sem - Question Paper
OlCM"i.CTDG
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR CHEMISTRY DEPARTMENT
Date of Examination:...... Time: 2 Hrs. Full Marks: 60.........No. of Students: OS
Semester: Autumn.2008-09 Department: Chemistry Subject No. CY2QJ.0I
2ndYear Int. MSc. Subject Name:
_Answer all questions. All questions carry equal marks._
{k = 1,38 x t(T23 J K"1; R = 8.314 J K~' mof1; 1 bar = 1 x 10 s Pa; 1 Faraday = 96,500 C mor'l
/ Discuss tlie features and the limitations of the van der Waal equation of gas.
Expressing the pressure (p) of a given van tier Waal gas as a function of volume (V) and temperature (T), deduce the expression for the total differential of pressure (dp) for the gas in terms of dVm and dT, where, Vm is the molar volume of the gas.
NJZ' (a) Derive the expression for the compressibility factor (z) of a gas that obeys the equation of state: p(V-nh) = nRT, where b and R are constants, (b) Calculate the numerical value of the compressibility factor if the pressure and temperature are such that molar volume of the gas is equal to 10b.
4. Deduce the expression for fugacity coefficient (ip) for a van der Waal gas for which the compressibility factor (z) is given as: 2 = 1+ h ( a p
jf. The fugacity coefficient (tp) for a certain gas at 290K and 2.1 MPa is 0.68. Calculate the difference of its chemical potential from that of a perfect gas in the same state.
jf. The percentage of helium molecules present per unit volume of the air is higher in the upper * atmosphere than near the surface of the earth. Comment on the statement.
A certain sample of gas lias a volume of 20 lit al 0C and latm. A plot of the experimental data of its volume (V) against the Celsius temperature (0) at constant pressure p, gives a straight line with a slope ofO. 0741 lit. (C)\ Using Ihe definition of absolute zero temperature and the given data, determine the absolute zero of temperature in degree Celsius.
The mass density of phosphorus vapor is given to be 3.71 g/lit at 100C and 0.157 aim. What will be the molecular formula of phosphorous under the given condition? [Mol wt of Phosphorous 3 I g/mol],
s
% Deduce an expression to relate the change in Gibbs energy to the heat of reaction for a chemical reaction under a given condition of pressure.
JSuppose benzene and ethyl benzene forms an ideal solution on mixing. What proportions of benzene and ethyl benzene should be mixed (a) by mole fraction; (b) by mass, to achieve the greatest entropy of mixing (Given: Mol wt of benzene and ethyl benzene are 78.115 and 1#. 169 respectively].
* X The experimental values of the partial molar volume of a salt at 298K in aqueous medium are given as follows: VSau (cm3 mol1) 6.218 +'5.146 b -7,147 b2 where, b is the numerical value of the molality of the salt. The molar volume of pure water at 298K is given to be 18.079 cm'1 mol '. Use the Gibbs-Duhem equation to derive the expression for the partial molar volume of water in the solution in terms of molality, b.
JUsing the fundamental equation of thermodynamics and the Maxwells relations, derive the following
expressions for an ideal eas: n = 7*1-I - f-l
AM!TA.(PATHAK).MAHANTY Signature of the paper setter Name in Capital Letters
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