Numerical Problems in Physical Chemistry for IITJEE

Numerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEENumerical Problems in Physical Chemistry for IITJEE

I m B I B ^^S^IIabli^aSenal Problems in AND ALL OTHER ENGINEERING ENTRANCE EXAMINATIONS Problems in AND ALL OTHER ENGINEERING ENTRANCE EXAMINATIONS G A S E O U S S T A T E Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution I MOLE A N D E Q U I V A L E N T C O N C E P T 61-146 • • • • • 61 63 96 130 135 Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution PR?!-Til Tiriaip ' t A T O M I C S T R U C T U R E Chapter at a glance Basic Problems with Solution Selected Problems.with Solution Problems for self assessment IIT-JEE Problems with Solution 411LLI t i l l R A D I O A C T I V I T Y Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution « i j M I M S • "> ' 203-247 203 204 215 234 237 | H ! li' 273-338 I REDOX T I T R A T I O N S • • • • • 273 274 283 316 321 Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution ELECTROCHEMISTRY • • • • • Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution I1 KPB liP) 339-404 339 340 356 383 387 DILUTE SOLUTIONS AND COLLIGATIVE PROPERTIES 405-462 Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution j i l t H I i i g CHEMICAL KINETICS " r i v , V % Ttm- V K " Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution 463 466 487 507 510 • • • • • Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution 11 IONIC EQUILIBRIUM • • • • Chapter at a glance -Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution wi F It T Ji- pesi- ~ - - 12 THERMODYNAMICS • • • • • Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution 13 THERMOCHEMISTRY Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution 14 CRYSTALLOGRAPHY Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment IIT-JEE Problems with Solution 705-747 I 705 707 714 735 742 • • • • Chapter at a glance Basic Problems with Solution Selected Problems with Solution Problems for self assessment • Selected Problems with Solution • Problems for self assessment • IIT-JEE Problems with Solution • SOME IMPORTANT TABLES 865-872 • LOG TABLE 873-876 Gaseous State Chapter at a Glance 1 lioyles law: /'V = constant ( limit's law: V/T = constant (>ay Lussac-Charles's law: P/T - constant Avogadro's hypothesis: V oc No of molecules (•as equalion: PV= nRT oi PV=(w/m)RT (at constant T and n) (at constant P and n) (at constant V and n) (at constant pressure and temperature) or (> Graham's law of diffusion: ; n -W MI r2~ M\ P = ~RT m (where I'roblcm >• I'roblcm > I'roblcm >• I'roblcm >• I'roblcm I'roblcm • I'roblcm > Problem > Problem 10 > Problem 11 > Problem 12 > Problem 13 > Problem 14 > Problem 15 « > Problem 16 >- I'roblcm 17 A vessel of 120 mL capacity contains a certain amount of gas at 35°C' and 1.2 bar pressure The gas is transferred to another vessel of volume 180 mL at 35°C What would be its pressure? What will be the minimum pressure required to compress 500 dm of air at bar to 200 dm at 30°C? A gas occupies 300 mL at 127°C and 730 mm pressure What would be its volume at STP? Calculate the volume occupied by 7g CO at 27°C and 750 mm Hg Calculate the temperature of 4.0 moles of a gas occupying dm at 3.32 bar (R = 0.083 bar dm K"1 mol -1 ) Calculate the weight of CH in a dm cylinder at 16 bar and 27"(\ (R = 0.083 bar dm K - ) A desiccator of internal volume one litre containing N at atm is partially evacuated to final pressure of 78 mm of Hg, while T remains constant What is the volume of gas at this stage? •J In a certain region of space, there are only molecules per cm of an average The temperature is K What is the average pressure of this gas Using the equation of state PV=nRT, show that at a given temperature density of a gas is proportional to gas pressure P Calculate the density of C at 100°C and 800 mm Hg pressure At 0°C, the density of a gaseous oxide at bar is same as that of nitrogen at bar What is the molecular mass of the oxide? The density of helium is 0.1784 kg/m3 at STP If a given mass of helium at STP is allowed to expand to 1.400 times of its initial volume by changing P and T, compute its resultant density Density of a gas is found to be 5.46 g/dm at 27°C at bar pressure What will be its density at STP? Calculate the volume occupied by 8.8 g of C at 31.1 °C and bar pressure R = 0.083 bar litre K _ l m o f 2.9 g of a gas at 95°C occupied the same volume as 0.184 g of hydrogen at 17°C, at same pressure What is the molar mass of the gas? Assuming the same pressure in each case, calculate the mass of hydrogen required to inflate a balloon to a certain volume Fat 100°C if 3.5 g helium is required to inflate the balloon to half the volume V at 25°C The densities of an unknown gas and were find 0.2579 kg/m3 and 0.2749 kg/m3 at the same P and T Calculate the mol weight of unkown gas 861 MLSCLI I ANBOUS P R O B L I MS 15 At 298 K, an aqueous solution ol iodine containing (J.0516 g per litre is in equilibrium with CCI4 solution containing '4.412 g of iodine per litre If the solubility of l in water is 0.340 g per litre at 298 K, what will be its solubility in CC14? 16.- The solubility of a substance is three times as great in ether as in water Calculate the quantities extracted from 100 mL of aqueous solution by using, (a) 100 mL of ether is one operation (b) 100 mL of ether in two successive operations, i.e., 50 mL in each (c) what fraction is left unextracted in each case? 17 Succinic acid was shaken in a mixture of water and ether The concentration of acid in two layers are as follows: C, (water layer per 10 mL) 0.024 g 0.071 0.121 C (ether layer per 10 mL) 0.004 g 0.013 0.022 (i) What is partition coefficient for system in favour of water (ii) If succinic acid has molecular weight 118 in water, find its molecular weight in ether 18 Benzoic acid is distributed between water and benzene according to the following data: Concentration in water 0.013 0.021 0.032 Concentration in C H 0.1818 0.4742 1.101 Find out molecular weight of benzoic acid in benzene NUMERICAL PHYSICAL CHEMIST RY 862 Answers — — — I -90.75 kcal mol - -618.7 kJ mol -1 -1981 kJ mol" ; ; ; For C P = - kJ.mol -1 , r = -307kJmol-1 ; -1 EA = 352 kJ mol ; 51.38 ; 1040 million, 3040 million ; 35 kg rosin, 20 kg each of shellac and beeswax ; -67.88 kcal ; 10 Succinic acid forms dimer in C^Hg ; II 25% ; 13 4.46 x 10 12 Dimer formation in C^H6 ; -4 gin 10 cm ; 14 (a) 2/3 W, (b) 3/4 W ; 15 29.07 g litre -1 ; 16 (a) 3/4 W (b) + 17 (i) 5.65 ; (ii) 118 = (c) (a) 25%, (b) 16% 18 n = 2, ; molecular weight = 244 • H6!> SOME IMPORTANT TABLES r Table-1 Physical Quantities, Symbols and Units S.No Physical Quantities Symbols SI Units Symbol of Units Area A Square meter m2 Volume V Cubic meter m3 Density d kilogram meter kg nrf Velocity u meter per sec m s-1 Acceleration g meter per sec Energy E joule J (kg m2s~2) Force F newton N (kg ms~2) Power Watt W (kg m2s~3 or Js - ) Pressure P pascal Pa (N m"2) 10 Frequency V Hertz Hz (s _1 ) II Electric charge Coulomb C (Ampere second) 12 Electric difference Q V Volt V (kg m s" A" ) 13 Electrical resistance R Ohm p i (kg m s" A'2) 14 Electrical conductance S Siemens s (n ') 15 Amount mole , f Weight mole , , , Mol wt — potential mole m s-2 V / 866 Table-2 Quantities with Traditional Units, SI and CGS Values S.No Quantity Mass Traditional Units amu SI and CGS Value 1.6605 x 10" 27 kg = 1.6605 x " g = amu Length A 10 - meter = 10~8 cm = A Volume- litre 10~3 m = 103 cm = litre Force dyne 10 Energy erg cal electron volt kilo watt hour horse power Pressure Newton = dyne N 10 joule = erg 4.184 joule = cal 1.602 x 10~19 joule = eV 3.6 x 106 joule = KWh 2.6845 x 106 joule = hp atmosphere cm mm or tonbar 101325 N m - or pascal = atm 1333.2237 N m _ = cm 133.32237 N m~ = mm 101325 N m~ = bar Temperature centigrade 273.15 K = 0°C Electric charge esu 3.3356 x " C = esu Work litre atm 101.3 J = litre atm Radioactivity Curie or Ci Rutherford 3.7 x 1010 dps or Bq = curie 10 106 dps = 106 Bq = rd 867 Table-3 Some direct Conversion factors erg = 10"7 Joule = 2389 x 1CT8 cal = 6.242 x 10 U eV calorie = 4.184 x 107 erg = 4.184 Joule = 2.613 x 1019 eV electron volt = 1.6021 x 10~12 erg = 1.6021 x 10"49 Joule = 3.827 x l t r calorie litre = 1000 mL or cm = 10 -3 m 1, angstrom = 10"8 cm = 10~10 m nanometer = 10" m = 10~7 cm coulomb = 2.9979 x 109 esu faraday = 9.6487 x 104 coulomb curie = 3.7 x 1010 disintegration sec"1 rutherford = 106 dps Table-4 Wave Lengths and Frequencies of Electromagnetic Radiations S.No Radiations Wavelength X (in A ) ' Frequency (y) (in Hz or s e c ) Radio wave x 109 to x 1013 x 105 to x 109 Micro wave x 106 to x 109 x 109 to x 1011 Infra red x 10 u to 3.95 x 1014 Visible rays x 109 to 7.6 x 103 3800 to 7600 3.95 x 1014 to 7.9 x 1014 Ultra violet rays 150 to 3800 7.9 x 1014 to x x 1016 X-rays 0.1 to 150 x 1016 to x 10 i Gamma rays (y) 0.01 to 0.1 x 10 19 t o x 1020 S Cosmic rays 0.00 to 0.001 x 1021 to infinite 868 Table-6 Physical Constants and their Values S.No Name Symbol CGS Value SI Unit Value Universal gas constant (R) 8.314 x 107 erg K"1 8.314 J K Boltzmann constant (*) 1.380 x 10~16 erg K"1 1.380 x 10~23 JK" Planck's constant (h) 6.626 x 10"27 erg sec 6.626 x 10"34 J sec Speed of light C 2.9979 x 10 ! cm sec -1 2.9979 x 108 msec" Molar volume at STP ' V 22414 cm 0.0224 m N 6.022169 x 1023 mol - 6.022169 x 1023 mol e 4.80291 x 10~10 esu 1.60210 x 10 C amu 1.660531 x 10~ 24 g 1.660531 x 10"27 kg 9.109558 x 10"28 g 9.109558 x 10"31 kg 1.67261 x 10~24 g 1.67261 x 10~27 kg 1.67492 x 10"24 g 1.67492 x 10~27 kg 1.097373 x 105 cm" 1.097373 x 10 m~' Avogadro's No Charge on electron Atomic mass unit Mass of electron in rest 10 Mass of proton 11 Mass of neutron m P m„ 12 Rydberg constant mol 1 13 Faraday (F) 2.89461 x 1014 9.6487 x 107 C/kg 14 Accelaration due to gravity 0?) 980.665 cm sec"2 9.80665 m sec" 15 I Bohr's radius (for H) r 0.529 x 10"8 cm 0.529 x 10"10 m 16 Atmospheric pressure (P) 1.013250 x 106 dyne cm" : 1.013250 x 105 N m '' lH 17 Specific charge of electron (e/m) 5.2764 x 1017 esu/g 1.75880 x 1011 C kg 18 Ice point (m.pt.) 273.150 K 273.150 K 273.16 K 273.16 K 19 Triple point of H2O 069 Table-6 Elements, their Symbols, Atomic No., Atomic mass and Isotopes Symbol Atomic number Actinium Aluminium Amercium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Ac A1 Am Sb Ar As At Ba Bk Be Bi B Br Cd Ca Cf C Ce 89 13 95 51 18 33 85 56 97 83 35 48 20 98 58 Cs CI Cr 55 17 ' 24 Cobalt Copper Curium Dysprosium Einsteinium Erbium Co Cu Cm Dy Es Er 27 29 96 66 99 68 Europium Fermi um Fluorine Eu Fm F Francium Fr 63 100 87 Element Atomic mass (227) 25.9815 (243) 121.75 39.948 74.9216 (210) 137.4 (247) 9.0122 208.980 10.820 79.904 112.40 40.08 (251) 12.01 140.12 132.905 35.453 51.996 58.9332 63.546 (247) 162.50 (294) 167.26 152.00 (253) 19.0 (223) * Known Isotopes — — — — 14 14 — 2 — — — — (contd.) •values in parentheses are mass numbers of the most stable or the best known isotopes 870 Gadolinium Gallium Germanium Gold Hafnium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Kurchatovium Lanthanum Lawrenchium Lead Lithium Luted um Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Gd Ga Ge Au Hf He Ho H In Ir Fe Kr Ku La Lw Pb Li Lu Mg Mn Md Hg Mo Nd Ne Np Ni Nb N No Os Pd P Pt Pu Po • 64 31 32 79 72 67 49 53 * 77 26 36 104 57 103 82 71 12 25 101 80 42 60 10 93 28 41 102 76 46 15 78 94 84 157.25 69.72 72.60 196.67 178.49 4.0026 164.930 1.00797 114.81 126.9044 192.2 55.847 83.80 (260) 183.91 (257) 207.19 6,94 174.97 24.312 54.9380 (256) 200.59 95.94 144.24 20.183 (237) 58.71 92.906 14.0067 (254) 190.2 15.9994 106.4 30.9738 195.09 (242) (210) 5 — 2 — — 16 — 8 — — 6 — — (con III.) 871 Polassium Praseodymium Promethium Protactinium Radium RadOn Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulphur Tantalum Technetium Tellurium Terbium Thallium Thorium 'Thulium Tin Titanium Tungusten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium K Pr Pm Pa Ra Rn Re Rh Rb Ru Sm Sc Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr 19 59 61 91 88 86 75 45 37 44 62 21 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 92 23 54 70 39 30 40 39.102 140.007 (147) (231) (226) (222) 186.2 102.905 85.47 101.07 150.35 44.956 78.96 28.086 107.868 22.9898 87.62 32.064 180.948 (99) 127.60 158.924 204.37 232.038 168.934 118.69 47.90 183.85 238.03 50.942 131.30 173.40 88.905 65.37 91.22 — — — 2 7 3 1 — 8 10 5 - 872 Table-7 Electrochemical Series Standard reduction potential at 25°C (in volts) Half reactions Li+ + e >Li -3.04 >K -2.92 Ba 2+ + 2e——» Ba -2.90 Sr 2+ + 2e Ca 2+ + 2e — > Ca + K +