Gaseous State Exercise # 1

GASEOUS STATE Exercise # 1 1. [Single Correct Choice Type Questions] A thin balloon filled with air at 47ºC has a volume of 3 litre. If on placing it in a cooled room its volume becomes 2.7 litre , the temperature of room is : (A) 42ºC (B) 100ºC 2. (C) 15ºC If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, the ratio of initial and final volume under the same temperature and pressure would be : (A) 3 : 1 (B) 1 : 3 (C) 2 : 1 3. (D) 200ºC (D) 1 : 2 SO2 at STP contained in a flask was replaced by O2 under identical conditions of pressure, temperature and volume. Then the weight of O2 will be _______ of SO2. (A) half 4. (B) one fourth (C) twice (D) four times. Assuming that O2 molecule is spherical in shape with radius 2 Å, the percentage of the volume of O2 molecules to the total volume of gas at S.T.P. is : (A) 0.09 % 5. 8. (B) 250ºC (C) 25ºC (B) 10.00  (C) 13.66  (D) 25 K (D) 20.00  Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of 1 atm but also a concentration of 1 mol litre 1. [ R = 0.082 litre atm mol 1 K 1 ] (A) at S.T.P. (B) when V = 22.42 L (C) when T = 12 K (D) impossible under any condition An amount of 1.00 g of a gaseous compound of boron and hydrogen occupies 0.820 liter at 1.00 atm and at 3 0C. The compound is (R = 0.0820 liter atm mole1 K1; at. wt: H = 1.0, B = 10.8) (A) BH3 (B) B4H10 (C) B2H6 9. (D) 0.045 % A gas is heated from 0°C to 100°C at 1.0 atm pressure. If the initial volume of the gas is 10.0  , its final volume would be : (A) 7.32  7. (C) 0.009 % If the pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1ºC its initial temperature must be : (A) 250 K 6. (B) 0.9 % (D) B3H12 A 0.5 dm3 flask contains gas A and 1 dm3 flask contains gas B at the same temperature. If density of A = 3 g/dm3 and that of B = 1.5 g/dm3 and the molar mass of A = 1/2 of B, the ratio of pressure exerted by gases is : PA (A) P = 2 B 10. 11. PA (B) P = 1 B PA (C) P = 4 B PA (D) P = 3 B A and B are two identical vessels. A contains 15 g ethane at 1atm and 298 K. The vessel B contains 75 g of a gas X2 at same temperature and pressure. The vapour density of X2 is : (A) 75 (B) 150 (C) 37.5 (D) 45 The density of neon will be highest at : (A) STP (B) 0°C, 2 atm (D) 273°C. 2 atm (C) 273°C. 1 atm 450 12. Equal weights of ethane & hydrogen are mixed in an empty container at 25º C, the fraction of the total pressure exerted by hydrogen is: (A) 1: 2 (B) 1: 1 (C) 1: 16 (D) 15: 16 13. A mixture of hydrogen and oxygen at one bar pressure contains 20% by weight of hydrogen. Partial pressure of hydrogen will be (A) 0.2 bar (B) 0.4 bar (C) 0.6 bar (D) 0.8 bar 14. A compound exists in the gaseous phase both as monomer (A) and dimer (A2). The atomic mass of A is 48 and molecular mass of A2 is 96. In an experiment 96 g of the compound was confined in a vessel of volume 33.6 litre and heated to 273ºC. The pressure developed if the compound exists as dimer to the extent of 50 % by weight under these conditions will be : (A) 1 atm (B) 2 atm (C) 1.5 atm (D) 4 atm 15. 20  of SO2 diffuses through a porous partition in 60 seconds. Volume of O2 diffuse under similar conditions in 30 seconds will be : (A) 12.14  (B) 14.14  (C) 18.14  (D) 28.14  16. See the figure-1 : NH3 HCl X B A C Y The valves of X and Y are opened simultaneously. The white fumes of NH4Cl will first form at: (A) A (B) B (C) C (D) A,B and C simultaneously 17. X ml of H2 gas effuses through a hole in a container in 5 sec. The time taken for the effusion of the same volume of the gas specified below under identical conditions is : (A) 10 sec. He (B) 20 sec. O2 (C) 25 sec. CO2 (D) 55 sec. CO2 18. Three identical footballs are respectively filled with nitrogen , hydrogen and helium at same pressure. If the leaking of the gas occurs with time from the filling hole, then the ratio of the rate of leaking of gases ( rN2 : rH2 : rHe ) from three footballs under identical conditions (in equal time interval) is :  (A) 1 : 14 : 7  (B)  14 :  7 :1 (C)  7 :1: 14   (D) 1 : 7 : 14  19. The rates of diffusion of SO3, CO2, PCl3 and SO2 are in the following order (A) PCl3 > SO3 > SO2 > CO2 (B) CO2 > SO2 > PCl3 > SO3 (C) SO2 > SO3 > PCl3 > CO2 (D) CO2 > SO2 > SO3 > PCl3 20. The kinetic energy of N molecules of O2 is x joule at  123ºC. Another sample of O2 at 27ºC has a kinetic energy of 2 x. The latter sample contains _______ molecules of O2. (A) N (B) N/2 (C) 2 N (D) 3 N 21. The average kinetic energy (in joules of) molecules in 8.0 g of methane at 27º C is : (A) 6.21 × 10-20 J/molecule (B) 6.21 × 10-21 J/molecule -22 (C) 6.21 × 10 J/molecule (D) 3.1 × 10-22 J/molecule 22. According to kinetic theory of gases, for a diatomic molecule : (A) The pressure exerted by the gas is proportional to the mean velocity of the molecule. (B) The pressure exerted by the gas is proportional to the r.m.s. velocity of the molecule. (C) The r.m.s. velocity of the molecule is inversely proportional to the temperature. (D) The mean translational K.E. of the molecule is proportional to the absolute temperature. 452 GASEOUS STATE 23. Temperature at which r.m.s. speed of O2 is equal to that of neon at 300 K is : (A) 280 K (B) 480 K (C) 680 K (D) 180 K 24. The R.M.S. speed of the molecules of a gas of density 4 kg m 3 and pressure 1.2  105 N m 2 is : (A) 120 m s 1 (B) 300 m s 1 (C) 600 m s 1 (D) 900 m s 1 25. The mass of molecule A is twice that of molecule B. The root mean square velocity of molecule A is twice that of molecule B. If two containers of equal volume have same number of molecules, the ratio of pressure P A/PB will be : (A) 8 : 1 (B) 1 : 8 (C) 4 : 1 (D) 1 : 4 26. Which of the following expression correctly represents the relationship between the average kinetic energy of CO and N2 molecules at the same temperature. (A) E (CO) > E (N2) (B) E (CO) < E (N2) (C) E (CO) = E (N2) (D) Cannot be predicted unless volumes of the gases are given 27. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is (A) two times that of a hydrogen molecules (B) same as that of a hydrogen molecules (C) four times that of a hydrogen molecules (D) half that of a hydrogen molecules 28. The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes : (A) 4v (B) 2v (C) v/2 (D) v/4 29. The ratio between the r.m.s. velocity of H2 at 50 K and that of O2 at 800 K is: (A) 4 (B) 2 (C) 1 30. Compressibility factor for H2 behaving as real gas is : (A) 1 31. (D) 1/4 a   (B) 1–   RTV  Pb   (C) 1 + RT   (D) RTV (1 – a) At low pressures (For 1 mole), the Vander Waal’s equation is written as a   T  p + V 2  V = RT   The compressibility factor is then equal to : a   (A) 1 –  RTV   RTV   (B) 1 –  a   a   (C) 1 +  RTV   RTV   (D) 1 +  a   32. Calculate the radius of He atoms if its Vander Waal's constant ‘b’ is 24 ml mol 1. (Note 1 ml = 1 cubic centimeter) (A) 1.355 Å (B) 1.314 Å (C) 1.255 Å (D) 0.355 Å 33. A real gas obeying Vander Waal's equation will resemble ideal gas , if the : (A) constants a & b are small (B) a is large & b is small (C) a is small & b is large (D) constant a & b are large 34. For the non-zero values of force of attraction between gas molecules, gas equation will be : nRT n 2a (A) PV = nRT – (B) PV = nRT + nbP (C) PV = nRT (D) P = V –b V 452 35. The correct order of normal boiling points of O2, N2, NH3 and CH4, for whom the values of vander Waal's constant ‘a’ are1.360, 1.390, 4.170 and 2.253 L2. atm. mol2 respectively, is : (A) O2< N2 < NH3 < CH4 (B) O2< N2 < CH4 < NH3 (C) NH3 < CH4 < N2 < O2 (D) NH3 < CH4 < O2 < N2 36. NH3 gas is liquefied more easily than N2. Hence: (A) Vander Waal’s constants 'a' and 'b' of NH3 > that of N2 (B) Vander Waal’s constants 'a' and 'b' of NH3 < that of N2 (C) a (NH3) > a (N2) but b (NH3) < b (N2) (D) a (NH3) < a (N2) but b (NH3) > b (N2) 37. In vander Waal's equation of state for a non ideal gas the term that accounts for intermolecular forces is : (A) nb (B) nRT (C) n2a/V2 (D) (nRT)-1 38. 7.5 ml of a gaseous hydrocarbon was exploded with 36 ml of oxygen. The volume of gases on cooling was found to be 28.5 ml, 15 ml of which was absorbed by KOH and the rest was absorbed in a solution of alkaline pyrogallol. If all volumes are measured under same conditions, the formula of hydrocarbon is (A) C3H4 (B) C2H4 (C) C2H6 (D) C3H6 39. A gaseous alkane is exploded with oxygen. The volume of O2 for complete combustion to CO2 formed is in the ratio 7/4. The molecular formula of alkane is : (A) C2H4 (B) C2H6 (C) CH4 (D) C4H12 40. LPG is a mixture of n - butane & iso - butane. The volume of oxygen needed to burn 1 kg of LPG at NTP would be : (A) 2240 t (B) 2510 t (C) 1000 t (D) 500 t 41. The volume of CO2 produced by the combustion of 40 ml of gaseous acetone in excess of oxygen is (A) 40 ml (B) 80 ml (C) 60 ml (D) 120 ml 42. 500 ml of a hydrocarbon gas burnt in excess of oxygen yields 2500 ml of CO2 and 3 lts of water vapours. All volume being measured at the same temperature and pressure. The formula of the hydrocarbon is (A) C5H10 (B) C5H12 (C) C4H10 (D) C4H8 43. 15 ml of a gaseous hydrocarbon was required for complete combustion in 357ml of air (21% of oxygen by volume) and the gaseous products occupied 327 ml (all volumes being measured at NTP). What is the formula of the hydrocarbon ? (A) C3H8 (B) C4H8 (C) C5H10 (D) C4H10 44. Two flasks of equal volume are connected by a narrow tube (of negligible volume) all at 27ºC and contain 0.70 mole of H2 at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C, while the other remains at 27º C. The final pressure in each flask is : (A) Final pressure = 0.5714 atm (B) Final pressure = 1.5714 atm (C) Final pressure = 0.5824 atm (D) None of these 45. On the surface of the earth at 1 atm pressure, a balloon filled with H2 gas occupies 500 mL. This volume is 5/6 of its maximum capacity. The balloon is left in air. It starts rising. The height above which the balloon will burst if temperature of the atmosphere remains constant and the pressure decreases 1 mm for every 100 cm rise of height is (A) 120 m (B) 136.67 m (C) 126.67 m (D) 100 m 46. A 40 ml of a mixture of H2 and O2 at 18 ºC and 1 atm pressure was sparked so that the formation of water was complete. The remaining pure gas had a volume of 10 ml at 18ºC and 1 atm pressure. If the remaining gas was H2, the mole fraction of H2 in the 40 ml mixture is : (A) 0.75 (B) 0.5 (C) 0.65 (D) 0.85 454 GASEOUS STATE 47. 48. I, II, III are three isotherms respectively at T1, T2 and T3 as shown in graph. Temperature will be in order (A) T1 = T2 = T3 (B) T1 < T2 < T3 I P (C) T1 > T2 > T3 II (D) T1 > T2 = T3 III V A vessel of volume 5 litre contains 1.4 g of nitrogen at a temperature 1800 K. The pressure of the gas if 30% of its molecules are dissociated into atoms at this temperature is : (A) 4.05 atm (B) 2.025 atm (C) 3.84 atm 49. One litre of a gaseous mixture of two gases effuses in 311 seconds while 2 litres of oxygen takes 20 minutes. The vapour density of gaseous mixture containing CH4 and H2 is (A) 4 (B) 4.3 (C) 3.4 50. (D) 46.6 A straight glass tube has 2 inlets X & Y at the two ends of 200 cm long tube. HCl gas through inlet X and NH 3 gas through inlet Y are allowed to enter in the tube at the same time and under the identical conditions. At a point P inside the tube both the gases meet first. The distance of point P from X is : (A) 118.9 cm (B) 81.1 cm (C) 91.1 cm 52. (D) 5 Pure O2 diffuses through an aperture in 224 second, whereas mixture of O2 and another gas containing 80% O2 diffuses from the same in 234 second. The molecular mass of gas will be (A) 51.5 (B) 48.6 (C) 55 51. (D) 1.92 atm (D) 108.9 cm Two flasks of equal volume are connected by a narrow tube (of negligible volume) all at 27º C and contain 0.70 moles of H2 at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C , while the other remains at 27º C. The number of moles of H2 in flask 1 and flask 2 are : (A) Moles in flask 1 = 0.4, Moles in flask 2 = 0.3 (B) Moles in flask 1 = 0.2, Moles in flask 2 = 0.3 (C) Moles in flask 1 = 0.3, Moles in flask 2 = 0.2 53. A teacher enters a classroom from front door while a student from back door. There are 13 equidistant rows of benches in the classroom. The teacher releases N2O, the laughing gas, from the first bench while the student releases the weeping gas (C6H11OBr) from the last bench. At which row will the students starts laughing and weeping simultaneously (A) 7 54. (B) 10 56. (C) 9 (D) 8 A real gas most closely approaches the behaviour of an ideal gas at (A) 15 atm and 200 K (B) 1 atm and 273 K (C) 0.5 atm and 500 K 55. (D) Moles in flask 1 = 0.4, Moles in flask 2 = 0.2 (D) 15 atm and 500 K Calculate the compressibility factor for CO2, if one mole of it occupies 0.4 litre at 300 K and 40 atm. Comment on the result. (A) 0.40, CO2 is more compressible than ideal gas (B) 0.65, CO2 is more compressible than ideal gas (C) 0.55, CO2 is more compressible than ideal gas (D) 0.62, CO2 is more compressible than ideal gas Which of following statement (s) is true  – Slope of isotherm at critical point is maximum.  – Larger is the value of TC easier is the liquification of gas.  – Vander waals equation of state is applicable below critical temperature at all pressure. (A) only  (B) &  (C) &  (D) only  454 57. 58. A certain volume of argon gas (Mol. Wt. = 40) requires 45 s to effuse through a hole at a certain pressure and temperature. The same volume of another gas of unknown molecular weight requires 60 s to pass through the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is : (A) 53 (B) 35 (C) 71 (D) 120 A sample of an ideal gas was heated from 300C to 600C at constant pressure. Which of the following statement(s) is/ are true. (B) Boyle’s law will apply (C) Volume of the gas will be doubled (D) None of the above The curve of pressure volume (PV) against pressure (P) of the gas at a particular temperature is as shown, according to the graph which of the following is incorrect (in the low pressure region): (A) H2 and He shows +ve deviation from ideal gas equation. (B) CO, CH4 and O2 show negative deviation from ideal gas equation. CO 61. Ideal gas 0 For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to liquifaction. Choose the correct statement. (A) at T = 500 K, P = 40 atm, the state will be liquid. (B) at T = 300 K, P = 50 atm, the state will be gas (C) at T < 300 K, P > 20 atm, the state will be gas (D) at 300 K < T < 500 K, P > 50 atm, the state will be liquid. Consider the following statements: The coefficient B in the virial equation of state (i) is independent of temperature (ii) is equal to zero at boyle temperature (iii) has the dimension of molar volume H2 He (C) H2 and He show negative deviation while CO, CH4 and O2 show positive deviation. (D) H2 and He are less compressible than that of an ideal gas while CO, CH4 and O2 more compressible than that of ideal gas. 60. P P 50 atm TC = 500 K T = 300 K 20 atm V   B C   PVm = RT 1 V  2  ..........  V m m   Which of the above statements are correct. (A) i and ii 62. (B) i and iii (C) ii and iii (D) i, ii and iii Consider the following statements: If the van der Waal’s parameters of two gases are given as a (atm lit2 mol–2) b (lit mol–1) Gas X: 6.5 0.056 Gas Y: 8.0 0.011 then (i) : VC (X) < VC (Y) (ii) : PC (X) < PC (Y) (iii) : TC (X) < TC(Y) Select correct alternate: (A) (i) alone (B) (i) and (ii) CH4 O2 PV 59. (A) Kinetic energy of the gas is doubled (C) (i), (ii) and (iii) (D) (ii) and (iii) GASEOUS STATE 63. Select correct statement(s): (A) we can condense vapours simply by applying pressure (B) to liquify a gas one must lower the temperature below T C and also apply pressure (C) at Tc, there is no distinction between liquid and vapour state, hence density of the liquid is nearly equal to density of the vapour (D) all the statements are correct statements 64. A chemist has synthesized a greenish yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/L at 36°C and 2.88 atm. Then the molecular formula of the compound will be (A) ClO3 (B) ClO2 (C) ClO (D) Cl2O2 65. At what temperature, the average speed of gas molecules be double of that at temperature, 27ºC? (A) 120ºC (B) 108ºC (C) 927ºC (D) 300ºC 66. Two glass bulbs A (of 100 mL capacity), and B (of 150 mL capacity) containing same gas are connected by a small tube of negligible volume. At particular temperature the pressure in A was found to be 20 times more than that in bulb B. The stopcock is opened without changing the temperature. The pressure in A will (A) drop by 75% (B) drop by 57% (C) drop by 25% (D) will remain same 67. The product of PV is plotted against P at two temperatures T 1 and T2 and the 'result is shown in figure. What is correct about T1 and T2? T2 PV T1 P(bar) (A) T1 > T2 (B) T2 > T1 (C) T1 = T2 (D) T1 + T2 = 1 68. 2.5 L of a sample of a gas at 27°C and 1 bar pressure is compressed to a volume of 500 mL keeping the temperature constant, the percentage increase in pressure is (A) 100 % (B) 400 % (C) 500% (D) 80% 69. At STP the order of mean square velocity of molecules of H2, N2, O2 and HBr is (A) H2 > N2 > O2 > HBr (B) HBr > O2 > N2 > H2 (C) HBr > H2 > O2 > N2 (D) N2 > O2 > H2 > HBr 70. A quantity of gas is collected in a graduated tube over the mercury. The volume of gas at 18 ºC is 50 ml and the level of mercury in the tube is 100 mm above the outside mercury level. The barometer reads 750 torr. Hence , volume at S.T.P. is approximately : (A) 22 ml (B) 40 ml (C) 20 ml (D) 44 ml 71. If equal weights of oxygen and nitrogen are placed in separate containers of equal volume at the same temperature, which one of the following statements is true? (mol wt: N2 = 28, O2 = 32) (A) Both flasks contain the same number of molecules. (B) The pressure in the nitrogen flask is greater than the one in the oxygen flask. (C) More molecules are present in the oxygen flask. (D) Molecules in the oxygen flask are moving faster on the average than the ones in the nitrogen flask. (E) The nitrogen has a greater average kinetic energy per mole. 456