Exercise - 1 (SubjectiveQuestionsBasedonFundamentals) SECTION (A) : GAS LAWS, PARTIAL PRESSURE & KINETIC THEORY OF GASES : 1. Certain amount of gas is present in 5 litre vessel at 1.5 atm pressure 1 litre of water is filled in the vessel and it is further connected to 2 litre empty vessel. Then find the final partial pressure of the gas in the vessel (Assume gas is not soluble in water) 2. The stopcock, connecting the two bulbs of volumes 5 litres and 10 litres containing an ideal gas at 9 atm and 6 atm respectively, is opended. What is the final pressure in the two bulbs if the temperature remained the same ? 3. A gas cylinder containing cooking gas can withstand a pressure of 15.0 atm. The pressure gauge of cylinder indicates 12 atm at 27°C. Due to sudden fire in the building, its temperature starts rising. At what tempera- ture the cylinder will explode ? 4. A flask of volume 1 litre contains vapour of CH3OH at a pressure of 1 atm and 25°C. The flask was then evacuated till the final pressure dropped to 10–4 mm. Find the number of molecules of methyl alcohol left in the flask. 5. A volume V of a gas at a temperature T1 and a pressure p is enclosed in a sphere. It is connected to another V sphere of volume by a tube and stopcock. The second sphere is initially evacuated and the stopcock is 2 closed. If the stopcock is opened the temperature of the gas in the second sphere becomes T2. The first sphere is maintained at a temperature T1 . What is the final pressure p1 within the apparatus ? 6. Two gases A and B having molecular weights 60 and 45 respectively are enclosed in a vessel. The weight of A is 0.5 g and that of B is 0.2 g. The total pressure of the mixture is 750 mm. Calculate the partial pressure of the two gases. 7. At what temperature will hydrogen molecules have the same root mean square speed as nitrogen molecules have at 35ºC ? 8. The root mean square speed of gas molecules at a temperature 27 K and pressure 1.5 bar is 1 x 104 cm/sec. If both temperature and pressure are raised three times, calculate the new rms speed of gas molecules. 9. 6.0 g He and 12.0 g Ne molecules both having average velocity 4 x 102 ms–1 are mixed. Calculate kinetic energy per mol of the mixture. 10. At what temperature would the most probable speed of CO2 molecules be twice that at 127ºC SECTION (B) : GRAHAMS LAW OF DIFFUSION : 11. 32 cc of hydrogen diffuses through a fine hole in 1 minute. What volume of CO2 will diffuse in 1 minute under the same conditions ? 12. A tube with a porous wall allows 0.53 litre of N2 to escape per minute from a pressure of 1 atm to an evacuated chamber. What will be the amount escaping under the same conditions for He, CCl4 vapour and UF6 ? (He = 4, N = 14, C = 12, Cl = 35.5, F = 19, U = 238) 13. A gaseous mixture contains oxygen and another unknown gas in the molar ratio of 4 : 1 diffuses through a porous plug in 245 seconds. Under similar conditions same volume of oxygen takes 220 sec to diffuse. Find the molecular mass of the unknown gas. 14. The pressure in a vessel that contained pure oxygen dropped from 2000 torr to 1500 torr in 40 min as the oxygen leaked through a small hole into a vacuum. When the same vessel was filled with another gas, the pressure dropped from 2000 torr to 1500 torr in 80 min. What is the molecular weight of the second gas ? 15. For 10 minute each, at 0 ºC, from two identical holes nitrogen and an unknown gas are leaked into a common v essel of 4 litre capacity. The resulting pressure is 2.8 atm and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknown gas? Page # 17 If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia. The density of neon will be highest at: (A) STP (B) 0°C. 20. 2 atm (C) 273° C. The ratio of their mole fraction is : SECTION (C) : REAL GASES : 17.70 mole of H2 at 0.2 to 1. the percentage of the volume of O2 molecules to the total volume of gas at S. is: (A) 0.2 6. the ratio of initial and final volume under the same temperature and pressure would be : (A) 3 : 1 (B) 1 : 3 (C) 2 : 1 (D) 1 : 2 4. The number of mole of H2 in flask 1 and flask 2 are : (A) Moles in flask 1 = 0. Find the temperature at which 3 moles of SO2 will occupy a volume of 10 litres at a pressure of 15 atms. the ratio of pressure exerted by gases is : PA PA PA PA (A) =2 (B) =1 (C) =4 (D) =3 PB PB PB PB Page # 18 . Moles in flask 2 = 0.3 (C) Moles in flask 1 = 0.3 . Moles in flask 2 = 0.045 % 5. One litre gas at 400 K and 300 atm pressure is compressed to a pressure of 600 atm and 200 K.4 .39 L2 atm mol–2 and b = 0.2 (D) Moles in flask 1 = 0. T2 and T3.If van der Waal’s constant are a = 20. A 0. The rates of diffusion of two gases A and B are in the ratio 1 : 4. 1 atm (D) 273° C. 2 atm 7. Calculate the final volume of the gas.4 % when heated by 1 ºC its initial temperature must be : (A) 250 k (B) 250 ºC (C) 25 ºC (D) 25 k 2.3 (B) Moles in flask 1 = 0. Moles in flask 2 = 0. Two flasks of equal volume connected by a narrow tube (of negligible volume) all at 27º C and contain 0.082 L atm mole–1 K–1) 19.0564 lit mole–1) 18. Assuming that O2 molecule is spherical in shape with radius 2 Å . Moles in flask 2 = 0.4 . If density of vapours of a substance of molar mass 18 gm/mole at 1 atm pressure and 500 K is 0. PARTIAL PRESSURE & KINETIC THEORY OF GASES : 1. I.P.2 .6 respectively. (a) low pressure region (b) high pressure region SECTION (A) : GAS LAWS.5 g/dm3 and the molar mass of A = 1/2 of B.9 % (C) 0. then calculate the value of Z for the vapours. If the ratio of their masses present in the mixture is 2 : 3.0 L. (Take R = 0. III are three isotherms respectively at T1.009 % (D) 0. 1 mole of CCl 4 vapours at 77°C occupies a volume of 35.5 atm.1383 L mol–1. (a = 6.5 dm3 flask contains gas A and 1 dm3 flask contains gas B at the same temperature. If the pressure of a gas contained in a closed vessel is increased by 0. II. calculate compressibility factor Z under.16. while the other remains at 27º C. One of the flask is then immersed into a bath kept at 127º C . If density of A = 3 g/dm3 and that of B = 1.09 % (B) 0. The compressibility factor is changed from 1.T.71 atm lit2 mole–2) (b = 0. Temperature will be in order (A) T1 = T2 = T3 (B) T1 < T2 < T3 (C) T1 > T2 > T3 (D) T1 > T2 = T3 3.36 kg m–3. A bottle of dry NH3 &.S. Temperature at which r.8 bar 10. (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 11. A mixture of hydrogen and oxygen at one bar pressure contains 20% by weight of hydrogen. The resultant pressure is : (A) 1.4 bar (C) 0.2 105 N m 2 is : (A) 120 m s 1 (B) 300 m s 1 (C) 600 m s 1 (D) 900 m s 1 16. Equal weights of ethane & hydrogen are mixed in an empty container at 25º C.255 Å (D) 0. 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 20. If the ratio of the rates of diffusion of the two gases A and B is 4 : 1.2 bar (B) 0.4 22. 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 15.46 g/L (C) 4 g/L (D) 4. One mole of N2O4(g) at 300 K is kept in a closed container under one atmosphere. Calculate the radius of He atoms if its Vander Waal's constant ‘b’ is 24 ml mol 1. the fraction of the total pressure exerted by hydrogen is: (A) 1: 2 (B) 1: 1 (C) 1: 16 (D) 15: 16 9. The R. It is heated to 600 K when 20% by mass of N2O4(g) decomposes to NO2(g).s. Which of the following expression correctly represents the relationship between the average kinetic energy of CO and N2 molecules at the same temperature. a bottle of dry HCl connected through a long tube are opened simultaneously at both ends. Partial pressure of hydrogen will be (A) 0. hydrogen and helium.m.92 g/L 13.314 Å (C) 1. (Note ml = cubic centimeter) (A) 1. the ratio of their densities is : (A) 1 : 16 (B) 1 : 4 (C) 1 : 8 (D) 1 : 2 17. The white ammonium chloride ring first formed will be: (A) at the centre of the tube (B) near the HCl bottle (C) near the NH3. bottle (D) throughout the length of tube SECTION (B) : REAL GASES : 19.23 g/L (B) 2.8.2 atm (B) 2. then the ratio of the rate of leaking of gases rN : rH : rHe from three footballs (in 2 2 equal time interval) is (A) 1 : 14 : 7 (B) 14 : 7 :1 (C) 7 : 1 : 14 (D) 1 : 7 : 14 18. Three footballs are respectively filled with nitrogen .4 14. speed of the molecules of a gas of density 4 kg m 3 and pressure 1. If the leaking of the gas occurs with time from the filling hole. A real gas obeying Vander Waal equation will resemble ideal gas .355 Å Page # 19 .4 atm (C) 2 atm (D) 1 atm 12. Two moles of methane is mixed with 1 mole of oxygen gas then the density of the gas at 27°C if the total 1 pressure exerted by the gas is mixture is 3 atm will be : (Take R = Litre atm/mol/K) 12 (A) 1.355 Å (B) 1.6 bar (D) 0.M. Density of oxygen gas at STP is : 20 1 16 (A) g/L (B) g/ L (C) g/L (D) 5 g / L 7 22. 21. m Vm a: is independent of temperature b: is equal to zero at boyle temperature c: has the dimension of molar volume Which of the above statements are correct..5 0.39.17. With respect to liquefaction.. the van der Waal’s equation is written as a p 2 V = RT V The compressibility factor is then equal to: a RTV a RTV (A) 1 (B) 1 (C) 1 (D) 1 RTV a RTV a Page # 20 ..011 then a : VC (X) < VC (Y) b : PC (X) < PC (Y) c : TC (X) < TC(Y) Select correct alternate: (A) a alone (B) a and b (C) a. and it had the following appearance. Which of following statement (s) is true – Slope of isotherm at critical point is maximum.. (A) at T = 500 K. the state will be liquid. 1. P = 50 atm. 2. 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. NH3 & CH4 are 1.36. b and c 26. The values of Vander Waals constant "a" for the gases O2. – Larger is the value of TC easier is the liquification of gas. b and c (D) b and c 27. At low pressures. In Vander Waals equation state for a non ideal gas the term that accounts for intermolecular forces is: (A) (V – b) (B) RT (C) (P + a/V2) (D) (RT)-1 22. the state will be gas (C) at T < 300 K. P > 50 atm. – Vender waals equation of state is applicable below critical temperature at all pressure. P = 40 atm. the state will be gas (D) at 300 K < T < 500 K. (B) at T = 300 K... Consider the following statements: The coefficient B in the virial equation of state B C PVm = RT 1 V 2 . 4.056 Gas Y: 8.0 0. 25.. Choose the correct statement. N2. the state will be liquid. (A) only (B) & (C) & (D) only 24. The gas which can most easily be liquified is: (A) O2 (B) N2 (C) NH3 (D) CH4 23.253 l2 atm mole-2 respectively. P > 20 atm... (A) a and b (B) a and c (C) b and c (D) a. For a real gas the P-V curve was experimentally plotted. For the non-zero values of force of attraction between gas molecules. (N is Avogadro number) 25 100 6. T = 273 K) (q) attractive forces are dominant (C) CO2 (P = 1 atm. T = 273 K) (r) PV = nRT (D) real gas with very large molar volume (s) P (V – nb) = nRT Page # 21 . At Boyle temperature.360.25 25 (A) N (B) N (C) N (D) 34. (B) CO. CH4 and O2 more compressible than that of ideal gas.253 L2. Exercise . for whom the values of vander Waals constant ‘a’ are 1. Compressibility factor for H2 behaving as real gas is: a Pb RTV (A) 1 (B) 1 (C) 1 (D) RTV RT (1 a) 30. according to the graph which of the following is incorrect (in the low pressure region): (A) H2 and He show +ve deviation from ideal gas equation.44 g cm–3 at a certain temperature. [IIT-JEE 2007] Column-I Column-II (A) hydrogen gas (P = 200 atm. The critical density of the gas CO2 is 0.170 and 2. (C) H2 and He show negative deviation while CO2. The correct order of normal boiling points of O2. gas equation will be- n2 a nRT (A) PV = nRT – (B) PV = nRT + nbP (C) PV = nRT (D) P = V V b 29. T = 273 K) (p) compressibility factor 1 (B) hydrogen gas (P ~ 0.390. CH4 and O2 show positive deviation. r3 in cm3 is approximately.5 atm and 500 K (D) 15 atm and 500 K 32. If r is the radius of the molecule. is (A) O2< N2 < NH3 < CH4 (B) O2< N2 < CH4 < NH3 (C) NH3 < CH4 < N2 < O2 (D) NH3 < CH4 < O2 < N2 33. mol2 respectively. The curve of pressure volume (PV) against pressure (P) of the gas at a particular temperature is as shown. the value of compressibility factor Z = (PVm / RT = Vreal/Videal) has a value of one over a wide range of pressure. 1. 4. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS. NH3 and CH4. CH4 and O2 show negative deviation from ideal gas equation. A real gas most closely approaches the behaviour of an ideal gas at - (A) 15 atmospheres and 200 K (B) 1 atm and 273 K (C) 0. N2. (D) H2 and He are less compressible than that of an ideal gas while CO2. This is due to the fact that in the van der Waal’s equation (A) the constant 'a' is negligible and not 'b' (B) the constant 'b' is negligible and not 'a' (C) both the constant 'a' and 'b' are negligible (D) the effect produced due to the molecular attraction compensates the effect produced due to the molecular volume 31. atm. Match gases under specified conditions listed in Column-I with their properties / laws in Column-II.3 (JEE/REE Questions of Previous Years) 1.28. P.2.2006] (A) The plot I is applicable provided the vander waals constant a is negligible.2002] 7. The Urms of gas is [JEE . (b) If the vapours behave ideally at 1000 K determine the average translational kinetic energy of a molecule [JEE .4 litres (D) Vm = 44. For one mole of gas the average kinetic energy is given as E.T. Which of the following volume (v)-temeprature (T) plots represent the behaviour of one mole of an ideal gas at one atmospheric pressure . [JEE 2000] (A) Vm > 22. The root mean square velocity of an ideal gas at constant pressure varies with density (d) as- (A) d2 (B) d (C) d (D) 1 d [JEE 2001] 9.m. (D) The plot IV is applicable provided the temperature of the gas is much higher than its critical temperature.36 Kg m–3.33 times faster than oxygen under the same conditions.2005] 1 1 (A) (B) 3 (C) (D) 2 2 3 4. 3. The compression factor (compressibility factor) for 1 mole of a van der Waals’ gas at 0ºC and100 atmosphere pressure is found to be 0. (a) Determine (i) molecular weight (ii) molar volume (iii) compression factor(z) of the vapours and (iv) which forces among gas molecules are dominating. therefore. The average velocity of gas molecules is 400 m/sec calculate its r.5.2001] 10.The vapour effuses through a small hole at a rate of 1.s. The compressibility of a gas is less than unity at S. Figure displays the plot of the compression factor Z verses p for a few gases IV I III II Which of the following statements is/are correct for a van-der waals gas ? [JEE . velocity at the same temperature [JEE .2004] 2E 3E 2E 3E (A) (B) (C) (D) M M 3M 2M 5. (C) The plot III is applicable provided the vander waals constants a and b are negligible. constant a. Assuming that the volume of gas molecule is negligible. Ratio of rates of diffusion of He and CH4 (under identical conditions) [JEE . [JEE .4 litres (C) Vm = 22.8 litres Page # 22 . (B) The plot II is applicable provided the vander waals constant b is negligible.2003] 6. calculate the van der Waals’.4 litres (B) Vm < 22. [JEE 2002] (A) (B) (C) (D) 8. The density of the vapours of a substance at 1 atm pressure and 500 K is 0. the attractive or repulsive. if the density of liquid water is 1. b = 0. Given that a = 3. If T is the temperature of the gas.0 g argon in a bulb is put in a bath having temperature higher by 50 K than the first one.11. at a given temperature the ratio of the rates of diffusion rA/rB of gases A and B is given by .06 cm3 13. At 100 °C and 1 atm. a =3. [JEE 1999] (A) low temperature and low pressure (B) low temperature and high pressure (C) high temperature and low pressure (D) high temperature and high pressure 16. The temperature T is equal to . [JEE 1999 ] (A) 510 K (B) 200 K (C) 100 K (D) 73 K 15. The rms velocity of hydrogen is 7 times the rms velocity of nitrogen.0006 g cm–3. According to Graham’s law.8 g of argon gas has to be removed to maintain original pressure. [JEE 1998] (A) (PA/PB)(MA/MB)1/2 (B) (MA/MB) (PA/PB)1/2 (C) (PA/PB) (MB/MA)1/2 (D) (MA/MB) (PB/PA)1/2 (where P and M are pressure and molecular weights of gases A and B respectively) Page # 23 . the pressure of 4. A gas will approach ideal behaviour at . then calculate the pressure exerted by one mole of CO2 gas at 273 K.592 atm liter2 mol-2. 0. that the volume occupied by water molecules in 1 liter of st eam at that temperature is .0427 liter mol–1 (b) If volume occupied by CO2 molecules is negligible.0 g cm–3 and that of water vapour is 0.Also report the pressure of gas if it behaves ideally in nature.2000] 14. (a) Calculate the pressure exerted by 5 mole of CO2 in one liter vessel at 47º C using van der Waals’ equation. At a temperature T K.592 dm6 atm mol-2 [JEE . [JEE 2000] (A) 6 cm3 (B) 60 cm3 (C) 0.6 cm3 (D) 0. then [JEE 2000] (A) T(H2 ) T(N2 ) (B) T(H2 ) T(N2 ) (C) T(H2 ) T(N2 ) (D) T(H2 ) 7 T(N2 ) 12. 1. C 11.3 1.149 lit. T = 22. A 17. (a) 18. 0. C 7.2 SECTION (A) : 1. D 31.25 × 10–3 .88 atm 14. A 29. (a) 0.73 x 104 cm/sec 9. A 20. D 9. D 4. D – r 2. 50. C – p. C 22.98 . 6. C 8. B 33. A – p. C 8. B 11. A 2. 131. A 5. B 15.16 J/mol 10. A 5.Exercise . C Exercise . A 21. s . B – r . 434 m/s 6. C 13. q . B SECTION (B) : 19./min.253 Litre2 mole2 atm 10. 2T2 T1 6. 808. C 12.07 × 10–20 J 7.1. D 27.4 14. 19.225 (b) 2. C Page # 24 . 3. 1. . 13. ABC 3.36 atm (b) 34. C 4. 0. 1/24 SECTION (C) : 50 1 17. D 10. 3.227 lit/min. B 16. 7 atm. M = 128 g/mol 15. D 9. 220 mm 7.2 x 1015 2pT2 5.25 atm 2. litre 20. 448 g mol–1 16.004 41 3 Exercise . B 15. (b) 1. B 24. C 3. B 12. B 13. (a) 77. 1.0 K 8. 70. 490 mm. A 14. D 25. 1. A 28. C 26. 375 K 4. A 18. C 32. A 6. C 16. C 23.82 cc 12. 1327ºC SECTION (B) : 11. C 30. 351°C 18.1 SECTION (A) : 1. C 34.218 atm.