Gaseous State Exercise # 5

Exercise # 5 1. (B) 313 293 (C) 313 293 (D) 1 2 In vander Waal’s equation of state of the gas law, the constant ‘b’ is a measure of : (A) Intermolecular collisions per unit volume (B) Intermolecular attractions (C) Volume occupied by the molecules 3. [Previous Year Questions] [AIEEE/JEE-MAIN] As the temperature is raised from 20oC to 40oC, the average kinetic energy of neon atoms changes by a factor : (A) 2 2. Part # I (D) Intermolecular repulsions Which one of the following statements regarding helium is incorrect ? (A) It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable (B) It is used as a cryogenic agent for carrying out experiments at low temperatures (C) It is used to produce and sustain powerful superconducting magnets (D) It is used in gas-cooled nuclear reactors 4. Which one of the following statements is not true about the effect of an increase in temperature on the distribution of molecular speeds in a gas ? (A) The area under the distribution curve remains the same as under the lower temperature (B) The distribution becomes broader (C) The fraction of the molecules with the most probable speed increases (D) The most probable speed increases 5. Equal masses of methane and oxygen are mixed in an empty container at 25°C. The fraction of the total pressure exerted by oxygen is (A) 1/3 (B) 1/2 (C) 2/3 (D) 1 273 × 3 298 6. ‘a’ and ‘b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because : (A) a and b for Cl2 > a and b for C2H6 (B) a and b for Cl2 < a and b for C2H6 (C) a and Cl2 < a for C2H6 but b for Cl2 > b for C2H6 (D) a for Cl2 > a for C2H6 but b for Cl2 < b for C2H6 7. When r, P and M represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion (rA/rB) of two gases A and B, is given as: 8. 9. (A) (PA/PB) (MB/MA)1/2 (B) (PA/PB)1/2 (MB/MA) (C) (PA/PB) (MA/MB)1/2 The molecular velocity of any gas is: (A) inversely proportional to absolute temperature. (B) directly proportional to square of temperature. (C) directly proportional to square root of temperature. (D) inversely proportional to the square root of temperature. (D) (PA/PB)1/2 (MA/MB) The compressibility factor for a real gas at high pressure is : (A) 1 + RT/pb (B) 1 (C) 1 + pb /RT (D) 1 –pb/RT 474 GASEOUS STATE 10. 11. For gaseous state, if most probable speed is denoted by C*, average speed by C and mean square speed by C, then for a large number of molecules the ratios of these speeds are : (A) C* : C : C = 1.225 : 1.128 : 1 (B) C* : C : C = 1.128 : 1.225 : 1 (C) C* : C : C = 1 : 1.128 : 1.225 (D) C* : C : C = 1 : 1.225 : 1.128 A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g. of CO2. The empirical formula of the hydrocarbon is : (A) C2H4 12. Pb RT (B) Z = 1 + Part # II RT Pb (D) Z = 1 – a VRT (C) 1 : 4 (D) 7 : 32 T1  T2  (B) 2pi  T  T   1 2 T2 T1  T1T2  (C) 2pi  T  T   1 2  T1T2  (D) pi  T  T   1 2 [Previous Year Questions][IIT-JEE ADVANCED] For one mole of gas the average kinetic energy is given as E. The Urms of gas is : 2E M (A) (B) 3E M 2E 3M (C) (D) 3E 2M Ratio of rates of diffusion of He and CH4 (under identical conditions). (A) 3. (C) Z = 1 + Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure p i and temperature T1 are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to T2. The final pressure pf is :  T1  (A) 2pi  T  T   1 2 2. Pb RT (B) 3 : 16 T1 1. (D) C7H8 The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is ; (A) 1 : 8 14. (C) C6H5 If Z is a compressibility factor, van der Waals equation at low pressure can be written as : (A) Z = 1 – 13. (B) C3H4 1 2 (B) 3 (C) 1 3 (D) 2 Figure displays the plot of the compression factor Z verses p for a few gases IV I II III 474 Which of the following statements is/are correct for a van-der waals gas : (A) The plot I is applicable provided the vander waals constant a is negligible. (B) The plot II is applicable provided the vander waals constant b is negligible. (C) The plot III is applicable provided the vander waals constants a and b are negligible. (D) The plot IV is applicable provided the temperature of the gas is much higher than its critical temperature. 4. Match gases under specified conditions listed in Column-I with their properties / laws in Column-II. Column-I Column-II (A) Hydrogen gas (P = 200 atm, T = 273 K) (p) compressibility factor  1 (B) Hydrogen gas (P ~ 0, 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 5. A gas described by van der Waals equation (A) behaves similar to an ideal gas in the limit of large molar volumes (B) behaves similar to an ideal gas is in limit of large pressures (C) is characterised by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature. (D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally 6. The term that corrects for the attractive forces present in a real gas in the vander Waals equation is : (A) nb (B) an 2 V2 (C) – an 2 V2 (D) –nb 7. At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is. 8. According to kinetic theory gases (A) collisions are always elastic (B) heavier molecules transfer more momentum to the wall of the container (C) only a small number of molecules have very high velocity (D) between collisions, the molecules move in straight lines with constant velocities. 9. To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0ºC) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0°C is close to 10. For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs.1/V plot is shown below. The value of the vanderWaals constant a (atm.liter2 mol–2) : 476 PV (liter atm mol–1 GASEOUS STATE 24.6 23.1 21.6 20.1 0 2.0 3.0 1/V(mol liter–1) (A) 1.0 11. (B) 4.5 (C) 1.5 (D) 3.0 The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at –73 C is "M" times that of the de Broglie wavelength of Ne at 727 C. M is Paragraph for Questions 12 to 13 A fixed mass 'm' of a gas is subjected to transormation of states from K to L to M to N and back to K as shown in the figure K L N M Pressure Volume 12. The succeeding operations that enable this transformation of states are (A) Heating, cooling, heating, cooling (B) Cooling, heating, cooling, heating (C) Heating, cooling, cooling, heating (D) Cooling, heating, heating, cooling 13. The pair of isochoric processes among the transormation of states is (A) K to L and L to M (B) L to M and N to K (C) L to M and M to N (D) M to N and N to K 476 14. One mole of a monatomic real gas satisfies the equation p(V – b) = RT where b is a constant. The relationship of interatomic V(r) and interatomic distance r for the gas is given by V(r) V(r) (A) 0 (B) r 0 r V(r) V(r) (C) 0 0 (D) r r 15. The diffusin coefficeint of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is 16. A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is 3 1 m , 5 bar, 400 k A 3 3 m , 1 bar, 300 K B Figure 1 B A Figure 2 478 GASEOUS STATE EXERCISE - 5 : PART # I 1. C 2. C 3. C 4. C 5. A 6. D 7. A 8. C 9. C 10. C 11. D 12. D 13. D 6. A,C,D 7. 14. B PART # II 1. 434 m/s 2. A 8. M = 4 A, B, C, D 9. 3. D 4. A, B, C 5. 10. 7 11. C A  (p, s), B  (r), C  (p, q), D  (r) 12. 5 13. C 14. B 15. C B 16. 2.22 486