REAL GASES. (B) pv. (D) pv. 3. The compressibility factor of a gas is less than unity at STP. Therefore, molar volume (V m.

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Bernard Newton
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1 SINGLE ORRET ANSWER REAL GASES 1. A real gas is suosed to obey the gas equation ( b) = at STP. If one mole of a gas occuies 5dm 3 volume at STP, then its comressibility factor is (b=.586 L mol 1F) (A) At critical temerature, which of the following grahs is correct? (A) 3. The comressibility factor of a gas is less than unity at STP. Therefore, molar volume ( m ) (A) m >.4 L m <.4 L m =.4 L m = 44.8 L 4. The behaviour of a real gas is usually deicted by lotting comressibility factor Z versus at a constant temerature. At high temerature and high ressure, Z is usually more than one. This fact can be exlained by van der Waals equation when (A) The constant a is negligible and not b Both constant a and b are negligible The constant b is negligible and not a Both constants a and b are not negligible 5. Given the value of their van der Waals constant a, arrange the following gases in the order of their exected liquefaction ressure at a temeraturet. T is below the critical oint the critical oint of all the gases. Gas a (atm L mol ) H 4 Kr N l (A) H 4 < Kr < N < l N < H 4 < Kr < l l < Kr < H 4 < N l < N < Kr < H 4 6. The comressibility factor for a gas under a given set of conditions is found to be The gas under the given set of conditions is the (A) Highly reactive Least reactive Almost real Almost ideal 7. The comressibility factor Z, er mole of a gas is. B The equation of state for a real gas can be exressed in the form Z 1... [virial equation. Given that a = 1.36 L atm/mol and b = L mol 1, what is the value of B (in mol/ L), the second virial coefficient for oxygen 0? (A)

2 8. For H gas the van der Waals equation reduces to a 1 R (A) = + b T 9. The van der Waals aramenters for gases A, B, and D are as follows : Gas a ( L atm/ mol ) A B D b ( L/mol) The increasing order of critical temerature is (A) A < B < < D < B < A < D < A < D < B < A < B < D 10. The sloe for an isochore lotted for a van der Waals gas neglecting molecular attractions is equal to (A) R b R R b R b 11. NH 3 gas is liquefied more easily than N. Hence, (A) an der Waals constant a and b of NH 3 > that of N an der Waals constant a and b of NH 3 < that of N a(nh ) a(n ) but b(nh ) b(n ) 3 3 a(nh ) a(n ) but b(nh ) b(n ) 3 3 MORE THAN ONE ORRET ANSWER 1. 1 mol of SO gas occuies.4 L at 73 and 1.1 atm. Identify the correct statement (A) omressibility factor of SO gas is 0.56 SO gas is more comressible than ideal gas ( M ) molar volume of the gas is lesser than ideal volume Ideal volume of the gas is less than molar volume of the gas 13. Select the correct statements (s) (A) A gas with Z > 1 will have a molar volume greater than.414 L at STP At high temerature, b 1 At high ressure, the volume correction factor of a gas can be neglected At low ressure, the ressure correction factor can be neglected

3 14. onsider the equation Z. Which of the following statements is/are incorrect? (A) When Z > 1 real gases are easier to comress than the ideal gas When Z = 1 real gases get comressed easily When Z > 1 real gases are difficult ot comress When Z = 1 real gases are diffcult ot comress 15. an der Walls constant for three different gases are given Gas a b X Y Z Which of the following is correctly matched? (A) Maximum critical temerature Y Maximum critical volume Z LINKED-OMPREHENSION TYPE QUESTIONS Most ideal behavior X Maximum critical ressure X Paragrah I : The gases which strictly follow the general equation ( = n) are called ideal or erfect gases. A very convenient method of studying deviation of real gases from ideal behaviour is through a comressibility factor (Z) Z. n 16. At low ressure, the van der Waals equation reduces to (A) a m Z 1 b m Z 1 m a m Z At Boyle s temerature, comressibility factor Z for a real gas is (A) Z = 1 Z = 0 Z > 1 Z < The behaviour of a real gas is usually deicted by lotting comressibility factor Z virus resure at a constant temerature. At high temerature and resure, Z is usually more than one. This fact can be exlained by van der Waals equation when (A) The constant a is negligible but not b The constant b is negligible but not a Both the constants a and b are negligible Both the constnats a and b are not negligible

4 an Paragrah II : The van der Waals equation for a moles of gas is reresented as v ( nb) = n where, a and b are van der Waals constants. As regard b, it is incomressible volume er mole of a gas. The constant a is measure of the van der Waals forces of cohesion existing between the molecules of a given gas. The greater the value of a, the greater is the strenth of the van der Waals forces. At low ressure (34.96 atm) volume of O will be sufficiently large and b may be ignored in comarision. Since, H have comaratively small masses, the attractive force between thier molecules are too small, hence correction factor negligible at ordinary temerature. an remains omressibility factor (Z) (at TemeratureT) H O If the sloe of H line (shown in Fig) at STP is 0.1 atm 1, what would be the van der Walls constant b? (A).4 L mol 1.4 L mol L mol L 0. What would be the comressibility factor (Z) of H gas at STP? (A) The van der Waals constant a for O gas is greater than that of H gas. Its mean that be (A) Strength of van der Waals force of O gas is less than that of H gas Strength of van der Waal s force of O gas is equal to that of H gas O gas can be more easily liquefied H gas can be more easily liquefied MATRIX MATH TYPE QUESTIONS. The van der Waals constants a and b of a real gas are 3.6 L atm mol and 0.05 L mol 1 resectively. If 00 g of gas (molecular mass 40) is laced in 10 L vesel at 300 K, match the following. olumn I olumn II (A) Pressure correction (atm) () 0.5 Free sace for the molecules to move about (L) (q) Actual volume of the gas molecules er mole (L) ( r) 0.9 Effective volume occuied by total gas molecules (L) (s) 9.75

5 3. Match the following olumn I (A) = a = + b () (q) olumn II Hydrogen gas an der Waals equation at high ressure = (r) an der Waals equation at extremely low ressure Z = 1 + b (s) Real gas behaves as an ideal gas (t) an der Walls equation at low ressure 4. Match gases under secified conditions listed in olumn -I with their roerties/laws in olumn II olumn I (A) Hydrogen gas ( = 00 atm, T = 73 K) () olumn II omressibility Factor = 1 Hydrogen gas ( ~0,T = 73 K) (q) Attractive forces are dominant O ( = 1 atm, T = 73 K) (r) = n Real gas with very large molar volume (s) ( nb) = n (t) ( + nb) = n INTEGER ANSWER TYPE QUESTIONS 5. Two moles of a gas are confined to a 5 L flask at 7. Its ressure using van der Waals equation is... atm (a = 6.5 atm L mol and b = L mol 1 ) 6. The volume to be excluded due to only two molecules of a gas in collision with a fixed oint of imact is L N (N A = Avogadro number). If the value of a is 3.5 atm L mol ), then the value A of Boyles temerature is, ( x) K. What is the value of x? (R = 0.08 L atm K 1 mol 1 ) 7. The comressibility factor for N at 330K and 800 atm is 1.90 and at 570 K and 00 atm is A certain mass of N occuies a volume of 1 dm 3 at 330 K and 800 atm. olume occuied by same quantity of N gas at 570 K and 00 atm in litres is Find the number of correct statements among the following (A) The comresibility factor for He is b 1 The numerical value of van der Waals constant a for H O is higher than 6 H 6 due to H- bonding Ideal gas does not show Joule-Thomson effect All molecules of an ideal gas move with same seed (E) Gases like O and NH 3 can never show ositive deviation

6 9. olume correction for (X) moles of O is 0.08 L. If volume correction constant is 0.04 L/mol, find the value of (X) 30. For a gas obeying ( b) = a grah is lotted between olume ( litre) on Y-axis and temerature (K) on X-axis at a constant ressure of atm. Find the sloe of the line? 31. alculate the ressure exerted by g of carbon dioxide in 0.5 dm 3 at 98.15K using : (A) The ideal gas law and ander waals equation Given : [a = kpa dm 6 mol and b = 4.67 cm 3 mol 1 ] 3. N molecule is sherical of radius 100 m. (A) What is the volume of molecules is one mole of a gas? What is the value of vander Waal s constant b? 33. From the given equation for a gas at 300 K, d P = P P... alculate the molecular weight of gas (in gm/mole) [Where P (Pressure) is in atm and d (density) is in gm/lit.] [Given R = 0.08 atm lit. mol 1 ] 34. At K and under a ressure of Ma, the comressibility factor of O is alculate the mass of O necessary to fill a gas cylinder of 100 dm 3 caacity under the given conditions mole of l 4 vaours at 7 occuies a volume of 40 lit. If ander Waals constant are 4.6 L atm mol 1 and 1.15 Lmol 1. alculate comressibility factor under (A) Low ressure region [Take R = 0.08 lit-atm/mol/k] High Pressure region 36. The vander waals constant for O are a = 1.36 atm L mol and b = L mol 1. alculate the temeratue at which O gas behaves, ideally for longer range of ressure. 37. For a real gas (mol. mass = 30) if density at critical oint is 0.40 g/cm 3 and its T c calculate ander Waal s constant a (in atm L mol ) K, then 38. Find the critical constant (P c, c and T c ) in terms of A and B, also find comressibility factor (z) for the following equation of state. A B P Where A and B are constant, P = ressure and = molar volume.

7 1. (A) ANSWER WITH EXPLANATION b Z 1 n (A) (A) (A) a Tc b (B,) 13. (A, B) 14. (A, B, D) 15. (A, B, ) 16. (A) 17. (A) 18. (A) 19. (A) b.4 Sloe b.4 L / mol For H, b Z 1 1 (0.11) 1.1. A r; B s; q; D

8 3. A t; B,q; r,s; D,q REAL GASES ab At high resure b and is negligible as comared to a b, hence, = = b, and b Z 1 4. A,s; B r;,q; D r 5. n an (9) nb 6. (9) Excluded volume = L mol NA 1 b L mol 1 As N A L is excluded volume of two olecules of gas N A b NA L/mol 7. (4) Boyle s temerature a K Rb n Z n 330 K R 330 n 8. () 9. () 30. () 570 K R 570 By equalizing these two we get = 4 L nb n b 0.04 = + b b R Sloe

9 31. (a) kpa, (b) 5.55 kpa 3. (a) l mol 1, (b) dm 3 mol kg 35. (a) 0.975; (b) K B A A,T,P, comressibilty factor A 6RB 108B P 1 3

is more suitable for a quantitative description of the deviation from ideal gas behaviour.

is more suitable for a quantitative description of the deviation from ideal gas behaviour. Real and ideal gases (1) Gases which obey gas laws or ideal gas equation ( PV nrt ) at all temperatures and pressures are called ideal or perfect gases. Almost all gases deviate from the ideal behaviour