Gaseous State Exercise # 4

Exercise # 4 [Subjective Type Questions] 1. A quantity of an ideal gas is collected in a graduated tube over the mercury. The volume of gas at 20 ºC is 50 ml and the level of mercury is 100 mm above the outside of the mercury level. The atmospheric pressure is 750 mm. Volume of gas at STP is : (Take R = 0.083 lt. atm/K/mole) 2. A quantity of hydrogen is confined in a chamber of constant volume. When the chamber is immersed in a bath of melting ice, the pressure of the gas is 1000 torr. (a) What is the Celsius temperature when the pressure manometer indicates an absolute pressure of 400 torr ? (b) What pressure will be indicated when the chamber in brought to 100ºC ? 3. An open vessel at 27ºC is heated until (3/5)th of the air in it has been expelled. Assuming that the volume of the vessel remains constant. Find out. (a) The temperature at which vessel was heated. (b) Volume of the air escaped out if vessel is heated to 900 K (c) The temperature at which half of the air escapes out. 4. A gas cylinder contains 320 g oxygen gas at 24.6 atm pressure and 27ºC. What mass of oxygen would escape if first the cylinder were heated to 133ºC and then the valve were held open until the gas pressure was 1.00 atm, the temperature being maintained at 133ºC ? (R = 0.0821 L. atm/K/mole) 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 sphere V by a tube and stopcock. The second sphere is initially evacuated and the stopcock is closed. If the 2 stopcock is opened the temperature of the gas in the second sphere becomes T 2. The first sphere is maintained at a temperature T1 . What is the final pressure p1 within the apparatus ? of volume 6. A gas occupies 100.0 mL at 50°C and 1 atm pressure. The gas is cooled at constant pressure so that volume is reduced to 50.0 mL. What is the final temperature of the gas. 7. A sample of gas at 27ºC and 1.00 atm pressure occupies 2.50 L. What temperature is required to adjust the pressure of that gas to 1.50 atm after it has been transferred to a 2.00 L container ? 8. Assuming the same pressure in each case, calculate the mass of hydrogen required to inflate a balloon to a certain volume V at 127ºC if 8 g helium is required to inflate the balloon to half the volume, 0.50 V, at 27ºC. 9. A mixture of gases at 760 torr contains 55.0% nitrogen, 25.0% oxygen and 20.0% carbon dioxide by mole. What is the partial pressure of each gas in torr ? 10. What will be pressure exerted by a mixture of 3.2g of methane of 4.4g of carbon dioxide contained in a 9dm3 flask at 27C ? 11. Oxygen and cyclopropane at partial pressures of 570 torr and 170 torr respectively are mixed in a gas cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen? 12. At the top of a mountain the thermometer reads –23ºC and the barometer reads 700 mm Hg. At the bottom of the mountain the temperature is 27ºC and the pressure is 750 mm Hg. Compare the density of the air at the top with that at the bottom. 13. A 300 mL sample of hydrogen was collected over water at 21ºC on a day and the pressure over water was 748 Torr and vapour pressure of water was 19 Torr. (a) How many mmoles of H2O were present ? (b) What is the mole fraction of H2 in the moist gas mixture ? (c) What would be the mass of the gas sample if it were dry ? 470 GASEOUS STATE 14. A container contains the mixture of water vapour and oxygen gas with total pressure 1.1 atm at certain temperature. If volume is made one third then find the total pressure (assume aqueous tension of water at this temperature is 0.1 atm.) ? 15. For 10 minute each, at 0 ºC, from two identical holes nitrogen and an unknown gas are leaked into a common vessel 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? 16. 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 ? 17. The rates of diffusion of two gases A and B are in the ratio 1 : 4. If the ratio of their masses present in the mixture is 2 : 3. The ratio of their mole fraction is : 18. 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. 19. The root mean square speed of gas molecules at a temperature 27 K and pressure 1.5 bar is 1 x 10 4 cm/sec. If both temperature and pressure are raised three times, calculate the new rms speed of gas molecules. 20. At what temperature would the most probable speed of CO2 molecules be twice that at 127ºC 21. Suppose a gas sample in all have 6 x 10 23 molecules. Each 1/3 rd of the molecules have rms speed 104 cm/sec, 2 x 104 cm/sec and 3 x 104 cm/sec. Calculate the rms speed of gas molecules in sample. 22. At what temperature will hydrogen molecules have the same root mean square speed as nitrogen molecules have at 35ºC ? 23. If density of vapours of a substance of molar mass 18 gm at 1 atm pressure and 500 K is 0.36 kg m–3, then calculate the value of Z for the vapours. (Take R = 0.082 L atm mole–1 K–1) 24 One litre gas at 400 K and 300 atm pressure is compressed to a pressure of 600 atm and 200 K. The compressibility factor is changed from 1.2 to 1.6 respectively. Calculate the final volume of the gas. 25. Reduced temperature for benzene is 0.7277 and its reduced volume is 0.40. Calculate the reduced pressure of benzene. 26. The critical temperature and critical pressure of a gas are 31ºC and 728 atmospheres respectively. Calculate the constants 'a' and 'b'. 27. Calculate the volume occupied by 2.0 mole of N2 at 200 K and 8.21 atm pressure, if PC VC 3 = and RTC 8 Pr Vr Tr = 2.4. 28. Explain the physical significance of van der waals parameters. 29. Using the van der Waals equation, calculate the pressure of 10.0 mol NH3 gas in a 10.0 L vessel at 27ºC.  2 a  T  P + n 2  (V – nb) = nRT V   30. a = 4.2 L2. atm/mol2 b = 0.037 L/mol 1 litre of a mixture of CO and CO2 is taken. This mixture is passed through a tube containing red hot charcoal. The volume now becomes 1.6 litres. The volumes are measured under the same conditions. Find the composition of the mixture by volume. 470 31. 40 ml of ammonia gas, taken in an eudiometer tube, was subjected to sparks till the volume did not further change. The volume was found to increase by 40 ml. 40 ml of oxygen gas then mixed and the mixture was further exploded. The gases remained were 30 ml. Deduce the formula of ammonia. 32. When 100 ml of a O2 – O3 mixture was passed through turpentine, there was reduction of volume by 20 ml. If 100 ml of such a mixture is heated, what will be the increase in volume? [Hint: O3 is absorbed by turpentine] 33. 60 ml of a mixture of nitrous oxide and nitric oxide was exploded with excess of hydrogen. If 38 ml of N2 was formed, calculate the volume of each gas in the mixture. 34. A mixture of formic acid and oxalic acid is heated with concentrated H2SO4. The gases produced are collected and on its treatment with KOH solution the volume of the gas decreased by one-sixth. Calculate the molar ratio of the two acids in the original mixture. [Hint : H2SO4 is a dehydrating agent. HCOOH produces H2O and CO; H2C2O4 produces H2O, CO2 and CO] 35. A sample of a gaseous hydrocarbon occupying 1.12 litres at NTP when completely burnt in air produced 2.2 g of CO2 and 1.8 g of H2O. Calculate the weight of the compound taken and the volume of O2 at NTP required for its burning. Find the molecular formula of the hydrocarbon. 36. A vertical hollow cylinder of height 1.52 m is fitted with a movable piston of negligible mass and thickness. The lower half of the cylinder contains an ideal gas and the upper half is filled with mercury. The cylinder is initially at 300 K. When the temperature is raised, half of the mercury comes out of the cylinder. Find the temperature, assuming the thermal expansion of mercury to be negligible. 37. A column of Hg of 100 mm in length is contained in the middle of a narrow tube 1 m long which is closed at both ends. Both the halves of the tube contained air at a pressure of 760 mm of Hg. By what distance will the column of Hg lie displaced if the tube is held vertical. Assume decrease in length of mercury column to be negligible , also take the process at constant temperature. (isothermal process). 38. A container holds 22.4 litre of a gas at 1 atmospheric pressure and at 0ºC. The gas consists of a mixture of argon, oxygen and sulphur dioxide in which : (a) Partial pressure of SO2 = (Partial pressure O2) + (Partial pressure of Ar) (b) Partial pressure of O2 = 2 × partial pressure of Ar Calculate the density of the gas mixture under these conditions. 39. A mixture of nitrogen and water vapours is admitted to a flask which contains a solid drying agent. Immediately after admission, the pressure of the flask is 760 mm. After some hours the pressure reached a steady value of 745 mm. (a) Calculate the composition, in mol and per cent of original mixture. (b) If the experiment is done at 20ºC and the drying agent increases in weight by 0.15 g, what is the volume of the flask ? (the volume occupied by the drying agent may be ignored) ? 40. A flask of 1.5 L capacity contains 400 mg of O2 and 60 mg of H2 at 100°C. Calculate the total pressure of the gaseous mixture. If the mixture is permitted to react to form water vapours at 100°C, what materials will be left and what will be their partial pressures. 41. A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP, from a cylinder containing the gas at 20 atm at 27° C. If the cylinder can hold 2.82 litre of water, calculate the number of balloons that can be filled up. 472 GASEOUS STATE 42. An LPG cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg & shows a pressure of 2.5 atm. In the course of use at 27° C. The weight of the full cylinder reduced to 23.2 kg. Find out the volume of the gas in cubic metres used up at the normal usage conditions and the final pressure inside the cylinder. Assume LPG to be nbutane with normal boiling point 0°C. 43. A closed container of volume 0.02 m3 contains a mixture of neon and argon gases, at a temperature of 27°C and pressure of 1 × 105 Nm–2. The total mass of the mixture is 28 g. If the gram molecular weights of neon and argon are 20 and 40 respectively. Find the masses of the individual gases in the container, assuming them to be ideal. (Universal gas constant R = 8.314 J/mole K) 44. 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. 45. 1 mole of CCl 4 vapours at 77°C occupies a volume of 35.0 L.If van der Waal’s constant are a = 20.39 L2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under, (a) low pressure region (b) high pressure region 46. At 27°C, hydrogen is leaked through a tiny hole into a vessel for 20 min. Another unknown gas at the same T & P as that of H2, is leaked through the same hole for 20 min. After the effusion of the gases the mixture exerts a pressure of 6 atm. The hydrogen content of the mixture is 0.7 mole. If the volume of the container is 3 litre, what is molecular weight of unknown gas. (Use R = 0.0821 L atm K–1 mole–1) 47. At 20ºC, two balloons of equal volume and porosity are filled to a pressure of 2 atm, one with 14 kg N2 and other with 1 kg of H2. The N2 balloon leaks to a pressure of 1/2 atm in 1 hr. How long will it take for H2 balloon to reach a pressure of 1/2 atm ? 48. A mixture of ethane & ethene occupies 40 litre at 1 atm pressure & 400 K temperature. The mixture reacts completely with 130 g of O2 to produce CO2 & H2O. Assuming ideal gas behaviour, calculate the mole fractions of ethane and ethene in the mixture. 49. 10 ml of a mixture of CH4, C2H4 and CO2 was exploded with excess of air. After explosion there was a contraction of 17 ml and after treatment with KOH, there was further reduction of 14ml. What was the composition of the mixture? 50. To an evacuated 504.2 mL steel container is added 25 g CaCO3 and the temperature is raised to 1500 K causing a complete decomposition of the salt. If the density of CaO formed is 3.3 g/cc, find the accurate pressure developed in the container using the Van der waals equation of state. The van der waals constants for CO2(g) are L2 – atm L a=4 , b = 0.04 . (Ca - 40, C - 12, O - 16) mol mol2 472