The States of matter : Numerical Questions : Part-(3):

(1) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

(2) A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

(3) A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

(4) Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in 

(a) mass and 

(b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )

(5) 1 mole of CCl4 vapours at 77oC occupies a volume of 35.0 L. If vander waal's constants are a = 20.39 L 2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under 

(a) low pressure region. 

(b) high pressure region.

(6) Two moles of ammonia gas are enclosed in a vessel of 5 litre capacity at 27oC. Calculate the pressure exerted by the gas, assuming that 

(i) the gas behaves like an ideal gas (using ideal gas equation). 

(ii) the gas behaves like a real gas (using van der Waal's equation). Given that for ammonia, a = 4.17 atm litre2 mol–2 and b = 0.037 litre mol–1

(7) The compressibility factor for 1 mole of a van der Waals gas at 0oC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.

(8) The rms speed of an ideal gas at 27°C is 0.3 ms–1 . Its rms speed at 927°C (in ms–1) is

(9) The rms speed of CO2 at a temperature T (in kelvin) is x cm s–1.At what temperature (in kelvin) the rms speed of nitrous oxide would be 4x cm s–1 ?

(10) A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

(11) One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

(12) 1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

(13) A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

(14) A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

(15) The density of methane at 2.0 atmosphere pressure and 27°C is

(16) A spherical balloon of 21 cm diameter is to be filled up with hydrogen at 0oC and 1 atm from a cylinder containing the gas at 20 atmosphere at 27oC. If the cylinder can hold 2.82 litre of water at 0oC and 1 atm, calculate the number of balloon that can be filled up.

(17) When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions?

(18) An open vessel at 27oC is heated at constant pressure until 3/5th of the air in it has been expelled. Find 

(a) the temperature at which vessel was heated ? 

(b) the moles of air eascaped out, if vessel were heated to 900 K ? 

(c) temperature at which half of the air escapes out ?

(19) In a barometeric tube Hg is replaced by H2O then find the height of H2O column to measure the atmospheric pressure.Assume that vapour pressure of H2O in negligible.

(20) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

(21) The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm, what is the depth of the lake ? The density of lake-water and Hg are 1.0 gm/ml and 13.6 gm/ml, respectively. Assume that temperature of lake water is equal to that of atmosphere.Also neglect the contribution of pressure due to surface tension.

(22) A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

(23) Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

(24) A 10 cm column of air is trapped by a column of Hg, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. Calculate the length of air column when the tube is fixed at the same temperature (a) vertically with open end up (b) vertically with open end down (c) At 45° from vertical, with open end up.