GASEOUS STATE IIT NUMERICALS
1. A mixture of N 2 , NO and NO2 gases was analyzed by selective absorption of the oxides of nitrogen following the decrease in volume of the original mixture. The initial mixture has a volume of 2 .74 ml. After treatment with water, which absorbed the N02, the volume was 2.02 ml. A ferrous sulphate solution was then shaken with the residual gases to absorb the NO, after which the volume was 0.25 ml. (All volumes were measured under identical P-T conditions). Neglecting the water vapour, find the composition composition of the gas mixture mixture by volume. 2. 0.553 g of a Boron-Hydrogen compound created a pressure of 0.658 atm in a bulb of 407 ml at 100C. Analysis Analysis showed it to be 85.7% 85.7% boron. Calculate its molecular formula . 3. A mixture of methane, ethene and carbondioxide measuring 10 ml was exploded with excess of air. After explosion there was a contraction of 17 ml and after treatment with KOH solution, there was a further contraction of volume by 14 ml. What was the composition of the mixture ? (Volume measurements refer to same P-T conditions) 4. A 20.0 cm^3 mixture of CO, CH 4 and He gases is exploded by an electric discharge at room temperature with excess of oxygen. The decrease in volume is found to be 13.0 cm^3. A further contraction of 14.0 cm^3 occurs when the residual gas is treated with KOH solution. Find out the composition of the gaseous mixture is terms of volume percentage. 5. 56 g of nitrogen are confined to a 5L flask at 37C. Calculate its pressure (i) assuming N2 as an ideal gas, (ii) using Vander Waals, equation, the coefficients for nitrogen being a = 4.17 atm L^-1 Mol^-2 and b=0.037 L mol^-1. 6. A certain gas occupies 0.418 L at 300 K 740 mm Hg. (i) What is its volume at STP? (ii) If the swne gas weighs 3.00 g, what is its rholecular weight? (iii) If we increase the weight of the gas to 7.50 g in the same vessel and the temperature is changed to 280 K, what would be its pressure? Report the results in 3 significant figures. 7. Assume that air contains 79% N 2 and 21%O2 by volume. Calculate Calculate the density of moist air at 25C and 1 atm pressure when relative humidity is 60%. The vapour pressure of water at 25C is 23.78 mm. Relative humidity is given by percentage relative humidity humidity =
100 x partial pressure of Water Vapour pressure of water at that terpperature 8. The allowed threshold limit for the poisonous gas H 2S is 10 mg/m^3 . What pressure does this correspond to at 20C assuming H2S as an ideal gas ? What is the volume of H2 S required at 600C & 1 atm pressure to carry out the sulphidation of 2.54 g copper to Cu2S" 9.An LPG cylinder weighs 14.8 kg when empty, when full, it weighs 29.0 kg and shows a pressure of 2.5 atm. In the course of use at 27C, the weight of full cylinder is 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 n - butane with normal B. P at 0C. 10.A water gas mixture has the composition by volume of 50% H2,45% CO and 5% C02. (i) Calculate the volume in litres at STP of the mixture which on treatment with excess steam will contain 5 litres of H2. The stoichiometry for the water gas shift reaction is CO + H20 ---- C0 2 + H2 (ii) Find the density of the water gas mixture in kg m^-3. (iii) Calculate the moles of the absorbents KOH, Ca(OH) 2 and ethanolamine, HO-CH2 -CH2-NH2 required respectively to collect the C0 2 gas obtained. 11.Calculate molecular diameter of He from its vander waal's constant b = 24 ml mole^-1. 12.Average velocity of CO 2 at T1 K and the most probable velocity at T 2 K is 9 x 10^4 cm/sec. Calculate the values of T 1 and T2. 13.The kinetic molecular theory attributes an average kinetic energy of 3 RT to each 2 N particle. What rms speed would a mist particle of mass 10^-12 g have at room temp (27C) according to kinetic theory of gases. 14.Calculate the change in pressure when 1.04 mole of NO and 20g O2 in a 20 litre vessel originally at 27C react to produce the maximum quantity of N02 possible according to the equation. 2NO (g) + 02 (g) ---- 2NO2 (g) 15.The rate of diffusion of a sample of ozonized oxygen is 0.98 times that of pure oxygen. Find the percentage (by volume) of ozone in the ozonised sample. Also report percentage weight. Ans.1. N2 =0.25mL(9.1%),NO=1.77mL(64.6%) & NO 2=0.75mL(26.3%) Ans.2. B5H9
Ans.3. CH4=4.5mL ,C2H4=4mL &CO2=1.5mL Ans.4. CH4=20% by vol ;CO=50% by vol ; He=30% by vol Ans.5. (i)10.17atm (ii)9.65atm Ans.6. (i)0.370, (ii)182,(iii)2.27 Ans.7. 1.171g/L Ans.8. 7.1 x 10^-6atm ; 1.43L Ans.9. P=1.50atm ; V=2.463m^3 Ans.10. (i)5.263L (ii)0.7Kg/m^3(iii)KOH -.2348 moles, Ca(OH) 2-0.1174 moles, Ethanolamine:0.2348moles Ans.11. 2.67A Ans.12. T1=1682.5K ; T2=2143K Ans13. 0.35cm/sec Ans.14. 40.64atm Ans15. 8.25% by volume ,11.86% by weight. 1. A 0.750 g sample of solid benzoic acid, C 7 H602 was placed in a 0.500 L pressurized reaction vessel (autoclave) filled with 02 at 10.0 atm. pressure and 298 K. The combustion products of benzoic acid are only water and C0 2 . Find the mole fractions of C02 and H20vapour in the resulting gas mixture brought to the initial temperature ? (The vapour pressure of water at 298 K is 23.8 torr) 2. A 1-L gas bulb contains 1.03 x 10^23 hydrogen molecules. If these molecules are confined under a pressure of I bar, find (i) the r m s velocity and (ii) the temperature. What is the energy required to double the rms velocity? 3. Calculate the pressure exerted by 10^23 gas molecules, each of mass 10^-25 kg in a container of volume 1 dm^-3 . Root mean square velocity of the gas molecule is 1 km/s What is the total kinetic energy of these molecules? What is the temperature of the gas? Using heat exchangers, when the temperature is reduced to half its original value find the rms velocity of the gas. 4. Density of dry air (only N 2 & 02 ) is 1. 146 g/ litre at 740 mm and 300 K. Calculate composition of air by weight assuming ideal nature. 5. A mixture of 90 mole % of H 2and 10 mole % D2 at 298 K and a total pressure of 1 atm is allowed to effuse through a small orifice of area 0.3mm^2.Calculate composition of the initial gas that passes through. 6. A 4:1 molar mixture of He and CH 4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out initially?
7. 2 g of a gas A are introduced into an evacuated flask kept at 25C. The pressure is found to be 1 atm. If 3 g of another gas B are added to the same flask, the total pressure becomes 1.5 atm, Assuming ideal gas behaviour, calculate: (a) The ratio of mol. weight Of M A and MB (b) the volume of the vessel, if A is 0 2 8. One of the best rocket fuels is dimethylhydrazine. When mixed with dinitrogentetroxide, N 204, it reacts according to the equation (CH3)2 N2H2(l) + 2N204(l) ------ 3N2(g) + 4H20(l) + 2CO2(g) If 2.5 mol of dimethylhydrazine reacts completely with N204 and if the product gases are collected at 20C in a 250 L vessel, what is the pressure in the vessel? 9. At room temperature the following reaction goes to completion : 2NO +02 ----- 4 2NO2 ------ 4 N204. Dimer N204 at 262 K is solid. A 250 ml flask and a 100 ml flask are separated by a stop contraction cock. At 300 K , the nitric oxide in the large flask exerts a pressure of 1.053 atm and the smaller one containsO 2 at 0.789 atm. The gases are mixed by opening the stop cock and after the end of the reaction, the flasks are cooled at 220 K. Neglecting the vapour pressure of dimer find out the pressure and composition of gas remaining at 220 K. 10.The mean kinetic energy of a molecule at 0C is 5.621 X 10 ^ -14erg. Calculate Boltzmann's constants If the value of R = 8. 314 x 10^7 erg, then also calculate the no. of molecules present in one mole of gas. 11.Calculate the temperature values at which the molecules of the first two members of the homologous series, C nH2n+2 Will have the same rms speed as C02 gas at 770 K. The normal b.p. of n-butane is 273 K. Assuming ideal gas behaviour of n-butane upto this temperature, calculate the mean velocity and the most probable velocity of its molecules at this temperature. 12.The mass of molecule A is twice the mass of molecule B. The rms speed of A is twice the rms speed of B. If two samples of A and B contain same no. of molecules, what will be the ratio of pressure of two samples in separate containers of equal volume. 13.Two gases in adjoining vessels are brought into contact by opening a stop cock between them. One vessel contains NO at 800 mm, 220 K, and has 0.25 litre volume. The other vessel of 0. 1 litre O 2 at 600 mm and 220 K. The reaction gives to the formation of solid N 204 and is continued till completion. Calculate
a) gas left after reaction and at what P? b) the weight of N20 4 formed. 14.A certain quantity of an organic liquid (mol. wt 85) was introduced into an air filled flask of volume 6.5 litre and sealed at a temperature of 17 C and 760 mm of Hg. The flask was heated to a temperature of 307 C where liquid is completely vaporized & the pressure is registered 4.3 atm. Calculate the amount of organic liquid introduced into the flask. 15.A bulb of three litre capacity filled with air is heated from 27 C to t C. The air thus expelled measured 1.45 litre at 17 C. Considering the pressure to be 1 atm. throughout the experiment and ignoring the expansion of bulb, calculate t. Ans.1. Mole Fraction of CO2=0.213 & mole fractio of H2 O vapour=0.0032 Ans.2. 934m/s ;71.3; 456.15J Ans.3. 3.33 x 10^6 pa ; 5KJ ; 2414K ; 1/ √2 Κ m/sec Ans.4. 72.42% , 27.58% Ans.5. H2 : D2 = 92.7 : 7.3(ratio of maole %) Ans.6. He : CH4=8.1 Ans.7. (a)1/3 ; (b)1.529L Ans.8. 1.203atm Ans.9. Mole of NO left=4.29 x 10^-3 , PNO left=0.221atm Ans.10. K=1.372 x 10^-16ergs/mol/K ; N=6.0587 x 10^23 Ans.11.280K , 525K ,3.157 x 10^2m/sec , 2.798 x 10^2m/sec Ans.12. PA=8PB Ans13. (a)NO, 227.48mm; (b)0.40g Ans.14. 26.69g Ans15. 327C
