# Chapter 4: Ideal Gases and Gas Mixtures (Solution)

**Problem 4.1: **How many kilograms of nitrogen will occupy a volume of 1000 m^{3} at a pressure of 1.2 bar and a temperature of 400 K?

**Problem 4.2: **A gas occupies a volume of 100 m^{3} at 375 K and 1.25⨯10^{5} N/m^{2}. What volume will the gas occupy at 275 K and 1 bar?

**Problem 4.3: **20 kg of chlorine is to be stored in a container at 0.9 bar and 295 K. What should be the volume of the container?

**Problem 4.4: **(a) How many kilograms of liquid water will be obtained by the complete condensation of 5 m^{3} water vapor at 200 kPa and 1000 K? (b) The steam tables give the specific volume of water vapor to be 2.937 m^{3}/kg. Using this data calculate the mass of water vapor obtained and compare it with the results in part (a).

**Problem 4.5: **Steam tables give the specific volume of superheated steam at 1200 kPa and 925 K to be 0.3534 m^{3}/kg. How does it compare with the value obtained by the ideal gas equation?

**Problem 4.6: **It is desired to compress 7.00 kg of nitrogen gas to a volume of 0.5 m^{3} at 305 K. Calculate the pressure required.

**Problem 4.7: **A fire-extinguisher tank can hold 1 m^{3} of gas. The tank contains 10 kg of CO_{2} at 300 K. What will be the pressure of the gas in N/m^{2}?

**Problem 4.8: **A 20 L glass vessel contains 28 g nitrogen. If the vessel cannot withstand a pressure exceeding 120 kPa, up to what temperature the gas in the vessel can be heated?

**Problem 4.9: **Calculate the density at standard temperature and pressure of (a) methane and (b) sulfur dioxide.

**Problem 4.10: **A 50 m diameter spherical balloon contains air at 300 K and 1 bar. How many kilograms of air is present in the balloon? Take the molecular weight of air to be 29.

**Problem 4.11: **Find the mass of methane in a 100 m^{3} gas holder at 293 K if the pressure on the holder is 20 kPa gauge. The barometric pressure is 100 kPa.

**Problem 4.12: **How many kilograms of hydrogen can be stored at 325 K and 100 bar in a compressed gas cylinder that normally holds 0.5 kg hydrogen at 300 K and 130 bar?

**Problem 4.13: **A tank contains oxygen gas at 1.40⨯10^{7} N/m^{2}. On withdrawing 140 L of oxygen measured at 1.01⨯10^{5} N/m^{2}, the pressure in the tank is observed to fall to 1.30⨯10^{5} N/m^{2}. Assume that there is no change in the temperature of the gas. What is the volume of the tank in m^{3}?

**Problem 4.14: **A cooking gas cylinder can withstand a pressure of 15.0 atm. The pressure gauge of the cylinder indicates 12 atm at 300 K. During a sudden fire in the building the temperature starts rising. At what temperature will the cylinder explode?

**Problem 4.15: **Calculate the volume occupied at 400 K and 2 atm pressure by the gas evolved from 2 ml of solid CO_{2}. The density of solid CO_{2} = 1500 kg/m^{3}.

**Problem 4.16: **A vessel of volume 0.02 m^{3} contains a mixture of hydrogen and helium at 320.15 K and 4.15⨯10^{5} N/m^{2} pressure. The mass of the mixture is 10 g. Calculate the individual masses of hydrogen and helium in the mixture.

**Problem 4.17: **The flow rate of a gas mixture consisting of 60% ethane, 25% hydrogen, and 15% carbon dioxide is found to be 200 m^{3}/h at 300 K and 1.2 bar. (a) Determine the composition of the gas in weight percent, (b) Express the composition in mol/L, and (c) what is the flow rate in kg/h?

**Problem 4.18: **2.0 cubic meters of oxygen at 200 kPa and 280 K is mixed with 10 kg of nitrogen at 95 kPa and 300 K and the resulting mixture is brought to 110 kPa and 290 K. (a) What is the partial pressure of oxygen in the final mixture (b) What is the final volume of the mixture?

**Problem 4.19: **In an air-naphthalene (C_{10}H_{8}) mixture at 70 kPa and 350 K, the partial pressure of naphthalene is found to be 7 kPa. What volume of this mixture will contain 1 kg of naphthalene?

**Problem 4.20: **15 kg each of nitrogen and hydrogen are mixed together at 300 kPa and 298 K. Determine the following: (a) The partial pressure of nitrogen (b) The pure-component volume of nitrogen (c) The specific volume of the mixture (m^{3}/kg).

**Problem 4.21: **0.66 g of a gas containing 81.8% C and 18.2% H by weight measures 0.369 L at 100 kPa and 295 K. What is the formula of the hydrocarbon?

**Problem 4.22: **N_{2}O_{4} decomposes to NO_{2} at high temperatures. 20 g of N_{2}O_{4 }when heated to 373 K at 96 kPa, is found to occupy a volume of 0.0125 m^{3}. Assuming the applicability of ideal gas law, calculate the percent dissociation of N_{2}O_{4} to NO_{2}.

**Problem 4.23: **In the manufacture of formaldehyde by the Monsanto process, air, methyl alcohol, and steam are used in the ratio 4:2:1 by weight at 800 kPa and 380 K. Calculate the partial pressure of the gases in N/m^{2}.

**Problem 4.24: **What is the average molecular weight of a flue gas having the following composition by volume? CO_{2}: 13.0%, CO: 3.0%, O_{2}: 4.0% and N_{2}: 80.0%.

**Problem 4.25: **Assuming that air contains 78.1% nitrogen, 21.0% oxygen, and 0.9% argon, calculate the average molecular weight and density of air at 298 K and 1.01325⨯10^{5 }N/m^{2}.

**Problem 4.26: **A natural gas has the following composition by volume: CO_{2}: 0.8%, N_{2}: 3.2%, and CH_{4}: 96.0%. Calculate (a) The composition in weight percent (b) The average molecular weight (c) The density at standard conditions in kg/m^{3}.

**Problem 4.27: **The average molecular weight of a gas mixture containing oxygen and other gases is 40. A student evaluated the average molecular weight as 36.8. He got the wrong result because he used an incorrect value of 16 as the molecular weight of oxygen in the calculation. What is the mole percentage of oxygen in the mixture?

**Problem 4.28: **A flue gas has the following percent composition by volume: CO_{2} =14.00, SO_{2 }= 0.50, CO = 2.00, O_{2 }= 2.5 and N_{2 }= 81.00. Determine (a) The average molecular weight of the gas (b) The composition of gas in weight percent (c) The density of the gas at 320 K and 1.5 bar (d) The specific gravity at 320 K and 1.5 bar.

**Problem 4.29: **A gas mixture contains 10.0% CO_{2}, 15.0% Cl_{2}, 12.5% N_{2,} and the rest hydrogen. Calculate the following: (a) The average molecular weight of the gas (b) The gas composition in weight percent.

**Problem 4.30: **200 kg of a gas mixture containing 20% SO_{2}, 20% NO_{2, }and 60% N_{2} is contained in a gas cylinder. Determine the average molecular weight of the mixture (a) if the analysis is on a mass basis (b) If the analysis is on a volume basis.

**Problem 4.31: **A sample withdrawn from a gas mixture at 120 kPa and 300 K gave the following results when separated into its constituents: C_{2}H_{6 }17.93 g, H_{2} 0.50 g, CO_{2} 6.57 g. Determine the following: (a) The average molecular weight (b) The density of the gas mixture.

**Problem 4.32: **In a gas mixture consisting of hydrogen, nitrogen, and carbon dioxide, the partial pressure are 25 kPa for hydrogen, 35 kPa for nitrogen, and 140 kPa for CO_{2}. For 50 m^{3 }of the gas mixture at 400 K, determine (a) The number of moles of the mixture (b) The number of moles and the mole fraction of hydrogen (c) The mass and mass fraction of hydrogen (d) The pure-component volume of hydrogen (e) The average molecular weight of the mixture.

**Problem 4.33: **The average molecular weight of a mixture of oxygen and sulfur dioxide is found to be 44.8. For 5 kg of this mixture at 298 K and 200 kPa calculate (a) The partial pressure of oxygen (b) The volume of the mixture (c) The density at the standard conditions.

**Problem 4.34: **An ammonia converter is charged with a 1:3 mixture of nitrogen and hydrogen at 1000 bar and 500 K. Calculate the following: (a) The partial pressures of nitrogen and hydrogen (b) The average molecular weight (c) The density of the mixture.

**Problem 4.35: **A blue gas has the following composition by volume percent: CO: 34.8, H_{2}: 42.0, CH_{4}: 0.4, CO_{2}: 5.5, O_{2}: 0.2, and N_{2}: 17.1. Calculate (a) The composition in weight percent (b) The average molecular weight (c) The density at standard conditions in kg/m^{3}.

**Problem 4.36: **A gas mixture has the following composition by volume: ethylene: 30.6%, benzene: 24.5%, oxygen: 1.3%, methane: 15.5%, ethane: 25%, and nitrogen: 3.1%. Calculate the following: (a) The average molecular weight (b) The composition by weight (c) The density of the mixture at STP in kg/m^{3}.

**Problem 4.37: **Air is dried from a partial pressure of 7 kPa of water vapor to a partial pressure of 1.5 kPa. The temperature of the entering air is 475 K. The pressure remains constant at 1 bar at the inlet and outlet. How much water in kilograms is removed per cubic meter of entering gas?

**Problem 4.38: **An ammonia-air mixture containing 10% ammonia is sent to an absorber in which 90%of ammonia is absorbed. (a) What is the mole fraction of ammonia in the gas leaving? (b) Express the composition of the exit gas from the absorber in weight percent. (c) What is the average molecular weight of the gas entering and leaving the column? (Average molecular weight of air is 29.)

**Problem 4.39: **Flue gas analyzing 80.0% nitrogen, 7.0% oxygen and 13.0% carbon dioxide is sent to a dryer at 500 K and 95 kPa. In the dryer it picks up moisture from the wet material and leaves at 90 kPa and 360 K with the following composition: N_{2}, = 50%, O_{2}, = 4.5%, CO_{2} = 8.0% and H_{2}O = 37.5% Per 100 m^{3} of gas entering the dryer, determine the following (a) The volume of gas leaving the dryer (b) The weight of water evaporated.

**Problem 4.40: **Hydrochloric acid is obtained by absorbing HCl gas in water. A gas mixture analyzing 30% HCI and 70% air enters the absorber at 95 kPa and 320 K and leaves at 90 kPa and 300 K. 95% of HCl present in the entering gas is absorbed. For 100 m^{3} of gas entering the absorber, determine the following: (a) The volume of gas leaving in m^{3} (b) The mass of HCI absorbed in kg (c) The percent composition by volume of the gas leaving.

**Problem 4.41: **Hydrochloric acid is obtained by absorbing HCl gas in water. A gas mixture consisting of HCI and air enters the absorber at 95 kPa and 320 K with a partial pressure of HCI of 28.5 kPa and leaves at 90 kPa and 300 K with a partial pressure of HCI of 2 kPa. For 100 m^{3} of gas entering the absorber determine the following: (a) The volume of gas leaving in m^{3} (b) The mass of HCI absorbed in kg.

**Problem 4.42: **Air is to be dehumidified by cooling and condensation of water vapor present in it. 100 m^{3} of air at 100 kPa and 305 K contains water vapor which exerts a partial pressure of 3 kPa Keeping the pressure constant, this air is cooled to 285 K and the condensed water is removed. The partial pressure of water in the air after cooling is found to be 1.5 kPa. Calculate the following: (a) The volume of air after dehumidification in m^{3} (b) The mass of water removed in kg.

**Problem 4.43: **The feed to an absorption column consists of 30% H_{2}S and 70% inerts. Only H_{2}S is removed from the gas by absorbing it in an alkaline solution. The gas enters the absorber at 700 kPa and 350 K and leaves at 600 kPa and 300 K containing 5% H_{2}S. If H_{2}S is removed at a rate of 100 kg/h, calculate the following: (a) Cubic meters of gas entering per hour (b) Cubic meters of gas leaving per hour (c) Percentage recovery of H_{2}S.

**Problem 4.44: **A flue gas containing 18% CO_{2}, enters an absorber at 120 kPa and 400 K. Only CO_{2}, is absorbed and the gas leaves the unit at 95 kPa and 310 K containing 2% CO_{2}, assuming that 100 m^{3} of gas is admitted to the unit, calculate (a) The volume of gas leaving in m^{3} (b) The weight of CO_{2} absorbed in kg.

**Problem 4.45: **100 m^{3} of a gas mixture in which benzene and nitrogen are present in the weight ratio 1:3 is sent to an absorption column to recover benzene. The gas enters the column at 120 kPa and 350 K. The gas leaving the absorber measures 95 m^{3} at 101.3 kPa and 300 K. Determine the following: (a) The average molecular weight of the gas entering (b) The average molecular weight of the gas leaving (c) Weight in kilograms of benzene absorbed (d) The percent recovery of benzene.

**Problem 4.46: **50 cubic meters per minute of a gas containing 5% oxygen is flowing through a pipe. It is desired to increase the oxygen content in the stream to 10% by (a) the addition of pure oxygen and (b) the addition of air containing 21% oxygen and 79% nitrogen. Determine the volumetric rate of addition (m^{3}/min) in both cases.

**Problem 4.47: **100 m^{3}/h of an ammonia-air mixture containing 20% ammonia by volume is admitted to an absorption column at 120 kPa and 300 K in order to recover ammonia by absorbing it in water. The gas leaves the column at 100 kPa and 280 K with a partial pressure of ammonia of 2 kPa. (a) What is the volume of gas leaving in one hour (b) How many kilograms of ammonia are recovered in one hour (c) What is the percent recovery?

**Problem 4.48: **100 m^{3} per hour of a mixture of toluene and air at 120 kPa and 375 K is passed through a cooler where some of the toluene is condensed. Toluene exerts a partial pressure of 50 kPa in the entering stream. The gases leaving the cooler measured 70 m^{3} at 100 kPa and 325 K. Assuming an average molecular weight of 29 for air, determine the following (a) The average molecular weight of gas leaving the cooler (b) The amount of toluene (C_{7}H_{8}) condensed (in kilograms).

**Problem 4.49: **Two tanks are initially sealed off from one another by means of a valve. Tank I initially contain 1 m^{3} of air at 7 bar and 340 K. Tank II initially contains a mixture of oxygen and nitrogen containing 95% nitrogen at 14 bar and 360 K. The valve is then opened allowing the contents of the tank to mix. After complete mixing had been done, the gas was found to contain 85% nitrogen. Calculate the volume of Tank II.

**Problem 4.50: **Ammonia reacts with sulphuric acid giving ammonium sulfate

(a) 20 m^{3} of ammonia at 1.2 bar and 300 K reacts with 40 kg of sulphuric acid. Which is the excess reactant and what is the percent excess? (b) How many kilograms of ammonium sulfate will be obtained?

**Problem 4.51: **Sulphur dioxide reacts with oxygen producing sulfur trioxide,

In order to ensure a complete reaction, twice as much oxygen is supplied than that required theoretically. However, only 60% conversion is obtained. The pressure was 500 kPa and the temperature was 800 K. 100 kg of SO2 is charged to the converter. Determine the following: (a) The volume of pure oxygen supplied at 1.5 bar and 300 K (b) The volume of sulfur trioxide produced (c) The volume of gases leaving the converter (d) The composition of gases leaving the converter (e) The average molecular weight of the gas leaving the converter.

**Problem 4.52: **Nitrogen dioxide shows a tendency to associate and form nitrogen tetroxide.

One cubic meter of nitrogen dioxide at 100 kPa and 300 K is taken in a closed rigid container and allowed to attain equilibrium at constant temperature and volume. The pressure inside the container has fallen to 85 kPa at equilibrium. (a) What is the degree of association? (b) What is the partial pressure of N_{2}O_{4} in the final mixture?

**Problem 4.53: **Ammonium chloride in the vapor phase dissociates into ammonia and hydrogen chloride according to

10.7 g ammonium chloride is taken in a container. When dissociation is complete and equilibrium has been attained the pressure, volume, and temperature of the gas mixture were measured to be 1.2 bar, 7.764⨯10¬3 m3, and 400 K, respectively. Determine the following: (a) The fraction of ammonium chloride dissociated (b) The partial pressure of HCI in the products.

**Problem 4.54: **One kilomole of methane is completely burnt to form CO_{2} and water vapor using 10% excess air than that required for complete combustion. The resulting gas mixture is treated to remove all the water content. (a) What will be the volume of dry gas leaving the burner at 110.3 kPa and 275 K? (b) What mass of water is removed from the products of combustion?

**Problem 4.55: **Pure sulfur is burned with excess air to give sulfur trioxide. Due to incomplete oxidation, some sulfur dioxide is also formed. The analysis of the burner gases showed 0.8% SO_{3}, 7.8% SO_{2}, 12.2% O_{2}, and 79.2% N_{2} Determine the following: (a) The percent excess air supplied (b) The volume of burner gases at 1.2 bar and 600 K per kg sulfur burned (c) The volume of air supplied at 1.013 bar and 288 K per kg sulfur burned.

**Problem 4.56: **An organic ester of formula C_{19}H_{36}O_{2} is to be hydrogenated at a rate of 100 kg/h to yield C_{19}H_{38}O_{2}. The hydrogen required for the plant which runs continuously, is available as 50 L cylinders in which the gas is contained at 70 bar and 300 K How many cylinders the company should order per week?

**Problem 4.57: **Formaldehyde is produced by the gas phase oxidation of methanol with air over a catalyst

100 m^{3} of methanol vapor at 1.013⨯10^{5} N/m^{2} and 550 K is to be treated. If 10% excess air is supplied and the reaction is only 80% complete, calculate (a) The composition of the product gas (b) The volume of product gases at 1.5⨯10^{5} N/m^{2} and 800 K.

**Problem 4.58: **A gaseous mixture consisting of 50% hydrogen and 50% acetaldehyde (C_{2}H_{4}O) is initially contained in a rigid vessel at a total pressure of 1 bar. Methanol is formed is according to

After a time, it was found that the total pressure in the vessel has fallen to 0.9 bar while the temperature was the same as that of the initial mixture. Assuming that the products are still in the vapor phase, calculate the degree of completion of the reaction.

**Problem 4.59: **A sample of a gas mixture containing NO and NO_{2} is contained in a standard cell of volume 10 L at 170 kPa and 300 K. If the mixture weighed 28.087 g, what percent of the gas mixture is NO?

**Problem 4.60: **A mixture of ethane (C_{2}H_{6}) and ethylene (C_{2}H_{4}) occupies 4.0⨯10^{-2} m^{3} at 1 atm and 400 K. The mixture reacts completely with 0.130 kg of O_{2} to produce CO_{2 }and H_{2}O. Assuming ideal gas behavior, calculate the mole fractions of C_{2}H_{4} and C_{2}H_{6} in the mixture.

**Problem 4.61: **Pure methane is completely burned with air. The gas leaving the burner which contain no oxygen is passed through a cooler where some of the water is removed by condensation. The mole fraction of nitrogen in the gas leaving the cooler was 0.8335. Calculate the following: (a) The analysis of the gas leaving the cooler (b) Water condensed in kg per kmol of methane burned (c) The partial pressure of water in the gas leaving the cooler at 325 K and 1.5 bar.

**Problem 4.62: **In the nitric acid manufacture, 100 m^{3}/h of ammonia at 290 K and 1 bar is mixed with air and passed over a catalyst in a converter and the following reaction takes place:

The gases from the converter are passed into an oxidizing tower where the oxidation is completed according to the following reaction

2NO+O_2\rightarrow2{NO}_2The gases from the oxidizing tower are passed into a cooling tower where NO_{2}, is absorbed in 50 kg/h of water and forms nitric acid according to the reaction

The overall reaction for the process is given by

{NH}_3+2O_2\rightarrow{HNO}_3+H_2OAir supplied is 20% in excess of that required for the complete oxidation of the ammonia to nitric acid and water. The degree of completion of the reaction in the converter is 85% and 90% of the nitric oxide entering the oxidizing tower is converted to nitrogen peroxide. Assume that the cooling tower exit gases contain no water vapor. Calculate the following: (a) The amount of air to be used in m^{3}/h at 1 bar and 290 K (b) The amount of gases leaving the converter in m^{3}/h at 0.95 bar and 1000 K (c) The amount in kg/h and concentration in weight % of nitric acid produced.