Read each of the following problems and select a suitable basis for solving each one Do not solve the problems.

**a. You have 130 kg of gas of the following composition: 40% N₂, 30% CO₂, and 30% CH₄ in a tank. What is the average molecular weight of the gas?

**b. You have 25 lb of a gas of the following composition: 80%, 10%, 10%. What is the average molecular weight of the mixture? What is the weight (mass) fraction of each of the components in the mixture?

****c. The proximate and ultimate analysis of coal is given in the following table. What is the composition of the “Volatile combustible material” (VCM)? Present your answer in the form of the mass percent of each element in the VCM.

*d. A fuel gas is reported to analyze, on a mole basis, 20% methane, 5% ethane, and the remainder CO₂. Calculate the analysis of the fuel gas on a mass percentage basis. ***e. A gas mixture consists of three components: argon, B, and C. The following analysis

of this mixture is given: 40.0 mol % argon, 18.75 mass % B, 20.0 mol % C. The molecular weight of argon is 40 and the molecular weight of C is 50. Find (1) the molecular weight of B and (2) the average molecular weight of the mixture.

***2.7.2. Two engineers are calculating the average molecular weight of a gas mixture containing oxygen and other gases. One of them uses the correct molecular weight of 32 for oxygen and determines the average molecular weight as 39.2. The other uses an incorrect value of 16 and determines the average molecular weight as 32.8. This is the only error in the calculations. What is the percentage of oxygen in the mixture expressed as mole percent? Choose a basis to solve the problem, but do not solve the problem.

**2.7.3. Choose a basis for the following problem: Chlorine usage at a water treatment plant averages 134.2 lb/day. The average flow rate of water leaving the plant is 10.7 million gal/day. What is the average chlorine concentration in the treatment water leaving the plant (assuming no reaction of the chlorine), expressed in milligrams per liter?

*2.8.1. You are asked to decide what size containers to use to ship 1000 lb of cottonseed oil of specific gravity equal to 0.926. What would be the minimum size drum expressed in gallons?

*2.8.2. The density of a certain solution is 8.80 lb/gal at 80°F. How many cubic feet will be occupied by 10,010 lb of this solution at 80°F?

*2.8.3. Which of the three sets of containers in Figure P2.8.3 represents respectively 1 mol of lead (Pb), 1 mol of zinc (Zn), and 1 mol of carbon (C)?

Figure P2.8.3

Section 2.9 Concentration

*2.9.1. Calculate the mass and mole fractions of the respective components in NaClO₃.

*2.9.2. The specific gravity of a solution of KOH at 15°C is 1.0824 and contains 0.813 lb KOH per gal of solution. What are the mass fractions of KOH and H₂O in the solution?

*2.9.3. You purchase a tank with a volume of 2.1 ft3. You pump the tank out and add first 20 lb of CO₂ gas and then 10 lb of N₂ gas. What is the analysis of the gas mixture in the tank?

*2.9.4. How many ppb are there in 1 ppm? Does the system of units affect your answer? Does it make any difference if the material for which the ppb are measured is a gas, liquid, or solid?

**2.9.5. The following table lists values of Fe, Cu, and Pb in Christmas wrapping paper for two different brands. Convert the ppm to mass fractions on a paper-free basis.

**2.9.6. Harbor sediments in the New Bedford, Massachusetts, area contain PCBs at levels up to 190,000 ppm, according to a report prepared by Grant Weaver of the Massachusetts

Coastal Zone Management Office [Environ. Sci. Technol., 16, No. 9, 491A (1982)]. What is the concentration of PCBs in percent? Does this seem reasonable?

This compound gives a ratio of 10.5 g cells/mol ATP synthesized in the metabolic reaction to form the cells. Approximately how many moles of C are in the cells per mole of ATP? ***2.9.8. A radioactive tracer-labeled microorganism (MMM) decomposes to NN as follows:

MMM(s) → NN(s) + 3CO₂(g)

If the CO₂(g) yields 2 × 107 dpm (disintegrations per minute) in a detection device, how many μCi (microcuries) is this? How many cpm (counts per minute) will be noted if the counting device is 80% efficient in counting disintegrations? Data: 1 curie = 3 × 1010 dps (disintegrations per second).

***2.9.9. Several alternative compounds have been added to gasoline, including methanol, ethanol, and methyl tert-butyl ether (MTBE), to increase the oxygen content of gasoline in order to reduce the formation of CO on combustion. Unfortunately, MTBE has been found in

groundwater at concentrations sufficient to cause concern. Persistence of a compound in water can be evaluated from its half-life, t_1/2, that is, the time for one-half of the compound to leave the system of interest. The half-life depends on the conditions in the system, of course, but for environmental evaluation can be approximated by

where [OH–] is the concentration of hydroxyl radical in the system that for this problem of the contamination of water is equal to 1.5 × 106 molecules/cm3. The values of k determined from experiment are

Calculate the half-life of each of the three compounds, and order them according to their persistence.

***2.9.10. The National Institute for Occupational Safety and Health (NIOSH) sets standards for CCl₄ in air at 12.6 mg/m3 of air (a time-weighted average over 40 hr). The CCl₄ found in a sample is 4800 ppb. Does the sample exceed the NIOSH standard? Be careful!

a. Convert the retained phosphorus to concentration in micrograms per liter, assuming that Lake Erie contains 1.2 × 1014 gal of water and that the average phosphorus retention time is 2.60 yr.

b. What percentage of the input comes from municipal water?

c. What percentage of the input comes from detergents, assuming they represent 70% of the municipal waste?

d. If 10 ppb of phosphorus triggers nuisance algal blooms, as has been reported in some documents, would removing 30% of the phosphorus in the municipal waste and all the phosphorus in the industrial waste be effective in reducing the eutrophication (i.e., the unwanted algal blooms) in Lake Erie?

e. Would removing all of the phosphate in detergents help?

**2.9.12. A gas contains 350 ppm of H₂S in CO₂. If the gas is liquefied, what is the weight fraction of H₂S?

**2.9.13. Sulfur trioxide (SO₃) can be absorbed in sulfuric acid solution to form a more

concentrated sulfuric acid. If the gas to be absorbed contains 55% SO₃, 41% N₂, 3% SO₂, and 1% O₂:

a. How many parts per million of O₂ are there in the gas? b. What is the composition of the gas on an N₂-free basis?

****2.9.14. Twenty-seven pounds (27 lb) of chlorine gas is used for treating 750,000 gal of water each day. The chlorine used up by the microorganisms in the water is measured to be 2.6 mg/L. What is the residual (excess) chlorine concentration in the treated water?

***2.9.15. A newspaper report says the FDA found 13–20 ppb of acrylonitrile in a soft-drink bottle, and if this is correct, it amounts to only 1 molecule of acrylonitrile per bottle. Is this

statement correct?

***2.9.16. Several studies of global warming indicate that the concentration of CO₂ in the

atmosphere is increasing by roughly 1% per year. Do we have to worry about the decrease in the oxygen concentration also?

Section 2.10 Temperature

Street Journal. Japan and the United States plan to join in developing technology to improve cars that run on methanol, a fuel that causes less air pollution than gasoline. An unspecified number of researchers from Japanese companies will work with the EPA to develop a methanol car that will start in temperatures as low as –10°C. What is this temperature in degrees Rankine, kelvin, and Fahrenheit?

*2.10.2. Can negative temperature measurements exist?

**2.10.3. The heat capacity C_p of acetic acid in J/[(g mol)(K)] can be calculated from the equation C_p = 8.41 + 2.4346 × 10–5 T

where T is in kelvin. Convert the equation so that T can be introduced into the equation in degrees Rankine instead of kelvin. Keep the units of C_p the same.

*2.10.4. Convert the following temperatures to the requested units: a. 10°C to °F

b. 10°C to °R c. –25°F to K d. 150K to °R

***2.10.5. Heat capacities are usually given in terms of polynomial functions of temperature. The equation for carbon dioxide is

C_p = 8.4448 + 0.5757 × 10–2 T – 0.2159 × 10–5 T2 + 0.3059 × 10–9 T3

where T is in °F and C_p is in Btu/[(lb mol)(°F)]. Convert the equation so that T can be in °C and C_p will be in J/[(g mol)(K)].

**2.10.6. In a report on the record low temperatures in Antarctica, Chemical and Engineering News said at one point that “the mercury dropped to –76°C.” In what sense is that possible? Mercury freezes at –39°C.

Section 2.11 Pressure and Hydrostatic Head

**2.11.1. From the newspaper:

BROWNSVILLE, TX. Lightning or excessive standing water on the roof of a clothes store are emerging as the leading causes suspected in the building’s collapse. Mayor Ignacio Garza said early possibilities include excessive weight caused by standing water on the 19-year-old building’s roof. Up to six inches of rain fell here in less than six hours.”

Flat-roof buildings are a popular architectural style in dry climates because of the economy of materials of construction. However, during the rainy season water may pool up on the roof decks so that structural considerations for the added weight must be taken into account. If 15 cm of water accumulates on a 10 m by 10 m area during a heavy rainstorm, determine (a) the total added weight from the standing water the building must support and (b) the force of the water on the roof in psi.

***2.11.2. A problem with concrete wastewater treatment tanks set belowground was realized when the water table rose and an empty tank floated out of the ground. This buoyancy problem was overcome by installing a check valve in the wall of the tank so that if the water table

rose high enough to float the tank, it would fill with water. If the density of concrete is 2080 kg/m3, determine the maximum height at which the valve should be installed to

prevent a buoyant force from raising a rectangular tank with inside dimensions of 30 m by 27 m that is 5 m deep. The walls and floor have a uniform thickness of 200 mm.

**2.11.3. A centrifugal pump is to be used to pump water from a lake to a storage tank that is 148 ft above the surface of the lake. The pumping rate is to be 25.0 gal/min, and the water

temperature is 60°F. The pump on hand can develop a pressure of 50.0 psig when it is pumping at a rate of 25.0 gal/min. (Neglect pipe friction, kinetic energy effects, and factors involving pump efficiency.)

a. How high (in feet) can the pump raise the water at this flow rate and temperature? b. Is this pump suitable for the intended service?

**2.11.4. A manufacturer of large tanks calculates the mass of fluid in the tank by taking the

pressure measurement at the bottom of the tank in psig, and then multiplying that value by the area of the tank in square inches. Can this procedure be correct?

**2.11.5. Suppose that a submarine inadvertently sinks to the bottom of the ocean at a depth of 1000 m. It is proposed to lower a diving bell to the submarine and attempt to enter the conning tower. What must the minimum air pressure be in the diving bell at the level of the

submarine to prevent water from entering the bell when the opening valve at the bottom is cracked open slightly? Give your answer in absolute kilopascals. Assume that seawater has a constant density of 1.024 g/cm3.

**2.11.6. A pressure gauge on a welder’s tank gives a reading of 22.4 psig. The barometric

pressure is 28.6 in. Hg. Calculate the absolute pressure in the tank in (a) lb/ft2, (b) in. Hg, (c) N/m2, and (d) ft water.

**2.11.7. John Long says he calculated from a formula that the pressure at the top of Pikes Peak is 9.75 psia. John Green says that it is 504 mm Hg because he looked it up in a table. Which John is right?

***2.11.8. The floor of a cylindrical water tank was distorted into 7 in. bulges because of the settling of improperly stabilized soil under the tank floor. However, several consulting engineers restored the damaged tank to use by placing plastic skirts around the bottom of the tank wall and devising an air flotation system to move it to an adjacent location. The tank was 30.5 m in diameter and 13.1 m deep. The top, bottom, and sides of the tank were made of 9.35-mm-thick welded steel sheets. The density of the steel is 7.86 g/cm3.

a. What was the gauge pressure in kilopascals of the water at the bottom of the tank when it was completely full of water?

b. What would the air pressure have to be in kilopascals beneath the empty tank in order to just raise it up for movement?

***2.11.9. Examine Figure P2.11.9. Oil (density = 0.91g/cm3) flows in a pipe, and the flow rate is measured via a mercury (density = 13.546 g/cm3) manometer. If the difference in height of the two legs of the manometer is 0.78 in., what is the corresponding pressure difference between points A and B in mm Hg? At which point, A or B, is the pressure higher? The temperature is 60°F.