Chemistry Everyday for Everyone edited by
Resources for Student Assessment
John Alexander University of Cincinnati Cincinnati, OH 45221
Appalachian Trail Problems Brian N. Akers Department of Biology, Box 10037, Lamar University, Beaumont, TX 77710
If one is an Appalachian Trail (AT) thru-hiker (one who walks the entire length), there is ample time to reflect on the material learned in one discipline and its application to other subject areas. A topic covered in general chemistry that is fundamental to all science fields is unit analysis in problem solving. Often the level of the questions presented in freshman chemistry (e.g., what is the volume in liters of a 12-ounce soft drink?) is considerably less complex than problems encountered in real life. While hiking, I contrived problems that should present a more realistic challenge to the average freshman chemistry student. The Problems 1. Obtaining clean water is a continual problem for most hikers. Because it rains regularly on the trail, hikers can often be seen collecting rainwater in whatever containers they have. If a typical rainstorm produces 0.50 inches of water, how many liters of water would collect in an 8.0-inch-diameter cylindrical pan? 2. Several areas along the AT are used by neighboring communities as a watershed to provide a source of water. Assume the area receives 45 inches of rain per year, 10% of the rainwater is recovered from the aquifer, and the average person uses 100 gallons of water per day. How many individuals can have their water needs met by 91,659 acres of watershed? 3. In the James River Face Wilderness in Virginia near the AT there are 8.0 acres of quartz boulders called the Devils Marbleyard. Assume the Marbleyard to be circular and determine its diameter in feet. 4. Consider the average step made by a hiker to be 22 inches long. How many steps does a thru-hiker make while hiking the 2160 mile trail? 5. The average thru-hiker spends 165 days of 10 hours hiking the trail. What is this individual’s average velocity while hiking in miles per hour (in km/h)? How many minutes would be required for a hiker to cover one mile? 6. One individual reported an initial weight of 210 pounds and after hiking 900 miles of the trail in 61 days had a weight of 168 pounds. What was this individual’s average weight loss in grams per hour and grams per mile? Assume the weight was lost throughout the 24-hour day. 7. Water is made potable on the trail by filtering or chemical action to remove or destroy microbial contaminants. A common method involves a device that has a filter attached to a small hand pump. One model required eighty 2.25-inch strokes of the pump’s cylindrical piston to pump one liter. What was the diameter of the piston in centimeters? 8. It is traditional for an individual to eat a half gallon of ice cream (in one sitting) after completing half (1080 miles)
of the AT. A common rectangular half gallon carton of ice cream has inside dimensions in a 1.00:1.38:1.92 ratio. What are the dimensions of the carton in centimeters? 9. Because all of the food on the AT is carried, a factor in its selection is to choose items that contain essentially no water, while offering the greatest number of calories per unit mass. Some typical trail foods are “trail mix” (a dried fruit and nut mixture), 10,650 Cal/4 pounds; peanut butter, 3150 Cal/18 ounces; cheese and crackers, 210 Cal/13/8 ounces; and macaroni and cheese, 950 Cal/7.25 ounces. Calculate the calorie density in Cal/g for each of these food items and, based on calorie density, order these from most to least desirable. 10. Typical values for the energy content of carbohydrates, proteins, and fats are 4, 4, and 9 Cal/g, respectively, considering one significant figure. Assume the four food items described in the previous problem to be anhydrous and to consist only of protein, fat, and carbohydrate. Calculate the fat content (percent by weight) of each food listed. 11. Assume the water balance in a hiker to be intake + metabolically produced = urinary + perspiration This assumes that fecal water content is small and exhaled and inhaled air have the same water content. The volume of intake water and urine volume were measured for two hikers for six days and found to be 4.4 L/day and 38 ounces/day, respectively. Calculate the amount of metabolic water, assuming the major source of the 3800 Cal/day (average for two hikers over six days) diet is from carbohydrates (rice and pasta), which are mainly starches, HO(C6H10O5)nH. The “n” in most starches is sufficiently large that the metabolism of starches can be assumed to be C6H10O5 + 6O2 → 6CO2 + 5H2O Determine the average daily perspiration volume in liters. 12. During the metabolism of foodstuffs, the carbon skeletons are oxidized and a portion of the energy is captured by the formation of ATP. Assume that the 3800 Cal/day diet of a hiker is essentially starches and that the reaction in problem 11 applies. During the metabolism of one mole of glucose or glucose moiety (C6H10O5) there is the production of 30 moles of ATP (C10H 13N 5O 13P3K3). Determine the number of pounds of ATP that are formed per day by a hiker. The Solutions/Answers Problem 1. π
(4 in.)2 0.5 in. (2.54 cm)3 (1 in.)
3
1 mL 1 cm
1L 3
1000 mL
= 0.4 L
JChemEd.chem.wisc.edu • Vol. 75 No. 12 December 1998 • Journal of Chemical Education
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Chemistry Everyday for Everyone
Problem 2. 91,659 45 2 2 acres 0.10* in. 1 mi (5280 ft) 1 yr 365 days
1 yr 640 (1 mi ) 2 acres
144 1 gal 1 personⴢ day in.2 = 3.1 × 105 people 2 231 1 ft in.3 100 gal
*10% of rainfall is recovered.
Problem 8.
Problem 3.
0.5 gal
4 qt
0.946 L
1000 mL
1 cm3
1 gal
1 qt
1L
1 mL
= 1892 cm3 8.0 acres
1 mi2
(5280 ft)2
640 acres
(1 mi)2
= 3.48 × 10 5 ft 2
3.48 × 105 ft2 = π(d/2)2; d 2 = 4.44 × 105 ft2; d = 666 ft
Let x be the length of the shortest side of the box. The dimensions are thus x cm, 1.38x cm, and 1.92x cm. The volume is V = (x cm) × (1.38x cm) × (1.92x cm = 2.65 x3 cm3. 1892 cm3 = 2.65x3 cm3 x3 = 714.0 cm3; x = 8.94 cm The dimensions are 8.94 cm, 12.3 cm, and 17.2 cm.
Problem 4. 2160 mi
5280 ft
12 in.
1 step
Problem 9. = 6.2 × 10 steps
10,650 Cal 1 lb
6
1 mi
1 ft
22 in.
Problem 5.
4 lb
Peanut butter:
2160 mi
1 day
165 days
10 h
2160 mi
1 day
= 1.3 mi/h
1 km
10 h
454 g
= 5.9 Cal/g
3150 Cal 16 oz 1 lb 18 oz
Cheese & crackers:
= 2.1 km/h 165 days
Trail mix:
Macaroni & cheese:
0.621 mi
1 lb
454 g
= 6.2 Cal/g
210 Cal
16 oz 1 lb
1.375 oz
1 lb
454 g
950 Cal
16 oz 1 lb
7.25 oz
1 lb
454 g
= 5.4 Cal/g
= 4.6 Cal/g
peanut butter > trail mix > cheese & crackers > macaroni & cheese 1 mi
1h
60 min
1.3 mi
1h
= 46 min
Problem 10. y Cal/g = 4 Cal/g (1.00 – x) + (9 Cal/g) x ; x = fraction that is fat
Problem 6.
peanut butter 40%; trail mix 40%; cheese & crackers 30%; macaroni & cheese 10%
(210 – 168) lb
1 day
454 g
61 days
24 h
1 lb
= 13 g/h
(210 – 168) lb
3800 Cal 1 g carbo 1 mol Glc
454 g = 21 g/mi
900 mi
Problem 11.
1 lb
day
day
80(length)π d 2/4 = 1 L
V=
π r 2ᐉ
=
ᐉ = 80 × 2.25 in. × (2.54 cm/1 in.) = 457.2 cm
d 2 = 4V/πᐉ = (4 × 1.0 × 103 cm3)/(π × 457.2 cm) = 2.78 cm2
1572
= 0.5 L/day
454 g 1 mL 1 L
16 oz 1 lb
1g
1000 mL
= 1.1 L/day
4.4 L/day + 0.5 L/day = 1.1 L/day + persp; persp = 4 L/day
π(d/2)2 ᐉ
V = l.0 L = 1.0 × 103 cm3
d = 1.7 cm
162 g carbo 1 mol Glc 1 mol H 2 O 1000 g
4 Cal
38 oz 1 lb
Problem 7.
5 mol H2O 18 g H 2 O 1 L
Problem 12. 3800 1 g 1 mol Cal carbo Glc day
4 Cal
30 mol 621 g 1 lb ATP ATP
162 g 1 mol carbo Glc
1 mol 454 g ATP
= 240 lb ATP/day a
aNOTE: This is about 1.5 times the weight of the individuals involved! Obviously, ATP leads a cyclic existence.
Journal of Chemical Education • Vol. 75 No. 12 December 1998 • JChemEd.chem.wisc.edu
