UW CHEM 120 Fall 2012 Name __________________________________________ Section _____________ WS 1: DIMENSIONAL ANALYSIS 1. A patient has developed a systemic bacterial infection. The antibiotic fauxicillin is ordered at a dosage of 500. µg per kilogram of body mass every 8 hours. If the patient weighs 175 lbs, what mass of fauxicillin should they receive? 3 sig figs
175 lbs
1 kg
2.205 lb
500. µg
1 kg
1 mg
1000 µg
=
87500 mg
2205
= 39.6825 mg per 8 hours
= 39.7 mg per 8 hours
convert lbs to kg
•
convert microg to mg
Its okay for this answer to be in micrograms, but they’ll need to use scientific notation to get the proper number of sig figs Scenario 1: Patient is conscious and capable of swallowing a pill. Fauxicillin is available in 20.-­‐
mg pills. How many pills should the patient take every 8 hours to ensure proper dosage? (39.7 per 8 h / 20. mg) = 1.98 or 1.99, depending on rounding 2.0 pills; or 2 pills, since this is a counted (exact) value Scenario 2: Patient is comatose, so the antibiotic must be delivered intravenously. a. At what flow rate (mL/min) should a 250-­‐mL IV bag of 0.024% fauxicillin solution be delivered to ensure proper dosage? 0.024 g of antibiotic
×100
100 mL of solution
⎛ 40. mg ⎞ ⎛ 250 mL ⎞ ⎛ 1 hour ⎞
⎟ ⎜
⎜
⎟ ⎜
⎟ = 0.347 mL/min = 0.35 mL/min
⎝ 8 hours ⎠ ⎝ 60. mg ⎠ ⎝ 60 min ⎠
0.024 % m/v =
b. Given the prescribed dosage, how often must the IV bag be replaced? ⎛ 250 mL ⎞ ⎛ 1 min ⎞⎛ 1 hour ⎞
⎜
⎟⎜
⎟⎜
⎟ = 11.9 hours/bag = 12 hours/bag
⎝ 1 IV bag ⎠ ⎝ 0.35 mL ⎠⎝ 60 min ⎠
⎛ 60. mg ⎞⎛ 8 hrs ⎞
⎜
⎟⎜
⎟ = 12 hours/bag 1
IV
bag
40.
mg
⎝
⎠⎝
⎠
if they use the unrounded value .347222 mL/min from part a, they will get exactly 12 hours/bag 1 of 4 UW CHEM 120 Fall 2012 2. After reading the section in the course textbook on LD50 values you become concerned that drinking coffee, which contains caffeine, could kill you. Assuming that you weigh 125 pounds, and using the data provided below, determine the volume of coffee that equals a 50% lethal dose (in metric units!). The LD50 for caffeine = 192 mg per kg body mass A strong cup of coffee (1.0 cups) contains 2.0 × 102 mg of caffeine Do you still feel like you may accidentally consume a lethal volume of coffee? •
•
192 mg per kg body mass
192 mg
caffeine
1 kg
1.0 cups
2.0 x 102
mg caffeine
measurement with least sig figs
1 qt
4 cups
1L
1.06 qt
24000 L
1 kg
125 lbs =
2.205 lbs
1869.84
= 12.8353 L
measurement with least sig figs
= 13 L
2 of 4 UW CHEM 120 Fall 2012 3. You decide to drive across the border into Canada and buy some delicious Canadian maple candy because it is your favorite. On the way back to the US border you are driving way too fast and get pulled over. The intimidating Mountie that pulls you over asks you to do a calculation using dimensional analysis. The Mountie wants you to express the mass of maple candy and your speed in a single measurement that explains how much maple candy you were hauling and how fast you were going in metric units (maple mass-­‐distance per hour). You know that you purchased seventeen tasty 12.0-­‐ounce bags of candy and when you last looked at your speedometer you were going 95 miles per hour. He wants your answer to be in metric units with correct sig figs. measurement with least sig figs
95 mi 5280 ft 12 in 2.54 cm
1m
1 km 28.35 g
8.842 x 1010 g km
17 bags 12.0 oz
=
candy bag candy 1 hour 1 mils 1 ft
1 in
100 cm 1000 m 1 oz
1 x 105 hour
exact numbers
=
8.842 x 105 g km
hour
= 8.8 x 105 g km per hour If your students use more concise conversion factors that’s fine, but this answer uses the conversion factors given within this worksheet. 3 of 4 UW CHEM 120 Fall 2012 Potentially helpful information. Conversion factors: Length 1 m = 1.094 yd 1 mi = 5280 ft 1 ft = 12 in 1 km = 103 m 1 mi = 1760 yd 1 Å = 10-­‐10 m 2
1 m = 10 cm (centimeters) 1 in = 2.54 cm (exact) 3
1 m = 10 mm (millimeters) Mass 1 kg = 2.205 lb 1 lb = 453.6 g 1 amu = 1.6605 x 10-­‐27 kg 1 dry oz (ounce) = 28.35 g Volume 1 L = 1000 mL = 1.06 qt 1 ft3 = 28.32 L 1 dL = 10-­‐1 L 1 mL = 1 cm3 1 gal = 3.785412 L 1 liquid oz (ounce) = 29.57 mL 16 cup = 4 quarts = 1 gallon Pressure 1 atm = 760. mmHg 1 torr = 1 mmHg 1 atm = 14.6959 lb/in2 (psi) 1 atm = 101,325 Pa 1 Pa = 1 N/m2 1 bar = 100 kPa Energy 1 eV = 1.602 x 10-­‐19 J 1 cal = 4.184 J (exact) Force 1 N = 0.22481 lb Metric prefixes: tera (T) = 1012 peta (P) = 1015 pico (p) = 10-­‐12 femto (f) = 10-­‐15 Equations: m
d=
V
q = s ⋅ m ⋅ ΔT
ΔT = T final − Tinitial
TF = 1.8 ⋅ TC + 32
TK = TC + 273.15
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