Dimensional Analysis Problems Key

Dimensional Analysis Problems The density of lead (Pb) is 11.4 g/cm³. What is the mass (in kg) of a lead brick with the dimensions 2.0 in. by 4.0 in. by 8.0 in.? (12 kg) 2 in * 4 in * 8 in = 64 in³ 64 in³ * (2.54 cm/in)³ = 1049 cm³ 1049 cm³ * (11.4 g/cm³) * (1 kg/1000 g) = 12 kg If gasoline cost $2.79/gallon, compare the expense of driving 10,000 miles in a big SUV that gets 14 mi/gal with that of a compact car that gets 15 km/L. (Given: 1.06 qt = 1.0 L) SUV: 10,000 mi * (1 gal/14 mi) * $2.79/gal = $1993 Compact Car: 10,000 mi * (1 km/0.62 mi) * (1 L/15 km) * (1.06 qt/1 L) * (1 gal/4 qt) * $2.79/gal = $795 In order to walk 3.5 miles, the average adult consumes 270 kcal. A can of pop contains 150 kcal. If you plan to walk a distance of 105 km, how much pop should you take along for fuel? (34 cans) 105 km * (0.62 mi/1 km) * (270 kcal/3.5 mi) * (1 can/150 kcal) = 33.48 cans ≈ 34 cans The radius of an aluminum (Al) atom is 0.125 nm (1 nm = 10⁻⁹ m). How many Al atoms would be lined up in a row to form a line 1.0 cm in length? (4 x 10⁷ atoms) 1.0 cm * (100 cm/1 m) * (1 m/10⁹ nm) * (1 atom/0.25 nm) = 4 x 10⁷ atoms Seawater is 4 percent salts, and the density of seawater is 62.4 lb/ft³. How many pounds of salt are there in 100 gallons of seawater? (Given: 1 ft³ = 7.5 gallons) 100 gal * (1 ft³/7.5 gal) * 62.4 lb/ft³ = 832 lbs 832 lbs * 0.04 = 33.28 lbs Copper (Cu) is a trace element that is essential for nutrition. Newborn infants require 80 µg of Cu per kilogram of body weight per day. (1µg = 10⁻⁶ g) The Cu content of a popular baby formula is 0.48 µg of Cu per milliliter. How many milliliters of formula should a 7.0-lb baby consume per day to obtain the minimum daily Cu requirement? (529 mL)   7.0 lb | 453.6 g | 80 µg | 1 mL | = 529 mL | 1 lb | 1 kg | 0.48 µg | A certain automobile engine has a displacement of 5.74 L. Convert this volume to cubic inches. (350 in³) 5.74 L | 1000 mL | 1 cm³ | (1 in)³ | = 350 in³ | 1 L | 1 mL | (2.54 cm)³ | How many seconds are required to run a 100 yard dash at an average speed of 10.0 m/s? (9.14 s) 100 yd | 3 ft | 1 mi | 1 km | 1000 m | 1 s | = 9.14 s | 1 yd | 5280 ft | 0.62 mi | 1000 m | 10 m | Calculate the density of mercury (Hg), given that a spherical droplet of Hg with radius of 0.328 cm has a mass of 2.00 g. (13.5 g/cm³) 2.00 g / (4/3 π(0.328 cm)³) = 13.5 g/cm³ On a certain day the concentration of carbon monoxide (CO) in the air over Detroit reached 1.8 x 10⁻⁵ g/L. Convert this concentration to milligrams per cubic meter. (18 mg/m³) 1.8 x 10⁻⁵ g/L | 1000 mg | 1000 mL | 1 cm³ | (100 cm)³ | = 18 mg/m³ | 1 g | 1 L | 1 mL | 1 m³ |