2.0.3: Dimensional Analysis (Problems)

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PROBLEM $\PageIndex{1}$

Write the conversion factors (as ratios) for the number of:

(a) kilometers in 1 mile

(b) liters in 1 liquid quart

Answer a: 1.6093 km : 1 mi

Answer b: 0.94635 L : 1 qt

Answer c: 28.35 g : 1 oz

PROBLEM $\PageIndex{2}$

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units.

Answer: $$\frac{2.0L}{67.6 fl oz.}=\frac{0.030 L}{1 fl oz.}$$

Click here to see a video of the solution

PROBLEM $\PageIndex{3}$

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units.

Answer: $$\frac{978 g}{34.5 oz}=\frac{28.35 g}{1 oz.}$$

PROBLEM $\PageIndex{4}$

Soccer is played with a round ball having a circumference between 27 and 28 inches and a mass between 14 and 16 oz. What are these specifications in cm and g?

Answer: 68.6 cm to 71.1 cm
396.9 g to 453.6 g

PROBLEM $\PageIndex{5}$

How many milliliters are in a 12 oz soda can?

Answer: 354.9 mL

PROBLEM $\PageIndex{6}$

A barrel of oil is exactly 42 gal. How many liters of oil are in the barrel?

Answer: 159 L

Click here to see a video of the solution.

PROBLEM $\PageIndex{7}$

The diameter of a red blood cell is about 3 x 10^-4inches. What is the diameter in centimeters?

Answer: 7.6 x 10^-4cm

PROBLEM $\PageIndex{8}$

The distance between the centers of two oxygen atoms in an oxygen molecule is 1.21 x 10^-8 cm. What is this distance in inches?

Answer: 4.76 x 10^-9in

PROBLEM $\PageIndex{9}$

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

Answer: Yes (They weigh 89.35 kg)

PROBLEM $\PageIndex{10}$

Complete the following conversions between SI units.

(a) 612 g = ? mg

(b) 8.160 m = ? cm

(d) 781 mL = ? L

(e) 4.18 kg = ? g

(f) 27.8 m = ? km

(g) 0.13 mL = ? L

(h) 1738 km = ? m

(i) 1.9 Gg = ? g

Answer a: 612,000 mg

Answer b: 816.0 cm

Answer c: 3.779 x 10^-3 g

Answer d: 0.781 L

Answer e: 4180 g

Answer f: 0.0278 km

Answer g: 1.3 x 10^-2L

Answer h: 1,738,000 m

Answer i: 1.9 x 10⁹ g

PROBLEM $\PageIndex{11}$

Make the conversion indicated in each of the following:

(a) the men's world record long jump, 29 ft 4.5 in, to meters

(b) the greatest depth of the ocean, about 6.5 mi, to kilometers

(d) The displacement volume of an automobile engine, 161 in³, to L

(e) the estimated mass of the atmosphere, 5.6 x 10¹⁵tons, to kilograms (1 ton = 2000 lbs)

(f) the mass of a bushel of rye, 32.0 lb, to kilograms

(g) the mass of a 5.00 grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

Answer a: 8.96 m

Answer b: 10.46 km

Answer c: 603.22 cm²

Answer d: 2.64 L

Answer e: 5.08 x 10¹⁸ kg

Answer f: 14.52 kg

Answer g: 324 mg

Click here to see a video of the solution(s).

PROBLEM $\PageIndex{12}$

Many chemistry conferences have held a 50-Trillion Angstrom (Å) Run. How long is this run in kilometers and in miles? (1 Å = 1 x 10^-10m)

Answer: 5 kilometers or 3.1 miles

PROBLEM $\PageIndex{13}$

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, the density of which is 1.83 g/mL?

Answer: Yes, because the acid's volume will be 122.95 mL

PROBLEM $\PageIndex{14}$

In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was the speed in miles per hour, meters per second, and feet per second?

Answer: 142.8 mi/h; 63.8 m/s; 209 ft/s

Click here to see a video of the solution.

PROBLEM $\PageIndex{15}$

Calculate these masses.

(a) what is the mass of 6.00 cm³ of mercury (density = 13.5939 g/cm³)?

(b) what is the mass of 25.0 mL octane (density = 0.702 g/cm³)?

(d) What is the mass of 125 mL gaseous chlorine (density = 3.16 g/L)?

Answer a: 81.5634 g

Answer b: 17.55 g

Answer c: 3.88 g

Answer d: 0.395 g

Click here to see a video of the soltion.

PROBLEM $\PageIndex{16}$

Calculate the following volumes.

(a) What is the volume of 25 g of iodine (density = 4.93 g/cm³)?

(b) What is the volume of 3.28 g gaseous hydrogen (density = 0.089 g/L)?

(d) What is the volume of 39.657 g bromine (density = 2.928 g/cm³)?

Answer a: 5.07 mL

Answer b: 36.9 L

Answer c: 5.02 mL

Answer d: 13.54 mL

Click here to see a video of the solution.

PROBLEM $\PageIndex{17}$

Convert 195.7 in²to m².

Answer: 0.126 m²

Click here to see a video of the solution.

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Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).
Adelaide Clark, Oregon Institute of Technology

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