Mrs. Wernau's Pre-AP Chemistry



DIMENSIONAL ANALYSIS

A conversion factor is a ratio with a value of one.

Ex: 1 ft = 12 inches 1 day= 24 hours 1 mole= molar mass

1.00 g water = 1 mL water 1 km= 1000 m 1 dozen = 12 ???

100 cm = 1m 1 Gg = 1 x 109 g 1 mole= 6.02 x 1023 atoms, molecules,

ions, formula units

Dimensional Analysis is also called the “factor label method” or “unit analysis method” of problem solving.

Make the following conversions:

1. 33 m = ____________km

2. 547 cL =___________L

3. 96.5 mg = ____________g

4. 52.5 m = ___________ mm

5. 73.2 kg = _______________ cg

6. 3.61 Gm = ___________________m

7. 467.89 nm = _________________cm

8. 76 .4 dm = ___________________hm

9. 7.00 days = ______________s

10. 3.21 moles Au = ____________ atoms Au (1 mole= 6.02 x 1023 atoms)

11. 7.83 X 1024 atoms Fe = ____________________moles Fe

12. 33.2 mi/hr = ________ m/s ( 1 mile = 1609.344 Meters)

13. 33.5 cm3 = ___________m3

Steps for solving word problems:

1. Find unknown

2. Find knowns

3. Plan solution

4. Calculate

5. Check

1. How many seconds are there in 2.5 years?

2. A clock gains 0.25 seconds per minute. How many seconds will it gain in exactly 180 days?

3. A fictitious unit of length called the “zither” is defined by the relationship 7.50 cm = 1.00 zither. How many zithers are in a 100.0 meter distance?

4. What is the mass of a 35.0 mL sample of concentrated sulfuric acid (density 1.84g/mL)?

5. Nolan Ryan threw a fastball 100.8 mi/hr. Calculate this velocity in m/s. 1 mi = 1.6093 km.

6. The density of copper is 8.96g/cm3 at 25oC. Determine its density in kg/m3.

7. Copper makes up 1.1 x 10-4 percent by mass of a normal healthy human. How many grams of copper would be found in the body of a person weighing 150 lb? (1.0 kg = 2.2 lb)

8. What is the mass of 6.56 moles of copper? ( 1 mole = molar mass)

9. How many moles are in 78.54 g Magnesium?

10. How many atoms are in 45.7 g of sodium?

Dimensional Analysis Practice WS #1

Metric Practice

1. 765km = __________ mm

2. 3.45 x 10-3kg = ______ng

3. 0.0239 g = ________(g

Word Problems

1. The acid in an automobile battery (a solution of sulfuric acid) has a density of 1.2 g/cm3. What is the mass of 2.00 x 102 mL of this acid?

2.If Jules Verne expressed the title of his famous book, Twenty Thousand Leagues under the Sea in basic SI units, what would the title be? (1 league = 3.45 mi, 1 mi = 1609 m)

3.A few years ago, a cartoon pictured a thief making his getaway, gun in one hand and a bucket of gold dust in the other. If the bucket had a volume of 8.00 qt. and was full of gold whose density is 19.3 g/cm3, what was its mass? Comment on the thief's strength. (1.057 qt = 1 L)

4. What is the cost in dollars for the nails used to build a fence 125 meters long if it requires 30 nails per meter? Assume that 40 nails are sold per box at a cost of 75 cents per box.

5.A light-year is the distance that light can travel in one year. If the sun is 1.5 x 108 km away, how many light years is the sun from earth? Assume that light travels at a speed of 3.0 x 1010 cm/s.

6. A budding young chemist decided to throw tradition overboard and include time in the metric system. To do this, she kept the unit "day" to refer to the usual 24-hour time interval we know. She then subdivided the day into centidays, millidays, and microdays. Solve the following problems, rounding them each to three significant digits:

A. A 100 yd dash done in 9.7 s took how many microdays?

B. A 50 min class period lasts for how many centidays?

C. A car going 60 mph goes how many miles per centiday?

D. What is the velocity of light in miles per milliday if it is 186,000 mi./s?

E. What is the acceleration of gravity in centimeters per microday2 if it is 980 cm/s2

Dimensional Analysis Practice WS #2

1. In the country of Ferdovia, the Ferds thrive on potatoes. The average Ferd earns 142 thrubs (the local currency of Ferdovia) per week and spends approximately 8.0% of his yearly income on potatoes. If potatoes cost 2 thrubs per pound, how many pounds of potatoes does the average Ferd consume per year?

2. The volume of seawater on earth is estimated to be 3.3 x 108 mi3. Assuming that seawater is 3.5% sodium chloride, by mass, and that the density of seawater is 1.03 g/cm3, what is the approximate mass of sodium chloride dissolved in the seawater on earth, expressed in kg? 1 mile = 5280 ft, 1 meter = 39.37 inches

3. A slow jogger runs a mile in 13 min. Calculate the speed in meters per second.

( 1 mi = 1.609 km; 1 in = 2.54 cm)

4. In a city with heavy automobile traffic such as Los Angeles or New York, it was estimated that about 9.0 tons of lead from exhaust was deposited on or near the highway each day before gasoline became “unleaded”. What is this amount in pounds per month? ( 1 ton = exactly 2000 lb; 1 month = 31 days)

5.The density of diamond is 3.51 g/mL. What is the volume of the Hope diamond if it has a mass of 44.0 carats? ( 1 carat = 0.200g)

6. Ipecac syrup is used to induce vomiting in people who have swallowed a poison. The syrup contains 7.0g of ipecac per 100.0 mL, and the recommended dosage is 1 tablespoon, or 15 mL. Calculate the amount of ipecac in the average dose.

7. The LD50 for a drug is the dose that would be lethal for 50% of the population. LD50 for sodium cyclamate in mice is 17.0grams per kilogram of body weight. Calculate how many cans of diet soda a 70.0 kilogram human would have to drink to achieve this dose, assuming each can of diet soda contains 0.096 grams of sodium cyclamate.

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