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Conversions

One of the aims of chemistry is to describe change - to tell what changed, how it changed, and what it changed into. Another aim of chemistry is to look at matter and its changes and to ask questions such as how much, how big, how hot, how many, how hard, and how long did it take.

For example, chemistry asks the following:

• How much energy is needed to start a reaction?

• How much will the volume of a gas increase if you heat it?

• How long will a reaction take?

• How much can a reaction produce?

• How much of the reactant is needed to produce a required amount of product?

• How much energy does a reaction release?

• How high will the temperature of the solution get as a reaction occurs?

To answer these questions, chemists must make measurements. Measurements in science can never be treated as just numbers; they must always involve both a number and a unit. When you use measurements to calculate any quantity, the unit must always accompany the number in the calculation. Sometimes the unit given is not the most appropriate unit for the situation or calculation. In this case, a conversion can change the impractical unit into a more useful one. For instance, you would not want to measure the distance from New York City to San Francisco in inches. A simple conversion can transform the number of inches between the two cities to the much more practical number of miles.

CONVERTING SIMPLE SI UNITS

SAMPLE PROBLEM 1

A small bottle contains 45.5 g of calcium chloride. What is the mass of calcium chloride in milligrams?

SOLUTION

1. ANALYZE

• What is given in the problem?

The mass of calcium chloride in grams

• What are you asked to find?

The mass of calcium chloride in milligrams

A table showing what you know and what you do not know can help you organize the data. Being organized is a key to developing good problem solving skills.

 Items Data Quantity given 45.5 g calcium chloride Units of quantity given Grams Units of quantity sought Milligrams Relationship between units 1 g = 1000 mg Conversion factor ? Quantity sought ? mg calcium chloride

1. PLAN

• What steps are needed to convert grams to milligrams?

Determine a conversion factor that relates grams and milligrams. Multiply the number of grams by that factor. Arrange the factor so that units cancel to give the units sought.

1. Mass of calcium chloride in g

Write the relationship between g and mg

2. 1 g = 1000 mg

Possible conversion factor:

1g/1000mg or 1000mg/1g

3. 1000mg/1g

Multiply by conversion factor

4. mass of calcium chloride in mg

Relationship between units: 1 g = 1000 mg

Possible conversion factors: 1g/1000mg or 1000mg/1g

The correct conversion factor is the one that when multiplied by the given quantity causes the units to cancel.

1. COMPUTE

45.5 g calcium chloride x 1000mg/1g = 45 500 mg calcium chloride

2. EVALUATE

• Are the units correct?

PRACTICE

1. State the following measured quantities in the units indicated:

1. 5.2 cm of magnesium ribbon in millimeters

2. 0.049 kg of sulfur in grams

3. 1.60 mL of ethanol in microliters

4. 0.0025 g of vitamin A in micrograms

5. 0.020 kg of tin in milligrams

6. 3 kL of saline solution in liters

1. State the following measured quantities in the units indicated:

1. 150 mg of aspirin in grams

2. 2500 mL of hydrochloric acid in liters

3. 0.5 g of sodium in kilograms

4. 55 L of carbon dioxide gas in kiloliters

5. 35 mm in centimeters

6. 8740 m in kilometers

7. 209 nm in millimeters

8. 500 000 µ g in kilograms

1. The greatest distance between Earth and the sun during Earth's revolution is 152 million kilometers. What is this distance in megameters?

SAMPLE PROBLEM 2

A metallurgist is going to make an experimental alloy that requires adding 325 g of bismuth to 2.500 kg of molten lead. What is the total mass of the mixture in kilograms?

SOLUTION

1. ANALYZE

• What is given in the problem?

The mass of bismuth in grams, the mass of lead in kg

• What are you asked to find?

The total mass of the mixture

 Items Data Quantity given 325 g of bismuth Units of quantity given Grams Units of quantity sought Kilograms Relationship between units 1000 g = 1 kg Conversion factor ? Quantity sought ? kg of bismuth Mass of lead 2.500 kg Total mass ? kg of mixture

1. PLAN

To be added, the quantities must be expressed in the same units - in this case, kilograms. Therefore, 325 g of bismuth must be converted to kilograms of bismuth.

• What steps are needed to convert grams to kilograms?

Determine a conversion factor that relates grams to kilograms. Apply that conversion factor to obtain the quantity sought.

• What steps are needed to find the total mass of the mixture in kilograms?

Add the mass of the lead in kilograms to the mass of bismuth in kilograms.

Relationship between units: 1000 g = 1 kg

Possible conversion factors: 1000g/1kg or 1kg/1000g

1. COMPUTE

325 g bismuth x 1kg/1000g = 0.325 kg bismuth

0.325 kg bismuth + 2.500 kg lead = 2.825 kg mixture

2. EVALUATE

• Are the units correct?

PRACTICE

1. How many milliliters of water will it take to fill a 2 L bottle that already contains 1.87 L of water?

2. A piece of copper wire is 150 cm long. How long is the wire in millimeters? How many 50 mm segments of wire can be cut from the length?

3. The ladle at an iron foundry can hold 8500 kg of molten iron. 646 metric tons of iron are needed to make rails. How many ladlefuls of iron will it take to make 646 metric tons of iron? (1 metric ton = 1000 kg)

CONVERTING DERIVED SI UNITS

SAMPLE PROBLEM 3

A balloon contains 0.5 m3 of neon gas. What is the volume of gas in cubic centimeters?

SOLUTION

1. ANALYZE

• What is given in the problem?

The volume of neon in cubic meters

• What are you asked to find?

Volume of neon in cubic centimeters

 Items Data Quantity given 0.5 m3 of neon Units of quantity given Cubic meters Units of quantity sought Cubic centimeters Relationship between units 1 m = 100 cm Conversion factor ? Quantity sought ? cm3 neon

1. PLAN

• What steps are needed to convert cubic meters to cubic centimeters?

Rewrite the quantity in simple SI units. Determine the relationship between meters and centimeters. Write a conversion factor for each of the units in the given quantity. Multiply that quantity by the conversion factor. Arrange the factors so that units will cancel to give the units of the quantity sought.

Rewrite the given quantity in simple units as follows:

m3 = m X m X m

Relationship between units: 1 m = 100 cm

Possible conversion factors: 1m/100cm or 100cm/1m

m3 neon X 100cm/1m X 100cm/1m X 100cm/1m = cm3 neon

1. COMPUTE

0.50 m3 neon = 0.50 X 100cm/1m X 100cm/1m X 100cm/1m = 500 000 cm3 neon

2. EVALUATE

• Are the units correct?

KEEP THE ABOVE PAGES; TURN IN ONLY THE PROBLEM SET. THE INSTRUCTIONS MAKE AN EXCELLENT STUDY GUIDE FOR THE 9 WEEKS TEST.

Chemistry I Problem Set 1

Instructions: Write each question, then show your work. You only need to turn in your work; you make keep the printed problem set for future study. If you do not show your work, you will not receive credit for work done.

1. Convert each of the following quantities to the required units.

1. 12.75 mm to kilometers

2. 277 cm to meters

3. 30 560 m2 to hectares (1 ha = 10 000 m2)

4. 81.9 cm2 to square meters

5. 300 000 km to megameters

1. Covert each of the following quantities to the required unit.

1. 0.62 km to meters

2. 3857 g to milligrams

3. 0.0036 mL to microliters

4. 0.342 metric tons to kilograms (1 metric ton = 1000 kg)

5. 68.71 kL to liters

1. Convert each of the following quantities to the required unit:

1. 856 mg to kilograms

2. 1 210 000 µ g to kilograms

3. 6598 µ L to cubic centimeters (1 mL = 1 cm3)

4. 80 600 nm to millimeters

5. 10.74 cm3 to liters

1. Convert each of the following quantities to the required unit:

1. 7.93 L to cubic centimeters

2. 0.0059 km to centimeters

3. 4.19 L to cubic centimeters

4. 7.48 m2 to square centimeters

5. 0.197 m3 to liters

1. An automobile uses 0.05 mL of oil for each kilometer it is driven. How much oil in liters is consumed if the automobile is driven 20 000 km?

2. How many microliters are there in a volume of 370 mm3 of cobra venom?

3. A baker uses 1.5 tsp of vanilla extract in each cake. How much vanilla extract in liters should the baker order to make 800 cakes? (1 tsp = 5 mL)

4. A person drinks eight glasses of water each day, and each glass contains 300 mL. How many liters of water will that person consume in a year? What is the mass of this volume of water in kilograms? (Assume one year has 365 days and the density of water is 1.00 kg/L.)

5. At the equator, Earth rotates with a velocity of about 465 m/s.

1. What is this velocity in kilometers per hour?

2. What is this velocity in kilometers per day?

1. A chemistry teacher needs to determine what quantity of sodium hydroxide to order. If each student will use 130 g and there are 60 students, how many kilograms of sodium hydroxide should the teacher order?

2. The teacher in item 10 also needs to order plastic tubing. If each of the 60 students needs 750 mm of tubing, what length of tubing in meters should the teacher order?

3. Covert the following to the required units.

1. 550 µ L/h to milliliters per day

2. 9.00 metric tons/h to kilograms per minute

3. 3.72 L/h to cubic centimeters per minute

4. 6.12 km/h to meters per second

1. Express the following in the units indicated.

1. 2.97 kg/L as grams per cubic centimeter

2. 4128 g/dm2 as kilograms per square centimeter

3. 5.27 g/cm3 as kilograms per cubic decimeter

4. 6.91 kg/m3 as milligrams per cubic millimeter

1. A gas has a density of 5.56 g/L. (Density = mass/volume; Mass = density X volume; Volume = mass/density)

1. What volume in milliliters would 4.17 g of this gas occupy?

2. What would be the mass in kilograms of 1 m3 of this gas?

1. The average density of living matter on Earth's land area is 0.10 g/cm2. What mass of living matter in kilograms would occupy an area of 0.125 ha?

16. A textbook measures 250 mm long, 224 mm wide, and 50 mm thick. It has a mass of 2.94 kg.

1. What is the volume of the book in cubic meters?

2. What is the density of the book in grams per cubic centimeter?

3. What is the area of one cover in square meters?

1. A glass dropper delivers liquid so that 25 drops equal 1.00 mL.

1. What is the volume of one drop in milliliters?

2. How many milliliters are in 37 drops?

3. How many drops would be required to get 0.68 L?

1. Express each of the following in kilograms and grams:

1. 504 700 mg

2. 9 200 000 µ g

3. 122 mg

4. 7195 cg

1. Express each of the following in liters and milliliters:

1. 582 cm3

2. 0.0025 m3

3. 1.18 dm3

4. 32 900 µ L

1. Express each of the following in grams per liter and kilograms per cubic meter.

1. 1.37 g/cm3

2. 0.692 kg/dm3

3. 5.2 kg/L

4. 38 000 g/m3

5. 5.79 mg/mm3

6. 1.1 µ g/mL

1. An industrial chemical reaction is run for 30.0 h and produces 648.0 kg of product. What is the average rate of product production in the stated units?

1. grams per minute

2. kilograms per day

3. milligrams per millisecond

1. What is the speed of a car in meters per second when it is moving at 100 km/h?

2. A heater gives off heat at a rate of 330 kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal = 4.184 J)

3. The instructions on a package of fertilizer tell you to apply it at the rate of 6.2 g/m2. How much fertilizer in kilograms would you need to apply to 1 ha? (1 ha = 10 000 m2)

4. A water tank leaks water at the rate of 3.9 mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year? Show your setup for solving this. Hint: Use one conversion factor to convert hours to days and another to convert days to years, and assume that one year has 365 days.

5. A nurse plans to give flu injections of 50 µ L each from a bottle containing 2.0 mL of vaccine. How many doses are in the bottle?