Activity Unit Conversions

Transcription

1 Activity Unit Conversions Directions: This Guided Learning Activity (GLA) focuses on performing unit conversions. Part A discusses how to write conversion factors and Part B uses conversion factors to perform single-step conversions, and Part C discusses unit conversions for temperature and units with powers. The worksheet is accompanied by instructional videos. See for additional materials. Part A Writing Conversion Factors Converting between units is an important part of any science. Below is a table with measurements that are common in chemistry. In the table, useful equalities are given. Measure Base unit Abbreviation Conversion to Know Length meter m 1 in. = 2.54 cm Mass gram g 1 lb = g Volume liter L 1 L = qt 1 ml = 1 cm 3 Temperature ⁰Celsius ⁰C ⁰C = (⁰F - 32)/1.8 K = ⁰C Energy joule J 1 cal = J To convert between different systems of measure, conversion factors can be applied. A conversion factor is written based on the equality between the two units. For example, a conversion factor for inches and centimeters can be written two ways: ccmm Or cccc Which of these two conversion factors is used depends on the desired conversion. Example #1. Write two conversion factors for the following unit equalities: a. 12 inches = 1 feet b. 1 mile = 1.61 kilometer ffff 11 ffff 11 c. 4 cups = 1 quart Another set of conversion factors that you ll need to know are the metric prefixes. The metric system includes a set of prefixes that are based on factors of 10. These prefixes are extremely useful because they are applied to many different types of measurements (e.g. length measurements, mass measurements, etc.) Activity Page 1 of 5

2 The following table includes a shortened list of unit prefixes and equalities that Chemistry 151 students should know. Prefix Equality (using meter as an example) Name Abbreviation General Notation Scientific Notation nano- n 1 m = 1,000,000,000 nm 1 m = 10 9 nm micro- μ 1 m = 1,000,000 μm 1 m = 10 6 μm milli- m 1 m = 1,000 mm 1 m = 10 3 mm centi- c 1 m = 100 cm 1 m = 10 2 cm (base units: g, m, L, J, M) kilo- k 1,000 m = 1 km 10 3 m = 1 km mega- M 1,000,000 m = 1 Mm 10 6 m = 1 Mm giga- G 1,000,000,000 m = 1 Gm 10 9 m = 1 Gm Example #2. Write two conversion factors that can be used to convert between: a. meters and kilometers b. microliters and liters mm 11 kkkk 11 kkkk mm c. milligrams and kilograms Often, conversion factors are not unit conversion factors per say, but are equivalencies that can be derived from physical or chemical properties of substances or systems. For example, the density of a substance is often used to relate its volume to its mass. Other common examples are given below. Property Common Units density g/ml, g/cm 3, lb/ft 3 velocity m/s, mi/hr concentration mol/l (e.g. M) percent composition - Example #3. Write a conversion factor for each of the following relationships. a. Gold has a density of g/cm gg 11 ccmm ccmm gg b. 1 tablet contains 250 milligrams of acetaminophen. c. A water molecule has two hydrogen atoms. d. Sodium chloride is 39.33% sodium. Activity Page 2 of 5

3 Part B Performing Simple Conversions To perform single step conversions, a conversion factor that relates the given value to the desired value is identified. The given value is multiplied by the conversion factor so that the given units are divided from the quantity. dddddddddddddd uuuuuuuuuu gggggggggg vvvvvvvvvv xx = dddddddddddddd vvvvvvvvvv gggggggggg uuuuuuuuuu When using this approach, it is important to include all units in calculations, treating them as algebraic quantities. Example #4. Perform the following conversions. a iiii cccc = cccc b cccc = iiii. c xx nnnn = mm Sometimes the conversion factors are based on chemical or physical properties. Example #5. Perform the following calculations. a. The density of iron is 7.87 g/cm 3. How much volume does 24.5 g of iron occupy? 11 ccmm gg = ccmm gg b. How far does light travel in 60.0 seconds? (c = x 10 8 m/s) ss = mm c. Magnesium chloride is 25.5% magnesium. How many grams of magnesium are present in 5.24 x10 4 g of magnesium chloride (MgCl 2)? xx gg MMMMMMll 22 = gg MMMM Part C Special Cases in Unit Conversions Temperature and Units with Powers Temperature conversions between the Celsius scale and the Kelvin scale require only subtraction, since the size of a degree in the Celsius and Kelvin scales is identical. When converting to and from the Fahrenheit scale, both the size of the degree and the occurrence of 0 must be accounted for. The conversion equations are given in the first table. Activity Page 3 of 5

4 Example #6. Perform the following conversions: a = b. 350 = KK c. What is absolute zero in the Fahrenheit scale? Finally, to convert between units with powers, we must account for the power in the unit conversion. To do so, the entire conversion equality is raised to the desired power. For example, the conversion factor between cubic inches (in. 3 ) and cubic centimeters (cm 3 ) can be determined from the inches to centimeters conversion factor. We know: = cccc Cubing the equality: ( = cccc) iiii. 33 = ccmm = ccmm 33 Example #7. a. How many cubic centimeters (cm 3 ) are equivalent to 2.00 in. 3? Using the calculated conversion factor from above: iiii. 33 b. How many square meters does an 80. ft 2 rug occupy? (1 ft = 12 in.) ccmm33 33 = ccmm33 Unit conversions are discussed further in GLA 151-2: Dimensional Analysis. Please refer to that GLA for more guidance. Activity Page 4 of 5

5 Part D Extra Practice 1. Perform the following unit conversions. a. 12 mg = lb. h. 12 L = cm 3 b km = mm i m = in. c in. = cm j g = oz. (1 lb. = 16 oz.) d cal = J k. 170 g/cm 2 = lb/in 2 e. 1.2 x 10-9 mg = μg l. 2.5 x 10 7 km = in. f. 5.2 m 3 = ft 3 m. 45 F = C g. 62 C = K n F = K 2. How many liters of air are in a room that is 1200 m 3? 3. What is the volume of a 59.5 g silver spoon? (d Ag = 10.5 g/cm 3 ). 4. The combustion of one gallon of gasoline will produce approximately 8.39 kg of carbon dioxide (CO 2). What volume will the CO 2 occupy? (d CO2 = 1.96 g/l). 5. The density of silver is 10.5 g/cm 3. Express this density in terms of lb/ft The USDA recommends that a person s sodium intake be limited to 2,400 mg. Table salt is 39.33% sodium. How many grams of table salt can Jenny consume without surpassing this limit? (Assume there are no other sources of sodium in her diet.) 7. If one cup of coffee contains 95 milligrams of caffeine, how many cups of coffee will contain 5.00 grams of caffeine? Activity Page 5 of 5