Unit 1: Matter, Measurement, and unit conversions ≈

Big Idea Chemistry, being the science of matter, requires that we have systems for classifying, describing and measuring quantities of matter.

Topic 5: Unit Conversions Learning Goal: You will be able to convert between common units of measurement. Success Criteria: You will know you have met the learning goal when you can truthfully say: 1. I can convert between units of measurement. 2. I can convert between the three common units of temperature. Materials: none

Success Criteria 1: I can convert between units of measurement If there is one skill you’ll learn in this class that if you master it, it will make your life easier, it is learning to use conversion factors and unit cancelling. In this lesson we’ll discuss conversion factors, and in the next, we’ll discuss unit cancelling.

Success Criteria 1: I can convert between units of measurement A conversion factor is a fraction equal to one, with one unit (such as feet or inches) in the numerator and a different unit in the denominator (see right). As you know, multiplying any number by 1 results in the same number. We’ll use this fact to convert from the units we have to the units we want. Writing the relationships between units as conversion factors makes going from a quantity in one unit (feet) to another (inches) much easier. We know the relationship between feet and inches: 1 foot = 12 inches This relationship can be written as a conversion factor in two ways: 1𝑓𝑜𝑜𝑡 12𝑖𝑛𝑐ℎ𝑒𝑠 𝑜𝑟 12𝑖𝑛𝑐ℎ𝑒𝑠 1𝑓𝑜𝑜𝑡 Since 12 inches = 1 foot, 12 inches divided by 1 foot equals one.

Success Criteria 1: I can convert between units of measurement Here are some other examples of conversion factors: 1𝑚 100𝑐𝑚 𝑜𝑟 100𝑐𝑚 1𝑚 2.2𝑙𝑏𝑠 1𝑘𝑔 𝑜𝑟 1𝑘𝑔 2.2𝑙𝑏𝑠 128𝑜𝑧 1𝑔𝑎𝑙𝑙𝑜𝑛 𝑜𝑟 1𝑔𝑎𝑙𝑙𝑜𝑛 128𝑜𝑧 1𝑑𝑎𝑦 24ℎ𝑟 𝑜𝑟 24ℎ𝑟 1𝑑𝑎𝑦 Task 1.5.1: a) There are three feet in one yard. Write both conversion factors for this relationship. b) There are approximately 8 kilometers for every 5 miles. Write both conversion factors for this relationship.

Success Criteria 1: I can convert between units of measurement There are 12 inches in one foot. How many inches are in 4.0 feet? You can probably do this particular problem in your head. However, we will definitely move on to more complex calculations, so let’s see how to solve this problem using conversion factors and unit cancelling (CF&UC). Start with the given quantity (4.0 feet). Multiply by a conversion factor that includes both your given (feet) and wanted (inches) units. Use the version of the conversion factor that places the same units diagonally across from each other. This is what allows for the “cancelling” in unit cancelling. 4.0𝑓𝑒𝑒𝑡 1 𝑥 12𝑖𝑛𝑐ℎ𝑒𝑠 1𝑓𝑜𝑜𝑡 =48 𝑖𝑛𝑐ℎ𝑒𝑠

Success Criteria 1: I can convert between units of measurement There are 2.54 cm in one inch exactly. How many inches are in 72 cm? 72𝑐𝑚 1 𝑥 1𝑖𝑛𝑐ℎ 2.54𝑐𝑚 =28𝑖𝑛𝑐ℎ𝑒𝑠 There are 2.20 lbs in 1.00 kg. There are 1000 grams per kg. How many grams are there in 38.2 lbs? 38.2𝑙𝑏𝑠 1 𝑥 1.00𝑘𝑔 2.20𝑙𝑏𝑠 𝑥 1000𝑔 1𝑘𝑔 =17400𝑔

Success Criteria 1: I can convert between units of measurement 3.785 liters = 1 gallon 1 inch 2.54 cm 1 light year 5.88 x 1012 miles 16 cups 1 mile 1.609 km 5280 feet 2.2205 lbs 1 kg 16.387 cm3 1 in3 1 m3 1 x 106 cm3 In addition to the metric prefix chart you have, use these equivalencies to help answer the questions in the following tasks. Table of Equivalencies

Success Criteria 1: I can convert between units of measurement Task 1.5.2: Perform these one-step conversions (show your work). a) 45 cm into meters b) 0.024 km into m c) 74 inches into feet d) 24.6 feet into inches e) 1.7 miles into feet (1 mile = 5280 ft) f) 152 pounds into kg (2.2046 lbs = 1 kg) g) 3.8 gallons into liters (3.785 L = 1 gal) h) 2580 mg into g i) 4.24 light-years into miles (1 ly = 5.88 x 1012 miles)

Success Criteria 1: I can convert between units of measurement Task 1.5.3: Perform these one or two-step conversions (show your work). a) 65 cm into mm b) 12600 mm into km c) 28 inches into m (1 in = 2.54 cm) d) 0.0256 miles into inches (1 mile = 5280 ft) e) 1.9 x 106 inches into miles f) 5.2 x 10-4 pounds into mg (2.2046 lbs = 1 kg) g) 32.8 gallons into dL (3.785 L = 1 gal) h) 1.00 x 106 seconds into days i) 24 months into hours

Success Criteria 1: I can convert between units of measurement Task 1.5.4: Perform these compound unit conversions (show your work). a) 62 miles/hr into m/s b) 1560 kg/m3 into g/cm3 c) km/hr into m/s e) 268 mg/L into g/dL g) 9.4 x 103 g/cm3 into kg/dL (1 mL = 0.01 dL) h) 4500 kcal/hr into cal/s

Success Criteria 1: I can convert between units of measurement Task 1.5.5: Use your knowledge of unit conversions and density to answer these questions a) A 10.0 cm3 block of iron has a mass of 78.7 g. What is its density in kg/m3? b) Platinum has a density of 21090 kg/m3. How many mL is a 22800 g sample? (remember 1 mL = 1 cm3) c) If 25.0 mg of diamond has a density of 3500 kg/m3, what is its volume in mL? d) Chlorine gas is 3.214 g/L. What is the volume in mL of a 0.500 kg sample?

Success Criteria 2: I can convert between the three common units of temperature In our daily lives, when we talk about how hot or cold it is outside, we use the Fahrenheit scale. When we say “It’s about 70 degrees outside” everyone assumes we mean 70 degrees Fahrenheit (°F). In science, and in most other countries, they use the Celsius scale (°C). 70 degrees Fahrenheit is roughly 21 degrees Celsius.

Success Criteria 2: I can convert between the three common units of temperature Converting between these two temperature scales is slightly trickier than converting between, say, kg and pounds, because °F and °C have different zero points. Zero degrees Celsius is equal to 32 degrees Fahrenheit. In fact, the Celsius scale uses the freezing point of water as one reference point (0 degrees). The boiling point of water (100 degrees) is another reference point.

°C = (°F – 32)/1.8 or °F = (°C x 1.8) + 32 Success Criteria 2: I can convert between the three common units of temperature The relationship to convert between the two systems is: °C = (°F – 32)/1.8 or °F = (°C x 1.8) + 32 Ex: What is 68° F in degrees Celsius? Solution: °C = (°F – 32)/1.8 thus °C = (68° F -32)/1.8 = 20° C Tip: To remember if you are doing it right, water freezes at 32° F and 0° C. If your formula doesn’t give you this, try the other one. 55 F = 12.77777 C = 13 C

Success Criteria 2: I can convert between the three common units of temperature Task 1.5.6: Perform these temperature conversions (remember it is okay to have a negative temperature) a) 28° F into °C b) 425° F into °C d) 218° C into °F e) -25° C into °F g) 5500° C into °F (an average star’s surface temp) h) -459.67° F into °C (the lowest possible temp)

Success Criteria 2: I can convert between the three common units of temperature Scientists have found it useful to create a third system based on the lowest possible temperature, aka: absolute zero. Absolute zero is the temperature where the atoms or molecules in the substance have zero heat energy (no motion), and is equal to -273.15 °C. This is called the Kelvin scale, and is related to the Celsius scale by the following equation: K = °C + 273.15 It is thus not possible to have a negative value in the Kelvin scale. At 0 Kelvins, there is no more heat energy left. 55 F = 12.77777 C = 13 C

Success Criteria 2: I can convert between the three common units of temperature Task 1.5.7: Perform these temperature conversions. a) 280° C into K b) -125° C into °K d) 830 K into °C e) 373 K into °F g) 620 °F into K h) -459.67° F into K

Wrap-up Task 1.5.8: Write in complete sentences eight things that you learned in this topic.