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Dimensional Analysis

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When you convert a given result from one system of units to another Method called unit factor method, or dimensional analysis

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Converting from one Unit to Another To convert from one unit to another, use the equivalence statement that relates the two units Derive the appropriate unit factor by looking at the direction of the required change (to cancel the unwanted units) Multiply the quantity to be converted by the unit factor to give the quantity with desired units

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Common Conversions 1 Kx = 1000 mx 1 mx = 1000 x 1 x = 100 cx 1 x = 10 dx X = grams (g), liters (L), etc

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Practice…. 1)A pencil is 7.00 in long. What is its length in centimeters? 7.00 in x 2.54 cm = (7.00)(2.54) = 17.8 cm 2) You want to order a bicycle with in frame, but the sizes in the catalog are given only in centimeters. What size do you order? 25.5 in x = 64.8 cm 1 in 2.54 cm 1 in

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3) Convert 29 km into m 29 km x 1000m = 29,000 m 4) Convert 35.4 cg into g 35.4 cg x 1g = 0.354 g 5) Convert 624 dm into mm 624 dm x 1 m x 1000 mm = 62,400 mm 1 km 100 cg 10 dm1 m

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Temperature Three main temp scales: Celsius, Fahrenheit, and Kelvin We mainly use Celsius and Kelvin in physical sciences Fahrenheit is mainly used in engineering sciences

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Temperature Conversions Kelvin = Celsius + 273.15 Celsius = Kelvin – 273.15

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Practice Convert 32 ᵒC into Kelvin K = ᵒC + 273.15 K = 32 + 273.15 K = 305.15 K Convert 298 K into Celsius C = K -273.15 C = 298.15 – 273.15 C = 25 ᵒC

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Density A property if matter that is often used by chemists as an “identification tag” for a substance Density = Mass (g) D = M g Volume (mL) VmL Units

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What is the most common substance on Earth? – Water – D = 1g/mL Therefore…. – If the density of an object is less than 1 g/mL then the object will float on water – If the density of an object is more than 1 g/mL then the object will sink in water

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Why do Boats Float?

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Practice… 1)A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density? D = M/V D = (40.5g) / (15.0cm 3 ) D = 2.7 g/cm 3 D= ?? M= 40.5 g V = 15.0 mL = 15.0 cm 3

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Practice… 2) What is the weight of the ethyl alcohol that exactly fills a 200.0 cm 3 container? The density of ethyl alcohol is 0.789 g/cm 3. D = M / V M = D x V M = (200cm 3 ) (0.789g/cm 3 ) M = 157.8 g D= 0.789 g/cm 3 M = ?? V = 200.0 cm 3

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