DERIVED UNITS Combining measurements to describe physical properties

DERIVED UNIT  Derived units are created from combining other base units  Examples:  Volume: the amount of space an object takes up  Density: how much mass is in a certain volume

VOLUME  Volume is derived by taking the following formula:  Volume = l x w x h  To solve, you do the same things to the units as you do to the numbers  If you have a box 10cm x 10cm x 10cm:  Volume = 10cm x 10cm x 10cm  Volume = 1000 cm 3  The derived unit is cm 3

NOTE 1 cm 3 = 1 mL  This is an important conversion. Make sure it is easily found in your notes  For example: 25cm 3 = 25mL

DENSITY  Density is the ratio of mass to volume  Mathematically this is expressed as follows:  Density = mass volume  Each variable is abbreviated  D = density  m = mass  V = volume

DENSITY  The density formula is summarized as:  D = m V  Again, the units are also divided by each other  Below are some examples of density units:  g/cm 3  g/mL  kg/m 3

EXAMPLE  An object has a mass of 15.0g and a volume of 5.0mL. What is the density?  NOTE: I am much more interested in the unit than the number answer

SOLUTION  D = M/V  D = (15.0g)/(5.0mL)  D = 3g/mL  NOTE: In addition to dividing the number, you also divide the units

TRY THESE  A car travels 200km in 4 hours, calculate the speed.  A student at college buys 8 books. His total price is $160. What is the price per book?  A bullet covers 5000m in 2 seconds, calculate the speed.

USING DENSITY TO SOLVE FOR MASS AND VOLUME  You can also solve for mass and volume.  Normally, you would use algebra  We are going to use a technique called dimensional analysis

TITLE: FLAME TEST LAB  Purpose: To determine an unknown substance using a flame test.  Procedure: 1. Insert flame loop into a chemical sample. 2. Make all of your observations about the flame. 3. Repeat for each of your known chemicals. 4. Insert flame loop into unknown sample. 5. Determine the unknown.

DIMENSIONAL ANALYSIS  Another way to solve problems is using a process called dimensional analysis  You will be solving density problems using dimensional analysis  Dimensional analysis : method of solving problems where the units cancel out

EXAMPLE  If a block has a density of 25kg/L and a volume of 10L, what is the mass?  For dimensional analysis, you need to be able to cancel out units until the one you are solving for is left Step 1: You always begin with the known value that has 1 UNIT after the number.  NOTE: 10L only has liters (L) after the number  Therefore, you start the problem with 10L

EXAMPLE Step 2: Find the conversion in the problem. The conversion is the number that has 2 units after the number.  NOTE: 25 kg/L has two units after the number, both kilograms (kg) and liters (L) Step 3: Put the two values together in a “T chart” so that 2 of the units cancel and you are left with 1 unit.

DIMENSIONAL ANALYSIS  Step 1:Write your known starting value  10L  Step 2: Set up a T chart to cancel out units using the conversion (density)  10L| 25kg_ | 1L  Step 3: Cancel out the units to solve (for mass)  10L | 25kg_= 250kg | 1L

TRY THIS OUT  A block has a density of 15g/mL. If the block has a mass of 5g, what is the volume?  NOTE: When you set it up, you will want to cancel grams (g)

TRY ONE OUT  A block has a density of 10g/mL. If the block has a mass of kg, what is the volume?  HINT: To cancel out units, they must be the SAME unit.

ANSWER  D = 10g/mL  M = 0.025kg = 25g (convert unit)  V= ?  25 g| 1mL= 2.5 mL | 10 g

USING DIMENSIONAL ANALYSIS IN METRIC  Before, we looked at using ratios to solve for metric conversions.  Now we will use dimensional analysis.  The steps are the same, the only difference is we use the 2 units from the chart to convert.  REMINDER:  Step 1: Convert to the base unit first  Step 2: Convert to the second unit next

EXAMPLE  Convert: 250mm = ??? hm  First, find the metric conversions on your sheet  1m = 1000mm  1hm = 100m  Second, take your starting value (250mm) and convert it to the base unit

CONVERT TO BASE UNIT 250mm | 1m_____ = 0.25m | 1000mm  NOTE: You put the mm on the bottom to cancel out the 250 mm on top  Since the 1000mm is on the bottom, you divide

CONVERT TO SECOND UNIT 0.25m | 1hm_____ = hm | 100m  NOTE: You use the answer from the first step in the second step  Since the 100m is on the bottom, you divide

TRY THESE  Convert the following metric units  225mg = ______g  33.4cm = ______hm  4.56x10 10 nL = ______ cL

HOW DO YOU DETERMINE SIG. FIGS. IN DERIVED UNITS  When multiplying or dividing, you find the number with the fewest number of sig. figs.  This is the number of sig. figs. in your answer  Example: x 2.11 = (4 sig. figs.) (3 sig. figs.) Change to correct sig. fig.= 6.38 (Fewest sig. figs. is 3)

TRY THE FOLLOWING x 2500 = x x x 10 2 = x 10 5 = x 10 2

ANSWER  x 2500 = 5.6 X 10 3 ( 2 sig. figs.)  2.04 x x x 10 2 = 1.80 ( 3 sig. figs.)  4.05 x 10 5 = 1.12 x 10 3 (3 sig. figs.) x 10 2  NOTE: You must round correctly, when doing significant figures

PROBLEM #1  Solve using significant figures: ______(367.21)*(24.783)_____ ( )*( )*( )

PROBLEM #2  An object has a mass of 2.25x10 3 mg and a density of 5.0g/mL. What is the volume?