Problem Solving Ch. 2

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Problem SolvingCh. 2

• Take out materials for notes believe me, youll
  want to take them

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Sig Figs!

• Significant figures important numbers
• 0.01 vs. 0.010 vs. 0.0100
• Which number is more precise?
• Deals with measured or computed values (as
  opposed to exact values like 2 eyes, 12 eggs)

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Remember the measurement lab?

• To what place can we record measurements on this
  graduated cylinder?
• It is given to the ones place, so we estimate to
  the tenths place
• Sig figs explain why 50 mL is not the same as
  50.0 mL

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Rules

• RULE 1 All nonzero digits are significant
• RULE 2 Zeroes between nonzero digits are
  significant.
• RULE 3 Leading zeros to the LEFT of the first
  nonzero digits are NOT significant such zeroes
  merely indicate the position of the decimal
  point.
• RULE 4 Trailing zeroes that are also to the
  RIGHT of a decimal point in a number ARE
  significant.
• RULE 5 When a number ends in zeroes that are not
  to the right of a decimal point, the zeroes are
  NOT necessarily significant

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See if you can figure out when numbers are
significant

• 515 3 sig figs
• 5050 3 sig figs
• 0.5050 4 sig figs
• 0.05050 4 sig figs
• 5000 1 sig fig
• 0.0500 3 sig figs
• 505.0 4 sig figs

• Based on these
• Can you guess how many are in the following s?
• 4301
• 1.05
• 0.568
• 0.00798
• 12000

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Or, you can try it this way

1. Figure out which side of the number to start from
   (Absent or Present)
2. Start counting at your first non-zero number
3. KEEP COUNTING!!!

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Rounding

• If digit next to last significant figure is
• 0-4 dont round
• 5-9, then round up
• 12488 (3 sig figs) 0.008209 (2 sig figs)
• 2.77549 (4 sig figs) 0.352 (1 sig fig)
• Make sure your new rounded number is close to
  your original number!!!!

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Calculating with sig figs

• Adding/subtracting line up the numbers, add em
  up, and cut off at the shortest tail (round if
  necessary)
• 3.31 12.565 25.0915
• 147.3 29.12 0.115
• 178.1 92.67
• 1505.22 500

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Multiplication/Division

• Count number of sig figs in each of your numbers
  the lowest number of sig figs is the number of
  sig figs that will be in your answer
• 32.7 x 2.5 19.9 x 100
• 135.5 ? 5.7 281 ? 9.341

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Lets practice

• 3.461728 14.91 0.980001 5.2631
• 0.04216 - 0.0004134
• 2.3 x 3.45 x 7.42  
• 208 / 9.0   

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WARM-UP

• Calculate, using sig figs
• 0.00783 0.022 1.057
• 225.112 14.78

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• Record your answer using the correct number of
  significant figures and proper units.
• a. 7.55 m x 0.34 m _____
• b. 2.10 m x 0.700m ____
• c. 2.4526 m / 8.4 sec _____
• d. 0.365 m / 0.0200 hr _____
• e. 8432 m / 12.5 hr _____
• f. 7 m x 1.22 m ____

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Whats the point?

• A student once needed a cube of metal that had to
  have a mass of 83 grams. He knew the density of
  this metal was 8.67 g/mL, which told him the
  cube's volume. Believing significant figures were
  invented just to make life difficult for
  chemistry students and had no practical use in
  the real world, he calculated the volume of the
  cube as 9.573 mL. He thus determined that the
  edge of the cube had to be 2.097 cm. He took his
  plans to the machine shop where his friend had
  the same type of work done the previous year. The
  shop foreman said, "Yes, we can make this
  according to your specifications - but it will be
  expensive."
• "That's OK," replied the student. "It's
  important." He knew his friend has paid 35, and
  he had been given 50 out of the school's
  research budget to get the job done.

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• He returned the next day, expecting the job to be
  done. "Sorry," said the foreman. "We're still
  working on it. Try next week." Finally the day
  came, and our friend got his cube. It looked
  very, very smooth and shiny and beautiful in its
  velvet case. Seeing it, our hero had a
  premonition of disaster and became a bit nervous.
  But he summoned up enough courage to ask for the
  bill. "500, and cheap at the price. We had a
  terrific job getting it right -- had to make
  three before we got one right."
• "But--but--my friend paid only 35 for the same
  thing!"
• "No. He wanted a cube 2.1 cm on an edge, and your
  specifications called for 2.097. We had yours
  roughed out to 2.1 that very afternoon, but it
  was the precision grinding and lapping to get it
  down to 2.097 which took so long and cost the big
  money. The first one we made was 2.089 on one
  edge when we got finished, so we had to scrap it.
  The second was closer, but still not what you
  specified. That's why the three tries."
• Oh!"

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There are 4 graduated cylinders and 4 triple
beams (with objects) around the room

• Youll be going to each graduated cylinder and
  triple beam
• Record the number graduated cylinder and its
  volume (be sure to estimate an extra place)
• Record the letter of the triple beam, and find
  the mass of the object (be sure to estimate an
  extra place)

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Perform the following operations with the data
you just found

• Be sure to use sig figs in your answers!
• 2 A - 1
• B 3
• 4 x D C

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You need a non-graphing calculator for today.

• If you dont have one, I have ones in the box at
  the front just sign one out
• Warm up
• Calculate, using sig figs
• 25.978 5.901 139.8
• 250 9.25

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Review

• Write the following numbers in scientific
  notation
• 840,000
• 3500
• 0.0000785
• 0.008812

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Multiplying/Dividing

• Perform function with base numbers
• Multiplying add exponents
• Dividing subtract exponents
• Putting answer in correct scientific notation
• decimal Left exponent Larger
• decimal Right exponent Reduced

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Estimate your answer before using a calculator

• (2.0 x 10 -1) x (8.5 x 105)
• (4.42 x 10-3) x (4 x 10-2)
• (9.4 x 10 2) ? (1.24 x 10-5)
• (9.2 x 10-3) ? (6.3 x 106)     

Now lets learn about the EE button!
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Adding/Subtracting

• (2.5 x 102 ) (5.2 x 104 )
• (4.1 x 103) (3.25 x 102)
• (9.86 x 104) - (1.2 x 102)
• How many sig figs should be in each answer?

Calculate, using the EE button
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Answers

• Addition/Subtraction
• i) 4.01 x 10-9
• j) 9.4 x 1010
• k) -2.8 x 107
• l) 4.62 x 10-1
• m) 2.5 x 106
• n) 6.6 x 1018

Multiplication/Division 8) 2.6 x106 9) -1.31 x
1014 10) 3.74 x 10-9 11) -2.1 x 1016 12)-8.9 x
1020 13) 4.3 x 1016 14) 1.4 x 1045
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Warm up

• Calculate, with correct number of sig figs
• 8.56 x 0.030 x 12.15
• (198.1 7.82) / 2.5

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Precision and Accuracy
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• Accuracy measurements are close to the given,
  accepted value
• Precision getting the same measurement each
  time also pertains to the number of places you
  use in a measurement
• 9.52 cm is more precise than 9.5 cm
• If I said I was 6 feet, 5 inches, 2.38 cm tall, I
  would be ________________ but not
  _________________.

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Percent Error- how wrong were you?

• A way to report how far off your values were from
  the accepted value
• The closer you are to 0, the better your results
• measured - accepted x 100
• accepted

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Examples

• A student measures the volume of a 2.50 liter
  container to be 2.38 liters. What is the percent
  error in the student's measurement?
• Dont forget about sig figs!
• 4.8 error

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Precision and Accuracy activity

• Carefully read and follow the instructions
• Percent error calculations use absolute value
• 5.00 measure x 100
• 5.00

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Turn in Accuracy and Precision activity and try
warm up

• The melting point of a chemical is 53.0oC. In a
  lab, two students try to verify this value. The
  first student records 51.5oC, 53.5oC, 55.0oC and
  54.2oC. The second student records 52.3oC,
  53.2oC, 54.0oC and 52.5oC.
• 1. Calculate the average value for each student
• 2. Calculate the error for each average
• 3. Which student is most precise? Most
  accurate? How do you know?

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Temperature conversions

• Celsius or Kelvin
• 0 Co 273 K Guess how you
• 10 Co 283 K
• 100 Co 373 K solve for Kelvin
• Fahrenheit to Celsius is a little harder
• Fo 1.8(Co) 32

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Temperature conversions

• Convert 60o C to Kelvin
• Convert 75o F to oC
• Convert 323 K to oC
• Convert 10o C to oF
• Convert 90o F to K
• Convert 400 K to oF

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Try this recipe

• Chocolate chip cookies
• 1 sugar
• 1 brown sugar
• 1 ½ butter
• 2 ½ all purpose flour
• ½ salt
• 1 baking soda
• 2 semisweet chocolate chips

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Units annoying but important

• SI Units Systeme Internationale dUnites
• A universal system of measurement that allows
  people all over to discuss and trade without
  confusion
• kilogram kilogram

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Base units
Second (s) Meter (m) Kilogram (kg) Kelvin
(K) mole (mol)

• Time
• Length
• Mass
• Temperature
• Amount of a substance

The standard kilogram kept in a vacuum sealed
container in France.
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Derived Units

• An SI unit that is defined by a combination of
  base units
• Density g/mL
• Volume cm3
• If you know the units, you can figure out the
  formula, or vice versa
• What is the unit for speed?
• What is the formula for speed then?

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Dimensional Analysis

• A way of converting from one unit to another
• Conversion factors
• 1 min 60 sec
• 12 in 1 foot
• 16 oz 1 lb

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Warm up

• Convert the following using the provided
  formulas
• 65 oF to oC
• 393 K to oF
• Formulas
• K oC 273
• oF 1.8(oC) 32

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• Convert
• 45 inches to miles
• 1. Start with your given
• 2. Figure out which conversion factors you need
• 3. Set it up so units cancel
• 4. Do the calculations
• Multiply across the top, divide across the
  bottom
• 3.6 miles to centimeters
• 1450 minutes to days
• 0.8 days to seconds
• 1.3 x 1010 seconds to years

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• WARM-UP
• Using dimensional analysis, solve the following
• If 25 zags 1 zangdoodle, and 3.5 zangdoodles
  1 raz, and 1.75 raz 1 zoom, how many zags would
  you have if you had 8.9 zooms?

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• Warm up
• Convert 450.0 oz to tons
• 1 ton 2000 lbs 1 oz 28.3 g
• 1 pound 454 g
• Lets rewrite our answers with sig figs!
• Only base the number of sig figs off of the
  given, NOT the conversion factors

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Dimensional Analysis with derived units

• The average student is in class 330 min/day.
• How many hours/day is the average student in
  class?
• What is changing?
• What conversion factors do I need?
• b. How many seconds is the average student in
  class per week?

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Practice

• How many mph is 23 km/hr?
• How many mph is 459 ft/sec?
• How many ft/hr is 4515 cm/min?

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What floats?

• Why does the tiny golf ball sink, and the much
  larger bowling ball floats?
• What 2 things does density take into
  consideration?
• What is the unit for density? (You can figure
  this out from the formula)
• What units must you be in to calculate density?

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Things you might need

• Density Mass/Volume
• Volume l x w x h
• 1 m 100 cm 1000 mm
• 1 km 1000 m
• 1 inch 2.54 cm
• 1 lb 16 oz
• 1 lb 454 g

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Density problem

• An oddly shaped piece of iron has a mass of 45.8
  g. A graduated cylinder contains 35.0 mL of
  water. After dropping the iron in to the water,
  the level rises to 43.6 mL. What is the density
  of iron?

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Three cubes, same size

• What do these 3 blocks have the same amount of?
• Volume
• Which one has more stuff in it?
• Which is the least dense? Most dense?
• If you were to draw what the atoms look like in
  each of the blocks, what would they look like?

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Candle trick

• Why does the candle sink more in one of the
  graduated cylinders than in the other?
• Something will float if it is (more, less) dense
  than the substance it is in.
• Rank the densities of the liquids in relation to
  the candle

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Any progress reports?

• Warm up
• If the following items were combined (and did not
  mix) put them in order from top to bottom
• densities
• alcohol 0.79 g/mL
• corn syrup 1.36 g/mL
• dishwashing liquid 1.03 g/mL
• vegetable oil 0.9 g/mL
• rubber stopper 1.5 g/cm3
• cork 0.2 g/cm3

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Density of water

• Using the provided equipment (and water from the
  sink), find and record the mass and volume of 4
  different amounts of water
• Be sure to use an estimated digit in your
  measurements
• Make sure you are finding the mass of just the
  water

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• From your data, calculate the density for each
  sample
• Be sure to use sig figs!
• Calculate the average density
• The actual density of water is 1.00 g/mL.
  Calculate your percent error

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Diet Coke vs regular Coke

• Do you think both will sink or float in water?
• Without dropping them in water, how could you
  figure this out?
• Something will float if it is (more, less) dense
  than the substance it is in.

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• An object has a mass of 35.0 grams.  On Hueys
  balance, it weighs 34.92 grams.  What is the
  percent error of his balance? 
• The Handbook of Chemistry and Physics lists the
  density of a certain liquid to be 0.7988 g/mL. 
  Fred experimentally finds this liquid to have a
  density of 0.7914 g/mL.  The teacher allows up to
  /- 0.500 error to make an A on the lab.  Did
  Fred make an A?  Prove your answer.

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• Each of five students used the same ruler to
  measure the length of the same pencil. These
  data resulted 15.33 cm, 15.34 cm, 15.33 cm,
  15.33 cm, 15.34 cm. The actual length of the
  pencil was 15.85 cm. Describe whether accuracy
  and precision are each good or poor for these
  measurements.
• A chemistry student measured the boiling point of
  naphthalene (C10H8) at 231.0C. What is the
  percent error for this measurement if the
  literature value is 217.9C?