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Measurement

Measurement. Scientific Notation. Used for numbers that are really big or really small. A number in exponential form consists of a coefficient multiplied by a power of 10. 1 x 10 4. 10,000 1,000,000 546,000 0.00001 0.00751. 0.00000029 12,450 15,230,000 0.0884. 2.9 x 10 -7.

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Measurement

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  1. Measurement

  2. Scientific Notation Used for numbers that are really big or really small A number in exponential form consists of a coefficient multiplied by a power of 10 1 x 104 10,000 1,000,000 546,000 0.00001 0.00751 0.00000029 12,450 15,230,000 0.0884 2.9 x 10-7 1 x 106 1.245 x 104 1.523 x 107 5.46 x 105 8.84 x 10-2 1 X 10-5 7.51 x 10-3

  3. If the coefficient does not fall between 1 and 10 , it must be re-written correctly If you move the decimal to the right, subtract from the exponent If you move the decimal to the left, add to the exponent x 103 0.0001 x 1012 4,490 x 10-7 0.0065 x 103 1 X 105 0.090 x 10-5 0.0112 x 108 150 X 1012 200 x 10-2 9 X 10 -7 1 X 108 1.12 x 106 4.49 x 10-4 1.5 x 1014 6.5 x 100 = 6.5 2 X 100

  4. calculations involving scientific notation Enter the coefficient, then EE or Exp Do not enter “x 10” (2.4 x 106) (3.1 x 103 ) = 7.44 x 109 (9.5 x 10-7) (5 x 10-4 ) = 4.75 x 10-10 4.8 x 109 = 2.4 x 102 2 X 107 7.5 x 10-5 + 4.2 x 10-6 = 7.92 x 10-5

  5. Two types of data Qualitative descriptive Ex: the burner flame is hot Quantitative numerical Ex: the flame is 1000 ° C Measurements should be both accurate and precise Accuracy how close the experimental value is to the accepted or true value calculating percent error % E = |accepted –experimental| accepted X 100

  6. Precision how close the measurements are to each other when the experiment is repeated Ex: a student does an experiment to determine the density of lead; she repeats the experiment two more times and gets these results: 10.1 g/cm3 9.4 g/cm3 and 8.5 g/cm3 poor comment on her precision If the actual density of lead is 11.4 g/cm3, calculate her percent error using her average density as the experimental value |11.4 – 9.3| 100 = 18.4 % Avg.= 9.3 % E = 11.4

  7. Quantities and their units Example units gram (g) kilogram (kg) milligram (mg) Mass (weight) meter (m) kilometer (km) millimeter (mm) Length (distance) Volume liter (L) milliliter (ml) any unit of length that is cubed

  8. 1m Vol. = L x W x H 1 m Vol. = 1 m3 1 m 1 mL = cm3 Temperature Celsius, ° C Kelvin, K Joules (J) Calorie (Cal) Heat

  9. number of particles mole 1 mole = 6.02 x 1023 Metric Conversions use dimensional analysis to convert between these units 1. 12 inches = ? cm 1 in. = 2.54 cm cm 12 in. 2.54 30.48 cm 1 in.

  10. 2. 95 miles = ? km 1 km = 0.62 mi 1 km 95 mi 153 km 0.62 mi 3. 400 lbs. = ? kg 1 kg = 2.2 lbs 1 kg 400 lbs 182 kg 2.2 lbs 4. 250 grams = ? oz. 1 oz = 28 g 1 oz 250 g 8.9 oz 28 g

  11. 5. 500 cm = ? in. 1 in. = 2.54 cm 1 in 500 cm 197 in 2.54 cm Metric Prefixes 1000 times larger kilo (k) deci (d) 10 times smaller (1/10) 100 times smaller (1/100) centi (c)

  12. 1000 times smaller (1/1000) milli(m) 1 x 106 times smaller(1/106) micro (µ) 1 x 109 times smaller(1/109) nano (n) Ex: 5 m = ? cm 100 cm 5 m 500 cm 1 m

  13. Ex: 25 mg = ? g 25 mg 1 g 0.025 g 1000 mg 1.50 L = ? mL 1.50 L 1000 mL 1500 mL 1 L 1 X 103 dg = ? g 1x 103 dg 1 g 100 g 10 dg

  14. 2.4 g = ? cg 2.4 g 100 cg 240 cg 1 g 3 X 1012 µg = ? g 3 x 1012 µg 1 g 3 X 106 g 1 X 106 µg 0.9 dm = m 0.9 m dm 1 0.09 m 10 dm

  15. 7.7 x 105 µm = ? m 1 m 7.7 x 105 µm 0.77 m µm 1 X 106 200 g = ? kg 1 kg 200 g 0.2 kg g 1000 0.25 L = ? mL 0.25 L ml 1000 250 mL 1 L

  16. 200 m = ? cm 100 cm 200 m 20,000 cm 1 m 3.5 x 10-4 g = ? mg 3.5 x 10-4 g mg 1000 0.35 mg 1 g 800 µL = L 800 µL 1 L 0.0008 dL 1 x106 µL

  17. Significant Figures all the numbers in a measurement that are known with certainty plus one that is estimated 6.35 uncertain 3 sig figs 6.3500 6.3 incorrect 6.4

  18. Rules for determining which numbers in a measurement are significant figures Any number in a measurement that is not zero is a significant figure Ex: 213.5 m has 5 4 12, 567 m has 2. Zeros between nonzero numbers are significant figures Ex: 205 g has 3 10.0002 g has 6 Zeros to the left of a number are not significant figures Ex: 0.078 L has 2 0.00005 has 1

  19. 4. Zeros to the right of a number and to the right of the decimal are significant figures Ex: 2.00 has 3 0.00100 has 3 5.Zeros at the end of a number are not significant figures unless the decimal point is shown Ex: 1200 has 2 1200. has 4 For numbers in exponential form, look only at the coefficient and not the exponent 4.50 x 108 has 3

  20. Identify the number of significant figures in each measurement: 2 5 1.______ 250 9.______ 13,979 2.______ 35,029 10.______ 3.00 x 102 3.______ 0.0075 11.______ 0.6000 4. ______ 9000 12.______ 50. 5.______ 0.0080 13.______ 4500 6.______ 10.00 14.______ 0.002 7._______ 3.6 x 105 15.______ 3.040 8._______ 15,000 5 3 2 4 1 2 2 2 4 1 2 4 2

  21. Rounding off numbers Begin counting from the first significant figure on the left; if the number being left off is 5 or higher, round up. Ex: round 65.31890 to 3 sig figs: 65.3 round 0.05981 to 3 sig figs 0.0598 round 43,925 to 2 sig figs 44,000 or 4.4 x 104 round 545,858 to 4 sig figs 545,900 or 5.459 x 105 round 9.9992 x 10-4 to 2 sig figs 1.0 x 10-3

  22. Round each number to 3 sig figs, then to 2 then 1 sig fig 6.77510 0.04031 18.298 0.0011299 892.153 6. 57,320 6.78 6.8 7 0.0403 0.040 0.04 18.3 18 20 0.00113 0.0011 0.001 892 890 900 57,320 57,000 60,000

  23. Significant Figures in Calculations When rounding off the answer after a calculation, the answer cannot be more accurate than your least accurate measurement Multiplication and Division Rule: The number of sig figs in the answer is determined by the number with the fewest sig figs

  24. Ex: 1.33 x 5.7 = 7.581 = 7.6 0.153 = 0.08 2 1.9125 = (5.00 x 103) ( 7.2598 x 102) = 3.6299 x 106 = 3.63 x 106

  25. Perform each calculation and round to the correct number of significant figures 520 x 367 = 2. 2.5 x 9.821 = 3. 0.02430 = 0.95880 4 x 10-8 = 1.5 x 10-2 190,840 = 190,000 or 1.9 x 105 24.5525 = 25 0.02534 0.02534418 = 2.6666 x 10-6 = 3 X 10-6

  26. Addition and Subtraction Rule: The number of decimal places in the answer is determined by the number with the fewest decimal places Ex: 10.25 + 11.1 = 21.35 = 21.4 515.3215 - 30.42 = 484.9015 = 484.90 1425 - 820.95 = 604.05 = 604

  27. Perform each calculation and round off to the correct number of significant figures 20.5 + 8.263 = 0.88 + 3.104 = 0.005 + 0.0066 = 4. 2291.7 - 1512.015 = 28.763 = 28.8 3.984 = 3.98 0.0116 = 0.012 779.685 = 779.7

  28. Density: Ratio of an object’s mass to its volume Density of water = 1 g/mL or 1 g/cm3 Which is more dense: the water in a tub or in a small cup ? both water samples have the same density

  29. Sample problems Calculate the density of a liquid if 50 mL of the liquid weighs 46.25 grams. D = M V 46.25 g D = 0.925 50 mL 0.9 g/mL A block of metal has the dimensions: 2.55 cm x 2.55 cm x 4.80 cm. If the mass of the block is 234.61 g, what is the density? V = L x W x H V = (2.55 cm)(2.55 cm)(4.80 cm) 234.61 g 7.51666 V = 31.212 cm3 7.52 g/cm3 D = 31.212 cm3

  30. 1. A marble weighing 53.87 g is placed in a graduated cylinder containing 40.0 mL of water. If the water rises to 64.9 mL, what is the density of the marble? V= 64.9 – 40.0 = 24.9 mL 53.87 g D = 2.16345 2.16 g/mL 24.9 mL

  31. Calculate the mass of a piece of aluminum having a volume of 8.45 cm3. The density of aluminum is 2.7 g/cm3 D = M V M= D x V M = (2.7 g/cm3) (8.45 cm3) 22.815 23 g What volume of mercury weighs 25.0 grams? Density of mercury = 13.6 g/mL D = M V V = M D M= D x V 25.0 g V = V = 1.838235 1.84 mL 13.6 g/mL

  32. What mass of gold (density= 19.3 g/cm3) has a volume of 12.80 cm3 ? D = M V M= D x V M = (19.3 g/cm3)(12.80 cm3) M= 247.04 = 247 g Calculate the volume of a cork if its mass is 2.79 grams and it has a density of 0.25 g/cm3 D = M V V = M D M= D x V V = 2.79 g 0.25 g/cm3 11.16 = 11 cm3

  33. Temperature 3 scales B.P. water F.P. water Lord Kelvin Anders Celsius

  34. Celsius Scale: Water freezes at 0°C , boils at 100°C Kelvin Scale: Water freezes at 273 K and boils at 373 K Absolute Zero: Lowest temperature that can be reached; all molecular motion stops 0 Kelvin K = °C + 273 Ex: 25 ° C = ? K 37 °C = ? K -50 °C = ? K 298 K 310 K 223 K 0 K = ?°C 600 K = ? °C -273 °C 327°C

  35. Heat Energy that flows from a region of higher temp to lower temp units: Joules (J) , Calories (Cal) 1 Cal = 4.18 J A measure of how well something stores heat Specific Heat Capacity: C, specific heat of water: 1.00 Cal/g°C or 4.18 J/g°C high compared to most substances; water heats up slowly and cools off slowly.

  36. Heat Calculations: temp change q = mCΔT heat mass specific heat m Problems How many Joules of heat energy are needed to raise the temperature of 50.0 grams of water from 24.5°C to 75.0°C ? specific heat of water = 4.18 J/g °C q= mCΔT ΔT C q = (50.0 g) (4.18 J/g°C) (75.0 – 24.5) q = 10,554.5 10, 600 J 50.5°C

  37. A piece of gold weighing 28 grams cools from 125°C to 23°C. To do this it must lose 362 Joules of heat energy. Calculate the specific heat of gold. q= mCΔT q= mCΔT mΔT mΔT 362 J C = C = q m ΔT 28 g 125- 23 102°C 0.13 J/g°C C = 0.12675

  38. What mass of graphite can be heated from 30°C to 80°C by the addition of 1500 Joules of heat? Specific heat of graphite = 0.709 J/g°C q= mCΔT q= mCΔT m = q CΔT CΔT CΔT 1500 J m = 42.3131 (0.709 J/g°C) (80-30) 40 g 50°C

  39. How many Joules of heat are needed to increase the temperature of 100.0 grams of iron metal by 80.0°C? specific heat of iron = 0.45 J/g°C q = (100.0 g)(0.45 J/g°C)(80.0°C) q= mCΔT q= 3600 J 25 grams of water absorb 150 calories of heat. What will be the temp change of the water? T= q mC 150 Cal______ (25 g)(1.00 Cal/g °C) 6°C

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