1. Scientific Measurement
Chemistry
Chapter 3

2. Measurements Are really, really important to sciences.
Important to be able to decide if measurements are correct.
Must have two parts:
A quantity
A unit
UNIT ARE VERY, VERY IMPORTANT!

4. Scientific Notation
Science deals with very large and very small numbers
Like:
atoms m
But zeroes are boring and are a waste of space.
So, we use scientific notation
1 number in front of the decimal, and all other important (significant) numbers behind the decimal
6.02 x 1023
2.50 x 10-17

6. Get the meter stick, Valz!

7. Significant Figures (or Digits)
How well you “know” and estimate your measurement
All the digits you are confident in, plus one that is estimated
Measurements must always be reported to the correct number of significant digits.
Answers depend on the correct number of digits to determine the most “honest” answer.

8. Counting significant digits
All zeroes before the first non-zero don’t count.
only has 1 sig digs
All non-zero numbers count.
21343 has 5 sig digs
All zeroes between non-zeroes count
2002 has 4 sig digs
All zeroes AFTER non-zeroes count IF there is a decimal
200.0 has 4 sig digs
200. has 3 sig digs (decimal at the end!)
200 has 1 sig digs

9. A simpler way of saying it.
The zeroes in the front NEVER count.
The zeroes at the end ONLY count if there is a decimal.
That’s it.

10. The Pacific/Atlantic Method
If the period is present (with a p) you start in the Pacific Ocean, on the left side (at the first non-zero), and count until you’re out of numbers.
If the period is absent (with an a) you start in the Atlantic, on the right side and don’t start counting until you hit the first non-zero.

11. Get some, scratch paper, yo. Number it 1 to 8.

12. How many sig digs? 20
3.0
40.1
300
5.71
20000
2100.0

13. How many sig digs?
20 1
3.0 2
40.1 3
300 1
5.71 3

14. Rules for Math with Sig. Digs.
Multiply or Divide:
Use the LEAST number of significant digits from your measurements.
Add or Subtract
Use the LEAST significant place value (which has the highest place value).
When both:
Use whichever method gives you the least number of significant digits as the answer
When averaging:
The number of numbers is NOT a measurement, and therefore does NOT count when determining the number of significant digits.

15. WHY?!?
When adding or subtracting numbers, they must be from the same type of measurement. That means that the units must be the same, so the place value must be the same.
When multiplying or dividing you are changing the units or converting, so it’s just the number of significant digits that matter.
Place VALUE doesn’t matter when converting
Don’t write this down.

16. Let’s try some… What is 3.3/1.55 in correct significant digits?

17. A couple more. What is (3.4751 + 80.41) x 62?

18. Back to scientific notation really quick…

19. Let’s try some out…
First, let’s convert to scientific notation.

20. Let’s try some out…
First, let’s convert to scientific notation.
3.251x108

21. Convert 4.78x10-5 to standard notation.
Okay, how about this…
Convert 4.78x10-5 to standard notation.

22. Okay, how about this… Convert 4.78x10-5 to standard notation.

23. Fine, do this one, smart guy.
Fix this number to proper scientific notation: 5541 x 105

24. Fine, do this one, smart guy.
Fix this number to proper scientific notation: 5541 x 105
5.541x108

25. Doing maff with Scientific Notation
Addition/subtraction
Change the exponent on one of the numbers until they are the same
Then line up the decimals and subtract/add
Adjust the coefficients until there is again 1 digit in front of the decimal
Multiplication/division
Divide or multiply the coefficients
Divide or multiply the base 10 exponents
Adjust the coefficients again
YOU STILL FOLLOW THE RULES OF SIGNIFICANT DIGITS!!!1ONE!1

26. Okay, now some fun stuff…
(2.73 x 109) x (3.14 x 10-8)

27. Okay, now some fun stuff…
(2.73 x 109) x (3.14 x 10-8)
x 101

28. Okay, now addition.
(2.73 x 109) + (3.14 x 108)

29. Okay, now addition.
(2.73 x 109) + (3.14 x 108)
3.044 x 109

30. Accuracy and Precision
How close the measurement is to the actual (true) value
Closeness to the “target”
Measured by ERROR.
Precision
How close measurements are to each other
Closeness to other measures of the same thing
Measured by the number of significant digits.

32. Determining Error
Error is the difference between a measured (experimental) value and the accepted value
Error = experimental value – accepted value
% error = |Error|*100/accepted value

33. Practice
You measure the world’s largest duck to be 15m long, but it is known to actually be 14m long.
What is the error?
What is the percent error?

34. Practice
You measure the world’s largest duck to be 15m long, but it is known to actually be 14m long.
What is the error?
15-14 = 1m
What is the percent error?
|15-14|*100/14
1*100/14
100/14
7.1 % = 7% (with sig figs)

35. Okay, now your turn…
You have a 17.1 kg sample of lead. It should displace liters of water. But when you measure it, it displaces exactly 1.50 liters. What is your error and percent error?

36. 3.1 Quiz Convert 3.2 x 104 to standard notation.
Convert to scientific notation.
Put x 10-4 in proper scientific notation.
How many significant digits are in 3,000,000?
Solve and answer in correct significant digits: x

37. 3.1 Quiz answers
32000
7.9x10-4
8.3 x 10-9 1
11.0

38. SI: International System of Units (System International)
The basis for all measurements made in science (and in this class)
Uses 5 most commonly used units:
Meter (distance)
Kilogram (mass)
Kelvin (temperature)
Second (time)
Mole (amount)
All measurements can be reported as some SI measurement.

39. Prefixes in SI
SI uses prefixes to shorten measurements (much like scientific notation)
These are put in front of measurements to give a certain place value (multiple) of the unit.
Ex) Rather than 1000m, you can write 1km, because kilo means 1000.
Ex) Rather than writing g, you can write 1 μg or 1 microgram, because micro means 10-6

41. Important SI measurements in Chemistry
Length
Meter, km, cm, mm, nm
Volume
Liter, mL, μL
Cubic meter (m3), cubic cm (cm3)
1cm3 = 1mL
Mass
Gram, kg, mg, μg
NOT the same as WEIGHT!!!!
Temperature
Celsius
Based on boiling and melting point of water
Kelvin
Absolute, based on the point at which matter stops moving
Energy
Joules, kJ, calories (stupid, based on water, don’t use)

42. Volume’s two “sets of units”
Volume is 3 measures of length multiplied together.
m, km, cm, or mm 3 times
m3, km3, cm3, or mm3
Volume can also be measure in terms of liters.
1000L = 1 m3
1L = 1000 cm3
1mL = 1 cm3
This is the one that you NEED to know.

43. How to convert cubic units to liter units
Convert your original number to mL or cm3.
Then it is a 1 to 1 conversion (same number, just change the unit)
Then convert to the unit you want.
Ex) 40L to mm3
40 L = 40,000 mL
40,000mL = 40,000 cm3
1cm = 10 mm
1 cm = 103 mm3 = 1000mm3
40,000 cm3 = 40,000,000 mm3

44. Temperature in SI
Celsius is a metric unit, but NOT an SI unit because it is not absolute.
It is based off of water, and is measured in degrees C = (°C)
We used Kelvin (K), which is measured from absolute zero
Where all matter has no movement.
To convert from C to K you just add
K = °C
°C = K
Still follow significant digits rules of place value for addition!

45. A problem? You’re the problem!
Convert 27°C to Kelvin.

46. A problem? You’re the problem!
Convert 27°C to Kelvin.
= K
300. K with correct SD

47. A problem? You’re the problem!
Convert 27°C to Kelvin.
= K
300. K with correct SD
Convert K to °C

48. A problem? You’re the problem!
Convert 27°C to Kelvin.
= K
300. K with correct SD
Convert K to °C
– = °C

49. Don’t worry about the calorie to Joule conversion.
Calories are a stupid unit of measurement.
If I want you to do a stupid conversion, I’ll give you the conversion and the units.

50. 3.2 Quiz What is the SI unit of length?
What is the name of the “before” measurement that is used to shorten SI measurements.
What is the “k” in “km” called (or the “c” in “cm”)?
What is the SI prefix for 1000?
What is larger mL or mm3?
Convert 95°C to K, using correct significant digits.

51. 3.2 Quiz
Meter (m)
prefix
Kilo mL
368K

52. Dimensional Analysis Also called “factor-label conversions”
Uses conversion factors to convert one measurement to an equal one using different units
Conversion factors are a ratio of two EQUAL measurements with different numbers
Ex) 1 mile = 1760 yards
Therefore mi = 1
1760 yards
This is a stack of pennies. It has nothing to do with dimensional analysis, but when I Googled “dimensional analysis” this image came up, and it’s pretty awesome.

53. Conversion Factors Conversion factors must always be equal to one
Will not change the actual value when multiplied by a measurement
Only changes the unit label to give you a different “looking” measurement
But nothing really changes

54. Another example problem.
Convert 1600km/hr (the airspeed of a fighter jet) to m/s.

55. Another example problem.
Convert 1600km/hr (the airspeed of a fighter jet) to m/s.
444.44… m/s
Rounds to 440 m/s with sig. figs.

56. https://youtu.be/hQpQ0hxVNTg?t=3m7s

57. Dimensional Analysis
A way to analyze and solve problems using units (or dimensions) of measurements
Provides a way to solve problems that are elephants.
Dimensional analysis allows unit conversions through one or more steps

58. Doing Dimensional Analysis
Start by turning whatever measurements you have into a fraction or a number that MUST have a unit.
Like this: 2000 miles or
4 cars

59. Completing Dimensional Analysis
Multiply by conversion factors until you have an answer in the units you want
Okay, lets do this:
Convert 1.4 miles into km.
1.62 km/1 mi

60. Completing Dimensional Analysis
Multiply by conversion factors until you have an answer in the units you want
Okay, lets do this:
Convert 1.4 miles into km.
1.62 km/1 mi
2.268 km.
But only 2 sig figs, so 2.3 km, right?

61. When sig digs matter.
Significant Digits only matter in MEASUREMENTS (which are estimates), not for conversions (which are definite).
This doesn’t count for converting from SI to non-SI, though.

62. Now the BIG problem.
The sink in the fume hood has been dripping since How much water in L has gone the drain since then?

63. On your own now… I have 3.12 x 103 papers to grade
I can grade 3 papers per hour
I can grade 8 hours per day
How many days will it take to grade them?
Present your answer in standard notation, with the correct number of significant digits.

64. Converting in SI 2 methods of conversion Dimensional Analysis method
Difficult, slow.
Lazy Mr. V method
Easy, quick.
DOES NOT WORK WITH NON-SI CONVERSIONS!!!

65. Practice Problems
Convert 1.75m into cm

66. Practice Problems Convert 1.75m into cm 0 – (-2) = 2
Move decimal 2 places to the RIGHT.

67. Practice Problems Convert 1.75m into cm Answer: 175cm 0 – (-2) = 2
Move decimal 2 places to the RIGHT.
Answer: 175cm

68. On your own
Convert 678µg to kg.

69. On your own Convert 678µg to kg. µ = -6 to kg = 3 -6 – 3 = -9
9 spots to the LEFT

70. Okay, how about this one? 3cm3 to mm3
If you have cubic units, you must do the conversion 3 times.
(IF you have square units, you must do the conversion 2 times.)

71. Okay, how about this one? 3cm3 to mm3
If you have cubic units, you must do the conversion 3 times.
(IF you have square units, you must do the conversion 2 times.)
cm = -2
mm= -3
-2 – (-3) = 1
1 * 3 = 3, so 3 spots to the right
3cm3 = 3000mm3

72. Try this one on for size:
Convert 3.71 cm3 to m3.
Remember, it’s an elephant, but you can just eat it one bite at a time!

73. 3.3 Quiz
Convert 80.0kL to mL, and put in correct scientific notation with correct significant digits.
Convert 211 m/s into km/hr.
Answer in correct sig figs.
A conversion factor is always equal to (or the same as) what number?
T/F: A conversion factor’s significant digits matter when determining the final answer’s number of significant digits.
Assume that the conversion is an absolute, and not just a measured value.
Convert 30.0 miles per gallon to km per liter if 1mi=1.61 km, and L=1 gallon

74. 3.3 Quiz Answers
8.00x107mL
760. km/hr 1 F
12.8 km/L

75. Density Density is an easily measured intensive property.
Does not matter how much matter you have.
Density is a ratio of mass divided by volume.
How much “stuff” fits in a certain space.
Density range:
Hydrogen ( g/mL)
Water (1.000 g/mL)
Osmium (22.57 g/mL)

76. Determining Density Density = mass volume
Okay, so let’s determine the density of an object with a mass of 37.2g, that requires a volume of 4.5mL.

77. Determining Density Density = mass = 37.2 g = 8.3 g/mL volume 4.5 mL
Okay, so let’s determine the density of an object with a mass of 37.2g, that requires a volume of 4.5mL.

78. So, what is it?
Density (g/mL)
Density is 7.9g/mL, rounded to 2 significant digits. Which metal is it?
Are you SURE?

79. Density used to calculate mass or volume
If you KNOW the material you can determine the mass or volume.
If D = m/V
What is m?
What is V?
If lead has a density of g/mL, and you need 100.0g of it, how much space will it occupy?

80. Determining Mass from Measurements
I have a fish aquarium with a height of 20.0cm, a width of 13.0cm, and a length of 16.5cm. If I fill it all the way up with water at 4°C (D = 1.00 g/mL) what will be the mass of the aquarium?

81. Density and Temperature
Usually density decreases as temperature increases
Solids are usually more dense than the liquids of the same compounds or elements
Water breaks this rule - ice is less dense than liquid water.
Matter “spreads out” when it gets warmer, so it has more volume, but the SAME MASS!

82. 3.4 Quiz Write the equation for calculating density.
When temperature decreases, density usually ______________.
Write an equation to determine the mass of an object based on its density and volume.
If an object has a mass of 36g, and a volume of 6.0 mL, what is its density in g/mL?
If an object has a mass of 3.00 g, and a density of 39.30g/m3, what is its volume?

83. 3.4 Quiz
D = m/V
increases
m=DxV
6.0 g/mL m3