1. Scientific Measurement Instructional PPT
Chapter 3

2. 3.1 Using & Expressing Measurements
In chemistry, you will often encounter very large or very small numbers
A single gram of hydrogen, for example, contains approximately 602,000,000,000,000,000,000,000 hydrogen atoms.
 This # is just way to challenging to work with!
You can work more easily with very large or very small numbers by writing them in scientific notation.

3. Scientific Notation
a given number is written as the product of two numbers: a coefficient and 10 raised to a power.
For example, the number 602,000,000,000,000,000,000,000 can be written in scientific notation as 6.02 x 1023.
The coefficient in this number is The power of 10, or exponent, is 23.

4. 6.02 x 1023
The coefficient is always a number greater than or equal to one and less than ten.
A positive exponent indicates how many times the coefficient must be multiplied by 10.
A negative exponent indicates how many times the coefficient must be divided by 10.

5. Sci. Notation: Positive Exponents
When writing numbers greater than ten in scientific notation, the exponent is positive and equals the number of places that the original decimal point has been moved to the left.
6,300,000. = 6.3 x 106
94,700. = 9.47 x 104

6. Sci. Notation: Negative Exponents
Numbers less than one have a negative exponent when written in scientific notation. The value of the exponent equals the number of places the decimal has been moved to the right.
= 8 x 10–6
= 7.36 x 10–3

7. Sci. Notation: Multiplication
To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.
(3 x 104) x (2 x 102) = (3 x 2) x = 6 x 106
(2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

8. Sci. Notation: Division
To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.
3.0 x
6.0 x 102 = (
6.0 )
x 105–2
0.5 x 103 = 5.0 x 102 =
**Remember that the coefficient must be between 1 & 10

9. Sci. Notation: Adding & Subtracting
If you want to add or subtract numbers expressed in scientific notation and you are not using a calculator, then the exponents must be the same.
In other words, the decimal points must be aligned before you add or subtract the numbers.

10. Sci. Notation: Adding & Subtracting
For example, when adding 5.4 x 103 and 8.0 x 102, first rewrite the second number so that the exponent is a 3. Then add the numbers.
(5.4 x 103) + (8.0 x 102)
= (5.4 x 103) + (0.80 x 103)
= ( ) x 103
= 6.2 x 103

11. Practice
Solve each problem and express the answer in scientific notation.
a. (8.0 x 10–2) x (7.0 x 10–5)
b. (7.1 x 10–2) + (5 x 10–3)

12. What is the difference between accuracy and precision?
Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision is a measure of how close a series of measurements are to one another, irrespective of the actual value.
Good Accuracy,
Good Precision
Poor Accuracy,
Poor Precision

13. Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

14. Determining Error
Suppose you use a thermometer to measure the boiling point of pure water at standard pressure.
The thermometer reads 99.1°C.
You probably know that the true or accepted value of the boiling point of pure water at these conditions is actually 100.0°C.

15. Determining Error
There is a difference between the accepted value, which is the correct value for the measurement based on reliable references, and the experimental value, the value measured in the lab.
The difference between the experimental value and the accepted value is called the error.
Error = experimental value – accepted value

16. Determining Error
Error can be positive or negative, depending on whether the experimental value is greater than or less than the accepted value.
For the boiling-point measurement, the error is:
99.1°C – 100°C = –0.9°C.

17. Determining Error Experimental value = 99.1°C Accepted value = 100.0°C
Often, it is useful to calculate the relative error, or percent error, in addition to the magnitude of the error.
The percent error of a measurement is the absolute value of the error divided by the accepted value, multiplied by 100%.
Solve Percent Error from the temp. problem.
Percent error =
error
accepted value
100% x

18. Checkpoint Are precise measurements always accurate?
No, measurements are precise if they are easily reproducible, but not accurate if they do not reflect the accepted value.

19. Reading and Recording Measurements
When using a piece of equipment, record the initial measurement that EVERYONE would agree with, AND THEN, give 1 degree of estimation.
“The general rule of thumb” is ….

20. Examples

21. Significant Figures
The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
Instruments differ in the number of significant figures that can be obtained from their use and thus in the precision of measurements.
More sig figs means more precise

22. Significant Figure Rules
Every nonzero digit in a reported measurement is assumed to be significant.
Each of these measurements has three significant figures:
24.7 meters
0.743 meter
714 meters

23. Significant Figure Rules
Zeros appearing between nonzero digits are significant.
Each of these measurements has four significant figures:
7003 meters
40.79 meters
1.503 meters

24. Significant Figure Rules
Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such place holding zeros.
Each of these measurements has only two significant figures:
meter = 7.1 x 10-3 meter
0.42 meter = 4.2 x 10-1 meter
meter = 9.9 x 10-5 meter

25. Significant Figure Rules
Zeros at the end of a number and to the right of a decimal point are always significant.
Each of these measurements has four significant figures:
43.00 meters
1.010 meters
9.000 meters

26. Significant Figure Rules
Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.
The zeros in these measurements are not significant:
300 meters (one significant figure)
7000 meters (one significant figure)
27,210 meters (four significant figures)

27. Significant Figure Rules
(continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear that these zeros are significant.
The zeros in this measurement are significant.
300. meters = 3.00 x 102 meters (3 significant figures)

28. Significant Figure Rules
There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact.
This measurement is a counted value, so it has an unlimited number of significant figures.
23 people in your classroom

29. Significant Figure Rules
(continued). The second situation involves exactly defined quantities such as those found within a system of measurement.
Each of these numbers has an unlimited number of significant figures.
60 min = 1 hr
100 cm = 1 m

30. Practice
Suppose that the winner of a 100-meter dash finishes the race in seconds. The runner in second place has a time of seconds. How many significant figures are in each measurement? Is one measurement more accurate than the other? Explain your answer.
There are three significant figures in 9.98 and four in Both measurements are equally accurate because both measure the actual time of the runner to the hundredth of a second.

31. How many sig figs are in each measurement?
40,506 mm
x 104 m
22 meter sticks m
98,000 m

32. Sig Figs in Calculations
In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.
The calculated value must be rounded to make it consistent with the measurements from which it was calculated.
Least Precise
3.5
More Precise
3.50

33. Sig Figs in Calculations - ROUNDING
To round a number, you must first decide how many significant figures the answer should have.
This decision depends on the given measurements and on the mathematical process used to arrive at the answer.
Once you know the number of significant figures your answer should have, round to that many digits, counting from the left.

34. Sig Figs in Calculations - ROUNDING
If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same.
Example: Round to 4 sig figs  3.457
If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1.
Example: Round to 3 sig figs  3.46

35. Practice
Round off each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation.
meters (four)
meter (two)
8792 meters (two)

36. Sig Figs in Calculations
Addition & Subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
12.52 meters meters meters
meters – meters

37. Sig Figs in Calculations
Multiplication & Division
In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures.
7.55 meters x 0.34 meter
2.10 meters x 0.70 meter
meters2 ÷ 8.4 meters
0.365 meter2 ÷ meter

38. 3.2 Units of Measurement What’s the forecast for tomorrow—hot or cold?
Will the high temperature tomorrow be 28°C, which is very warm? Or 28°F, which is very cold? Without the correct units, you can’t be sure.

39. SI Units (International System)
SI Base Units
Quantity
SI base unit
Symbol
Length
meter m
Mass
kilogram kg
Temperature
kelvin K
Time
second s
Amount of substance
mole
mol
Luminous intensity
candela cd
Electric current
ampere A
**Metric System – based on multiples of 10. Makes conversions easy!
 prefixes
What quantity does centi & milli define?
Think about century & millennium
Ex.
1m = 100cm = 1000mm
All metric units are based on multiples of 10. As a result, you can convert between units easily.

40. Commonly Used Metric Prefixes
**Refer to Table C in NYS Chemistry Reference Table
Commonly Used Metric Prefixes
Prefix
Symbol
Meaning
Factor
mega M
1 million times larger than the unit it precedes
106
kilo k
1000 times larger than the unit it precedes
103
deci d
10 times smaller than the unit it precedes
10-1
centi c
100 times smaller than the unit it precedes
10-2
milli m
1000 times smaller than the unit it precedes
10-3
micro μ
1 million times smaller than the unit it precedes
10-6
nano n
1 billion times smaller than the unit it precedes
10-9
pico p
1 trillion times smaller than the unit it precedes
10-12

41. Units of Volume What unit of volume are you most familiar with?
The liter is a NON SI unit of measurement!
The SI unit of volume is the amount of space occupied by a cube that is 10 cm along each edge.
This volume is a cubic centimeter (cm3).
(10 cm × 10 cm × 10 cm = 1000 cm3 = 1 L).
If 1000 mL = 1L
Then 1000 cm3 = 1000 mL
Thus 1 cm3 = 1 mL
1 cm3 = 1mL is a NEED to know for IB Chem

42. Units of Volume – common quantities
The volume of 20 drops of liquid from a medicine dropper is ≈ 1 mL.
A sugar cube has a volume of 1 cm3. 1 mL is the same as 1 cm3.

43. Units of Mass – common quantities
The mass of $1 is ≈ 1 g
The mass of a 10 grains of salt is ≈ 1 mg
The mass of a textbook is ≈ 1 kg

44. Units of Mass How does weight differ from mass?
Weight is a force that measures the pull on a given mass by gravity.
Mass is a measure of the quantity of matter.
The weight of an object can change with its location.
An astronaut in orbit is weightless, but not massless.

45. Units of Energy
The capacity to do work or to produce heat is called energy.
The SI unit of energy is the joule (J), named after the English physicist James Prescott Joule (1818–1889).
A common non-SI unit of energy is the calorie.
One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.

46. Units of Temperature Celsius Fahrenheit Kelvin
Temperature is a measure of how hot or cold an object is.
Almost all substances expand with an increase in temperature and contract as the temperature decreases.
These properties are the basis for the common bulb thermometer.
Thermometers are used to measure temperature. a) A liquid-in-glass thermometer contains alcohol or mineral spirits. b) A dial thermometer contains a coiled bimetallic strip. c) A Galileo thermometer contains several glass bulbs that are calibrated to sink or float depending on the temperature. The Galileo thermometer shown uses the Fahrenheit scale, which sets the freezing point of water at 32°F and the boiling point of water at 212°F.

47. Heat Transfer
Lower temperature
Higher
temperature
When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature.

48. Units of Temperature
Celsius
Kelvin
Fahrenheit
Reference Points

49. Units of Temperature
The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to  °C.

50. Units of Temperature
Because one degree on the Celsius scale is equivalent to one Kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.

51. Practice
Normal human body temperature is 37C. What is that temperatures in kelvins?

52. Practice
Liquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius?

53. SOME important units that you need for Chemistry are organized on your NYS Chemistry Reference Table

54. Thought Provoking
Which is heavier, a pound of lead or a pound of feathers?

55. Thought Provoking
Why can boats made of steel float on water when a bar of steel sinks?

56. Density Common unit: g/cm3 SI unit: kg/m3
The relationship between an object’s mass and its volume tells you whether it will float or sink.
Density is the ratio of the mass of an object to its volume.

57. Density
Which substance would float in water?
Each of these 10-g samples has a different volume because the densities vary.
- A 10-g sample of pure water has less volume than 10 g of lithium, but more volume than 10 g of lead. The faces of the cubes are shown actual size. Inferring Which substance has the highest ratio of mass to volume? Lead
Ask students: What would be the volume of a 10-g sphere of each of the substances shown? The volumes would all remain the same because each sample is still Lithium, water, and lead, and the masses of each have not changed. Just because you change the “shape” does not mean that the mass or volume has changed and thus the density hasn’t either.
This is your seg-way into the next slide: The volumes of each of these substances vary because they have different densities.

58. Density What is the substance made of?
Density is an intensive property that depends only on the composition of a substance, not the size of the sample.
What is the substance made of?
Corn Oil – g/cm3
Water – 1.00 g/cm3
Corn Syrup – 1.35 – 1.38 g/cm3
Corn oil
Water
Corn syrup

59. Densities of Some Common Materials
Solids and Liquids
Gases
Material
Density at 20°C (g/cm3)
Density at 20°C (g/L)
Gold
19.3
Chlorine
2.95
Mercury
13.6
Carbon dioxide
1.83
Lead
11.3
Argon
1.66
Aluminum
2.70
Oxygen
1.33
Table sugar
1.59
Air
1.20
Corn syrup
1.35–1.38
Nitrogen
1.17
Water (4°C)
1.000
Neon
0.84
Corn oil
0.922
Ammonia
0.718
Ice (0°C)
0.917
Methane
0.665
Ethanol
0.789
Helium
0.166
Gasoline
0.66–0.69
Hydrogen
0.084

60. Density ?
Temperature
Density
What happens to the density of a substance as its temperature increases?
The volume of most substances increases as the temperature increases, while the mass remains the same.
Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases.
Water is an important exception.
 Under what temperature conditions does H20 density decrease?

61. Practice
A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?

62. Practice
A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612g. Calculate the density. Is the metal aluminum?
Go back a couple slides to see that aluminums density is 2.70 g/cm3

63. Ask students: What are we looking at. Current Currency Exchange Rates
Ask students: What are we looking at? Current Currency Exchange Rates. How would you decide which amount of money would be worth more – 75 euros or 75 British pounds? Convert these values to a familiar currency – US dollars

64. Can you think of any other examples in which quantities can be expressed in several different ways?

65. Conversion Factors Consider the conversion units of distance:
These are all different ways to express the same length.
In addition, conversion factors within a system of measurement are defined quantities or exact quantities.
Unlimited significant figures – DO NOT affect the rounding of a calculated answers
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters

66. Conversion Factors
1 meter
100 centimeters
Larger unit
Smaller unit
100 1 m cm
Smaller number
Larger number
The smaller number is part of the measurement with the larger unit.
The larger number is part of the measurement with the smaller unit.

67. Conversion Factors
When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.
For example, even though the numbers in the measurements 1 kg (kilogram) and 1000 g differ, both measurements represent the same mass.
1000 g
1 kg
and

68. Some instruments multiple scales on them like these food scales.

69. Dimensional Analysis
Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.
Example: How many seconds are in a workday that lasts exactly eight hours?

70. Practice
The directions for an experiment ask each student to measure 1.84 g of copper wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?
In chemistry, as in everyday life, you often need to express a measurement in a unit different from the one given or measured initially.

71. BASE UNIT

72. Practice
Express 750 dg in grams.

73. Practice
What is the volume of a pure silver coin that has a mass of 14 g? The density of silver is 10.5 g/cm3.

74. Practice
The diameter of a sewing needle is cm. What is the diameter in micrometers?

75. Practice
The density of manganese (Mn), a metal, is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3?