2. Chapter 1: Matter and Measurements2

3. A gas pump measures the amount of gasoline delivered.

4. Measurement Quantitative Observation
Comparison Based on an Accepted Scale
e.g. Meter Stick
Has 2 Parts – the Number and the Unit
Number Tells Comparison
Unit Tells Scale 2

5. When describing very small distances, such as the diameter of a swine flu virus, it is convenient to use scientific notation.

6. Scientific Notation
Technique Used to Express Very Large or Very Small Numbers
Based on Powers of 10
To Compare Numbers Written in Scientific Notation
First Compare Exponents of 10
Then Compare Numbers 3

7. Writing Numbers in Scientific Notation
Locate the Decimal Point
Move the decimal point to the right of the non-zero digit in the largest place
The new number is now between 1 and 10
Multiply the new number by 10n
where n is the number of places you moved the decimal point
Determine the sign on the exponent n
If the decimal point was moved left, n is +
If the decimal point was moved right, n is –
If the decimal point was not moved, n is 0 4

8. Writing Numbers in Standard Form
Determine the sign of n of 10n
If n is + the decimal point will move to the right
If n is – the decimal point will move to the left
Determine the value of the exponent of 10
Tells the number of places to move the decimal point
Move the decimal point and rewrite the number 5

9. Related Units in the Metric System
All units in the metric system are related to the fundamental unit by a power of 10
The power of 10 is indicated by a prefix
The prefixes are always the same, regardless of the fundamental unit 6

10. Length SI unit = meter (m) About 3½ inches longer than a yard
1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light
Commonly use centimeters (cm)
1 m = 100 cm
1 cm = 0.01 m = 10 mm
1 inch = 2.54 cm (exactly) 7

11. Volume
Measure of the amount of three-dimensional space occupied by a substance
SI unit = cubic meter (m3)
Commonly measure solid volume in cubic centimeters (cm3)
1 m3 = 106 cm3
1 cm3 = 10-6 m3 = m3
Commonly measure liquid or gas volume in milliliters (mL)
1 L is slightly larger than 1 quart
1 L = 1 dL3 = 1000 mL = 103 mL
1 mL = L = 10-3 L
1 mL = 1 cm3 8

12. Mass Measure of the amount of matter present in an object
SI unit = kilogram (kg)
Commonly measure mass in grams (g) or milligrams (mg)
1 kg = pounds, 1 lbs.. = g
1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg
1 g = kg = 10-3 kg, 1 mg = g = 10-3 g 9

17. Figure 2.1: Comparison of English and metric units for length on a ruler.

19. Figure 2.2: The largest drawing represents a cube that has 1 m in length and a volume of 1 m3. The middle-size cube has sides 1 dm in length and a volume of 1 dm3. The smalles cube has sides 1 cm in length and a volume of 1cm3.

20. Source: Glenn Izett/U.S. Geological Survey.

21. Uncertainty in Measured Numbers
A measurement always has some amount of uncertainty
Uncertainty comes from limitations of the techniques used for comparison
To understand how reliable a measurement is, we need to understand the limitations of the measurement 10

22. Figure 2.3: A 100-mL graduated cylinder.

23. Figure 2.4: An electronic analytical balance used in chemistry labs.

24. A student performing a titration in the laboratory.

25. Reporting Measurements
To indicate the uncertainty of a single measurement scientists use a system called significant figures
The last digit written in a measurement is the number that is considered to be uncertain
Unless stated otherwise, the uncertainty in the last digit is ±1 11

26. Figure 2.5: Measuring a pin.

27. Rules for Counting Significant Figures
Nonzero integers are always significant
Zeros
Leading zeros never count as significant figures
Captive zeros are always significant
Trailing zeros are significant if the number has a decimal point
Exact numbers have an unlimited number of significant figures 12

28. Rules for Rounding Off If the digit to be removed
is less than 5, the preceding digit stays the same
is equal to or greater than 5, the preceding digit is increased by 1
In a series of calculations, carry the extra digits to the final result and then round off
Don’t forget to add place-holding zeros if necessary to keep value the same!! 13

29. Exact Numbers Exact Numbers are numbers known with certainty
Unlimited number of significant figures
They are either
counting numbers
number of sides on a square
or defined
100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm
1 kg = 1000 g, 1 LB = 16 oz
1000 mL = 1 L; 1 gal = 4 qts.
1 minute = 60 seconds 14

30. Calculations with Significant Figures
Calculators/computers do not know about significant figures!!!
Exact numbers do not affect the number of significant figures in an answer
Answers to calculations must be rounded to the proper number of significant figures
round at the end of the calculation 15

31. Multiplication/Division with Significant Figures
Result has the same number of significant figures as the measurement with the smallest number of significant figures
Count the number of significant figures in each measurement
Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures
4.5 cm x cm = cm2
2 sig figs 3 sig figs sig figs 16

32. Adding/Subtracting Numbers with Significant Figures
Result is limited by the number with the smallest number of significant decimal places
Find last significant figure in each measurement
Find which one is “left-most”
Round answer to the same decimal place
450 mL mL = mL
precise to 10’s place precise to 0.1’s place precise to 10’s place 17

33. Problem Solving and Dimensional Analysis
Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another
Conversion factors are relationships between two units
May be exact or measured
Both parts of the conversion factor should have the same number of significant figures
Conversion factors generated from equivalence statements
e.g. 1 inch = 2.54 cm can give or 18

34. Problem Solving and Dimensional Analysis
Arrange conversion factors so starting unit cancels
Arrange conversion factor so starting unit is on the bottom of the conversion factor
May string conversion factors 19

35. Converting One Unit to Another
Find the relationship(s) between the starting and goal units. Write an equivalence statement for each relationship.
Write a conversion factor for each equivalence statement.
Arrange the conversion factor(s) to cancel starting unit and result in goal unit. 20

36. Converting One Unit to Another
Check that the units cancel properly
Multiply and Divide the numbers to give the answer with the proper unit.
Check your significant figures
Check that your answer makes sense! 21

37. Temperature Scales Fahrenheit Scale, °F Celsius Scale, °C
Water’s freezing point = 32°F, boiling point = 212°F
Celsius Scale, °C
Temperature unit larger than the Fahrenheit
Water’s freezing point = 0°C, boiling point = 100°C
Kelvin Scale, K
Temperature unit same size as Celsius
Water’s freezing point = 273 K, boiling point = 373 K 22

38. Figure 2.7: The three major temperature scales.

39. Figure 2.6: Thermometers based on the three temperature scales in (a) ice water and (b) boiling water.

40. Figure 2.8: Converting 70. °C to units measured on the Kelvin scale.

41. Figure 2.9: Comparison of the Celsius and Fahrenheit scales.

42. Density
Density is a property of matter representing the mass per unit volume
For equal volumes, denser object has larger mass
For equal masses, denser object has small volume
Solids = g/cm3
1 cm3 = 1 mL
Liquids = g/mL
Gases = g/L
Volume of a solid can be determined by water displacement
Density : solids > liquids >>> gases
In a heterogeneous mixture, denser object sinks 23

43. Figure 2. 10: (a) Tank of water
Figure 2.10: (a) Tank of water. (b) Person submerged in the tank, raising the level of the water.

44. Spherical droplets of mercury, a very dense liquid.

45. Using Density in Calculations24

47. Figure 2.11: A hydrometer being used to determine the density of the antifreeze solution in a car’s radiator.