1. Measurements and Calculations
Chapter 2
Chemistry Chapter 2

2. Scientific Method A logical approach to solving problems by:
Observing and collecting data
Formulating hypotheses
Testing hypotheses, and
Formulating theories that are supported by data
Chemistry Chapter 2

3. Observing Using the five senses to gather information
Often involves making measurements and collecting data
Chemistry Chapter 2

4. Qualitative data Descriptive Not numerical Example – the sky is blue
Chemistry Chapter 2

5. Quantitative data Numerical Measurable or countable
Example – the temperature of the water went up 1 °C
Chemistry Chapter 2

6. System A specific portion of matter in a given region of space
Has been selected for study during an experiment or observation
Must be defined by the experimenter
Chemistry Chapter 2

7. Formulating hypotheses
Hypothesis – testable statement
Generalizations about data
Basis for making predictions and designing experiments
Usually if-then statements
Chemistry Chapter 2

8. Testing hypotheses Doing experiments
You must be ready to reject a hypothesis that is proven wrong
Chemistry Chapter 2

9. Theorizing
Model – an explanation of how phenomena occur and how data or events are related
May include a physical object or drawing
May be visual, verbal, or mathematical
Theory – a broad generalization that explains a body of facts or phenomena
Must predict to be successful
Chemistry Chapter 2

10. Discuss
Section Review
Page 31
Chemistry Chapter 2

11. Quantity Something that has magnitude, size, or amount.
Chemistry Chapter 2

12. SI Measurement Le Système International d’Unités Metric system
Seven base units – the rest are derived
Chemistry Chapter 2

13. Standards of measurement
Objects or phenomena that are of constant value, easy to preserve and reproduce, and practical in size.
Note – ten thousand is written , not 10,000. Some countries use the comma as a decimal point.
Chemistry Chapter 2

14. Mass Measure of the quantity of matter Kilogram is base unit kg
Your textbook has a mass of about 1 kg
A paper clip has a mass of about 1 g, or 1/1000 of a kg
Chemistry Chapter 2

15. Mass vs. weight
Weight is the measure of the gravitational pull on matter.
The weight of an object on the moon is 1/6 its weight on earth, but its mass is the same.
Chemistry Chapter 2

16. Length Meter m About 39 inches – width of a doorway 1 km = 1000 m
1 m = 100 cm
Chemistry Chapter 2

17. Other base units Time – seconds – s Temperature – kelvin – K
Amount of substance – mole – mol
Electric current – ampere – A
Luminous intensity – candela – cd
Chemistry Chapter 2

18. Prefixes Used to indicate multiples of 10 See table 2-2 on page 35
Chemistry Chapter 2

19. Derived SI units Combinations of base units Can also use prefixes
Chemistry Chapter 2

20. Volume Amount of space occupied by an object.
SI unit is cubic meters, or m3
We often use cubic centimeters, or cm3
Important – 1 cm3 = 1 mL
1 m3 = cm3
We also use the liter, or L
Equal to 1 cubic dm, or dm3
There are 1000 mL in 1 L
Chemistry Chapter 2

21. Density
The ratio of mass to volume
Chemistry Chapter 2

22. Density SI unit is kg/m3 We often use g/mL or g/cm3 in Chemistry
g/L or kg/m3 might be used for gases
Chemistry Chapter 2

23. Conversion factors Used to convert from one unit to another
A ratio derived from equality
Chemistry Chapter 2

24. Example
How many seconds are in 1 day?
Chemistry Chapter 2

25. Example
How many centigrams are there in 6.25 kg?
Chemistry Chapter 2

26. Units When doing conversions, keep track of your units.
They should cancel out to get units you want at the end.
Chemistry Chapter 2

27. Examples using table Convert 10 cm to m. Convert 25 mL to L.
Convert 50 mg to kg.
Convert 33 cm3 to mm3.
Chemistry Chapter 2

28. Discuss
Section Review
Page 42
Chemistry Chapter 2

29. Accuracy vs. Precision
Accuracy – closeness to correct or accepted value
Precision – closeness of a set of measurements of the same quantity made the same way
See page 44, figure 2-3
Chemistry Chapter 2

30. Percent error Finds accuracy of a single value or an average value.
See sample problem 2-3 on page 45
Chemistry Chapter 2

31. Reading instruments Estimate the last digit.
Example – a ruler is marked to a tenth of a centimeter.
Your measurement should be to the nearest hundredth of a centimeter.
Example – a thermometer is marked to the nearest degree.
Your measurement should be to the nearest tenth of a degree
Chemistry Chapter 2

32. Significant Figures
All the digits known in a measurement, plus one that is somewhat uncertain.
All nonzero digits are significant
Zeros are governed by four rules
Zeros between nonzero digits are significant
203 has 3 sig figs
has 5 sig figs
Chemistry Chapter 2

33. Significant Figures
Zeros in front of all nonzero digits are not significant
has 2 sig figs
has 1 sig fig
Zeros at the end of a number and after the decimal point are significant.
has 5 sig figs
has 3 sig figs
Chemistry Chapter 2

34. Significant Figures
Zeros at the end of a number but before the decimal point may or may not be significant.
If a zero is just a placeholder, it is not significant.
If it has been measured, it is significant. To show all zeros are significant, use a decimal point.
To show some are, use scientific notation (tomorrow)
2000 has 1 sig fig
2000. has 4 sig figs
Chemistry Chapter 2

35. How many sig figs?
2.5
2 sig figs
2.50
3 sig figs
250
2.50 x 102
250.0
4 sig figs
0.0025
2 sig figs
3 sig figs
1-2 min
modeling
Chemistry Chapter 2

36. Rounding If the next digit is less than five, round down.
3.044 → 3.04
If the next digit is more than five, round up.
3.046 → 3.05
If the next digit is a five and there are nonzero digits after it, round up
→ 3.05
If the next digit is a five and not followed by nonzero digits round to the even number
3.045 → 3.04
3.035 → 3.04
Chemistry Chapter 2

37. Adding or subtracting with sig figs
The answer must have the same number of digits after the decimal point as there are in the measurement with the fewest digits after the decimal point.
Chemistry Chapter 2

38. Example
Since only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Round the answer to 1.253
1 min
modeling
Chemistry Chapter 2

39. Multiplication and Division
The result should have the same number of significant figures as the least number of significant figures in any factor.
1 min
instruction
Chemistry Chapter 2

40. Example
Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would round our answer to 1.6
1 min
modeling
Chemistry Chapter 2

41. Conversion factors
Are not considered when finding the number of significant figures.
Are exact
Chemistry Chapter 2

42. Discuss
How do you round a number that ends in a five if you are rounding to the place before the five?
What is the difference between accuracy and precision?
How many significant figures are in the answer when you multiply? When you subtract?
Chemistry Chapter 2

43. Scientific Notation
Useful when writing very small or very large numbers
m = 6.96 x 108 m
km = 4 x 106 km
0.012 kg = 1.2 x 10-2 kg
s = 5.67 x s
Chemistry Chapter 2

44. Scientific notation
The mantissa (number in front) is greater than or equal to 1 but less than 10.
Only significant figures are shown.
All digits shown are significant figures.
2000 has 1 sig fig
2000. has 4 sig figs
2.0 x 103 has 2 sig figs
2.00 x 103 has 3 sig figs
Chemistry Chapter 2

45. Multiplying in Scientific Notation
Multiply the mantissas.
Multiply the units.
Add the exponents.
Chemistry Chapter 2

46. Example
Chemistry Chapter 2

47. Dividing in scientific notation
Divide the mantissas.
Divide the units
Subtract the exponents.
Chemistry Chapter 2

48. Example
Chemistry Chapter 2

49. Addition and subtraction
If the exponents (and units) are the same, you can simply add or subtract the mantissas and keep the exponents and units the same.
If the exponents are different, do it on your calculator.
Your book shows you how, but most people don’t like to do it that way.
If the units are different, you can’t add or subtract.
Chemistry Chapter 2

50. Direct proportions
Two quantities are directly proportional if dividing one by the other gives a constant.
Graph is a straight line that passes through the origin
General forms of the equation:
Chemistry Chapter 2

51. Inverse proportions
Two quantities are inversely proportional if their product is constant.
Graph is a hyperbola (see page 57)
General forms of the equation:
Chemistry Chapter 2