1. Zumdahl • Zumdahl • DeCoste
World of
CHEMISTRY

2. Measurements and Calculations
Chapter 5
Measurements and Calculations

3. 5.1 Scientific Notation
Scientific nation is a method for making very large or very small numbers core compact and easier to write.
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4. Scientific notation simply expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.
e.g. 93,000,000 = 9.3 X 107
*whenever the decimal point is moved to the left, the exponent of 10 is positive.
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5. Using scientific notation with numbers smaller than 1:
= 1.0 x 10-2
*whenever the exponent is moved to the right the exponent is negative.
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6. Practice Examples: 5.1 & 5.2 pg. 115/116
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7. 5.2 Units
The units part of a measurement tells us what scale or standard is being used to represent the results of the measurement.
International System (SI): The Si units are based on the metric system and units derived from the metric system
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8. Some Fundamental SI Units
Table 5.1 Pg. 117
Physical Quantity
Name of the Unit
Abbreviation
Mass
Kilogram Kg
Length
Meter M
Time
Second s
Temperature
Kelvin K
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9. Table 5.2
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10. Daily Planner Review 5.1 – 5.2 Chapter questions – to be collected 1-2
3 – 10 (black)
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11. 5.3 Measurements of Length, Volume, and Mass
SI Unit for length = Meter
1 meter = inches
The metric system is set up in units of ten.
The metric system can be expressed by powers of 10
FYI 1 inch = 2.54 centimeters
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12. Table 5.3
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13. Figure 5.1: Comparison of English and metric units.
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14. Volume
Volume is the amount of three-dimensional shape occupied by a substance.
SI Unit of Volume = cube – measured 1 meter on each side (13)
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15. Figure 5.2: Cube representations.
1m X 1m X 1m = 1m3 Or
1 cubic meter
1dm3 = 1L
1 cm3 = 1 mL
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16. Figure 5.3: A 100 mL graduated cylinder.
Note the measurements
on this graduated cylinder
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17. Mass Mass is the quantity of matter present in an object.
SI unit of mass = kilogram
We determine mass using a balance
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18. Table 5.5 The most commonly used metric units for mass
SYMBOL
GRAM EQUIVALENT
KILOGAM kg
1000g = 10g 3 =1 kg
GRAM g
1 g
MILLIGRAM mg
0.001g = 10-3 g = 1 mg

19. Sections 5.1 – 5.3
1. What is the difference between a qualitative observation and a quantitative observation? 2. When you are writing numbers using scientific notation, very large numbers have ________exponents and very small numbers have ______exponents.
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20. 3. Change the following to scientific notation:
8,475,000
1000
4. Why is a unit a necessary part of a measurement
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21. 5.4 Uncertainty in Measurements
When we measure, there is always a level of interpretation, requiring some form of an estimate:
Every measurement has some degree of uncertainty
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22. Figure 5.5: Measuring a pin.
a)The pin appears
to be between
2.8 & 2.9
b) We imagine the
distance between
2.8 – 2. 9 in units
of 10 and estimate
our answer

23. Certainty and uncertainty
Person
Possible interpretation 1
2.85 cm 2
2.84 cm 3
2.86 cm 4
2.85cm 5
Note: The first two numbers are the same they are the CERTAIN
measurement. The last number , the estimate, is the UNCERTAIN
measurement. When we measure always record the certain
number + the first uncertain number.
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24. Daily Planner Chapter questions pg. 149 (to be collected)
Sections 5.3 and 5.4, # 13, 14, 15, 17, 19, 20 & 21
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25. 5.5 Significant Figure
The numbers recorded in a measurement (all of the certain numbers plus the first uncertain number) are termed
SIGNIFICANT FIGURES (SIG FIGS)
The number of sig figs is determine by he measuring device
e.g kg = /- .01kg
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26. Significant Figures Rules for counting Significant Figures
1. Nonzero Integers ALWAYS counts as significant figures.
2. Zeros – there are three classes of zeros
a) Leading Zeros = Zeros that precede all of the nonzero
They never count as significant
The example above only has two sig figs = 2 & 5
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27. Zeros – the three classes cont.,
b). Captive zeros are zeros that fall between nonzero digits.
They ALWAYS count as sig figs.
1.008 has four sig. figs
c). Trailing Zeros are zeros at the right end of a number. They are significant only if the number is written with a decimal point.
100 = one sig. fig.
100. = three sig. fig.
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28. 3. Exact Numbers – numbers that are counted: 3 apples, 2 molecules Exact numbers are assumed to have an unlimited amount of sig. figs. 1 inch = 2.54 cm
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29. Numbers Written in Scientific Notation
100 = 1.00 X 102 = 3 sig. figs.
= 6.0 X = 2 sig figs.
Example 5.3 pg 125
A sample of orange juice containing
g of vitamin C:
1.08 X 10-2 = 3 sig. figs
Self Check Exercise 5.2
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30. Rounding Off Numbers If the digit to be removed
Is less than five, the preceding digit stays the same = 1.3
Is ≥ 5, then the preceding digit is increased by one: = 1.4
In a series of calculations carry the extra digits through to the final result then round off.
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31. Rounding significant figures
If only two numbers are significant than we look at only the first number to the right of the significant figures.
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32. Determining Sig. Figs. In Calculations
Multiplication and division – the number of sig figs in the result is the same as the smallest number of sig figs. in the measurement.
4.56 X 1.4 = → 6.4
Note: for multiplication sig. figs are counted
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33. Addition and Subtraction – limiting term is the one with the smallest number of decimal places
For +/- decimal
places are counted
1.013
→ 31.1
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34. Practice
Example 5.4 & 5.5 pg Self Check 5.3 pg. 129 Great website for practice
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35. Focus Question 5.4 – 5.5
Why are all measurements uncertain to some extent?
Mark the zeros that are sig figs:
0.060
How many sig fig. are in each example?
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36. Without doing the calculations, how many sig figs should be in each of the following results? – x (4.2 X 10-5) X 3.74 ÷ –
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37. 5.6 Problem Solving and Dimensional Analysis
How do we convert one unit of measurement to another?
Conversion Factor: a ration of the two parts of the statement that relates the two units.
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38. Converting from one unit to another
Need to know an equivalence statement
(12 inched = 1 ft; 2.54 cm = 1 inch)
Arrange your equation so the units cancel out. Leaving you with the unit you are trying to solve for.
Multiply
Check that you have the right number of sig figs.
Does your answer make sense?
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39. How to use Conversion Factors
Unit 1 x Conversion factor = Unit 2 Example: 2.85 cm = _____inches 2.54 cm = 1 inch 2.85 cm X 1 inch = 1.12 inched 2.54cm
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40. Practice Pg. 132 – 134 Examples 5.6, 5.7 Self check 5.4, 5.5
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41. Daily Planner Homework: to be collected next class
Chapter questions pg 150 #35 – 37; 39 – 43 (black).
Significant Figures Worksheet
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42. 5.7 Temperature Conversion: An Approach to Problem Solving
There are three scales to measure temperature:
Fahrenheit Scale (F)
Celsius Scale (C)
Kelvin Scale or absolute scale (K)
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43. Figure 5.6: The three major temperature scales.
Note: zero points
are different.
The number of
degree units are
different.
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44. Figure 5.7: Converting 70 degrees Celsius to Kelvin units.
The size of each degree unit
on the Kelvin and Celsius
scale are the same.
The zero points are different
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45. Figure 5.8: Comparison of the Celsius and Fahrenheit scales.
Fahrenheit degrees are
smaller than Celsius
degrees.
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46. Concerting between the Kelvin and Celsius Scale
100° C = 373K 0° C = 273K -18° C +273 = 255K In each scenario above We needed to add 273 .
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47. Formuls T°C + 273 = TK TK - 273 = T°C TK - T°C = 273
Examples 5.8, 5.9 and self check 5.6 pg
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48. Converting Between Fahrenheit and Celsius
T°F = 1.80 (T°C) + 32 Examples 5.10, and self check 5.7 & 5.8 pgs
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49. Temperature Conversion Formulas
Celsius to Kelvin
T°C = TK
Celsius to Fahrenheit
T°F = 1.80 (T°C) + 32
Kelvin to Celsius
TK = T°C
Fahrenheit to Celsius
T°C = (T°F – 32) /1.80
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50. 5.8 Density
Density is the amount of matter present in a given volume of a substance.
Density = Mass
Volume
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51. The volume of a solid object is often determined indirectly by submerging it in water and measuring the volume of water displaced.
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52. Figure 5.9: Tank of water.
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53. Figure 5.9: Person submerged in the tank.
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54. Focus Questions 5.6 – 5.8 What is an equivalence statement?
An equation that shows two measurements stand for the same thing
How many conversion factors can be created from one equivalence statement? 2
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55. 3. How can you decide which conversion factor to choose in a problem
3. How can you decide which conversion factor to choose in a problem? the proper conversion factor cancels out the units to be discarded leaving you with the desired unit as your result. 4. Write the conversion factors for these problems. 37 cm X ___________= ? in 4.2 qts X __________ -= ? L 2.2 kg X ___________ = ? Pounds 3.5 ml X ___________= ?m
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56. When you make a temperature conversion, how many significant figures should be in the converted temperature?
The conversion will be based upon the degree of precision of the instrument used.
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57. Practice Problems Example 5.14; 5.15 and self check 5.9 pgs. 144- 145
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58. Daily Planner
Homework : to be collected next class Chapter problems: pg. 150 – – 46; 47 – 50 (blk); 51 – 55; 58, 61
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