1. Measurement and Calculations in Chemistry
Review Chapter
Measurement and Calculations in Chemistry

2. Quantitative observation consisting of two parts. number scale (unit)
Nature of Measurement
Measurement
Quantitative observation consisting of two parts.
number
scale (unit)
Examples
20 grams
6.63 × 10–34 joule·seconds
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3. The Fundamental SI Units
Physical Quantity
Name of Unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
kelvin K
Electric current
ampere A
Amount of substance
mole
mol
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4. Prefixes Used in the SI System
Prefixes are used to change the size of the unit.
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5. Prefixes Used in the SI System
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6. A digit that must be estimated is called uncertain.
A measurement always has some degree of uncertainty.
Record the certain digits and the first uncertain digit (the estimated number).
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7. Measurement of Volume Using a Buret
The volume is read at the bottom of the liquid curve (meniscus).
Meniscus of the liquid occurs at about mL.
Certain digits: 20.15
Uncertain digit: 20.15
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8. Types of Errors
Every measurement has some uncertainty  experimental error.
Experimental error is classified as either systematic or random.
Maximum error v.s. time required

9. = Determinate error = consistent error
Systematic error
= Determinate error = consistent error
- errors arise: instrument, method, & person
- can be discovered & corrected
- from fixed cause, & is either high (+) or low (-) every time.
- ways to detect systematic error:
examples (a) pH meter (b) buret

10. Random error = Indeterminate error
Is always present & cannot be corrected
Has an equal chance of being (+) or (-).
(a) people reading the scale
(b) random electrical noise in an instrument.
(c) pH of blood (actual variation: time, or part)
Precision & Accuracy
reproducibility
confidence of nearness to the truth

11. Precision and Accuracy
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12. Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures.
3456 has 4 sig figs (significant figures).
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13. Rules for Counting Significant Figures
There are three classes of zeros.
a. zeros that precede all the nonzero digits: do not count.
0.048 has 2 sig figs.
b. zeros between nonzero digits: always count.
16.07 has 4 sig figs.
c. zeros at the right end of the number: significant only if the number contains a decimal point.
9.300 has 4 sig figs.
150 has 2 sig figs.
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14. Rules for Counting Significant Figures
3. Exact numbers have an infinite number of significant figures.
1 inch = 2.54 cm, exactly.
9 pencils (obtained by counting).
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15. Example Two Advantages Exponential Notation 300. written as 3.00 × 102
Contains three significant figures.
Two Advantages
Number of significant figures can be easily indicated.
Fewer zeros are needed to write a very large or very small number.
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16. Significant Figures in Mathematical Operations
1. For multiplication or division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation.
1.342 × 5.5 =  7.4
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17. Significant Figures in Mathematical Operations
2. For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.
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18. Logarithms and Antilogarithms
The base 10 logarithm of n is the number a, whose value is such that n=10a:
The number n is said to the antilogarithm of a.
P.64

19. In converting a logarithm to its antilogarithm, the number of significant figures in the antilogarithm should equal the number of digits in the mantissa.
P.65

20. Logarithms and Antilogarithms
pH=-log(2.010-3) = -( )=2.70
antilogarithm of  1.18
logarithm of 12.1  1.083
log 339 = … = 2.530
antilog (-3.42) = = = 3.8x10-4

21. Concept Check
You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).
How would you write the number describing the total volume?
3.1 mL
What limits the precision of the total volume?
The total volume is 3.1 mL. The first graduated cylinder limits the precision of the total volume with a volume of 2.8 mL. The second graduated cylinder has a volume of 0.28 mL. Therefore, the final volume must be 3.1 mL since the first volume is limited to the tenths place.
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22. The Organization of Matter
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