review chapter measurement and calculations in chemistry
TRANSCRIPT
Section R.1
Units of Measurement
Return to TOC
Copyright © Cengage Learning. All rights reserved
• Quantitative observation consisting of two parts. number scale (unit)
Nature of Measurement
Measurement
• Examples 20 grams 6.63 × 10–34 joule·seconds
Section R.1
Units of Measurement
Return to TOC
Copyright © Cengage Learning. All rights reserved
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
Section R.1
Units of Measurement
Return to TOC
Copyright © Cengage Learning. All rights reserved
• Prefixes are used to change the size of the unit.
Prefixes Used in the SI System
Section R.1
Units of Measurement
Return to TOC
Copyright © Cengage Learning. All rights reserved
Prefixes Used in the SI System
Section R.2
Uncertainty in Measurement
6
Return to TOC
Copyright © Cengage Learning. All rights reserved
• 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).
Section R.2
Uncertainty in Measurement
7
Return to TOC
Copyright © Cengage Learning. All rights reserved
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 20.15 mL. Certain digits: 20.15 Uncertain digit: 20.15
Section R.2
Uncertainty in Measurement
8
Return to TOC
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
Section R.2
Uncertainty in Measurement
9
Return to TOC
1) 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
Section R.2
Uncertainty in Measurement
10
Return to TOC
2) 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)
3) Precision & Accuracy
reproducibility
confidence of nearness to the truth
Section R.2
Uncertainty in Measurement
11
Return to TOC
Copyright © Cengage Learning. All rights reserved
Precision and Accuracy
Section R.3
Significant Figures and Calculations
Return to TOC
12Copyright © Cengage Learning. All rights reserved
1. Nonzero integers always count as significant figures. 3456 has 4 sig figs (significant figures).
Rules for Counting Significant Figures
Section R.3
Significant Figures and Calculations
Return to TOC
13Copyright © Cengage Learning. All rights reserved
• There are three classes of zeros.a. zeros that precede all the nonzero digits: do not count.
0.048 has 2 sig figs.
Rules for Counting Significant Figures
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.
Section R.3
Significant Figures and Calculations
Return to TOC
14Copyright © Cengage Learning. All rights reserved
3. Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly. 9 pencils (obtained by counting).
Rules for Counting Significant Figures
Section R.3
Significant Figures and Calculations
Return to TOC
15Copyright © Cengage Learning. All rights reserved
• Example 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.
Exponential Notation
Section R.3
Significant Figures and Calculations
Return to TOC
16Copyright © Cengage Learning. All rights reserved
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 = 7.381 7.4
Significant Figures in Mathematical Operations
Section R.3
Significant Figures and Calculations
Return to TOC
17Copyright © Cengage Learning. All rights reserved
2. For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.
Significant Figures in Mathematical Operations
Corrected
23.445
7.83
31.2831.275
Section R.3
Significant Figures and Calculations
Return to TOC
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
Section R.3
Significant Figures and Calculations
Return to TOC
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
Section R.3
Significant Figures and Calculations
Return to TOC
20
[H+]=2.010-3
pH=-log(2.010-3) = -(-3+0.30)=2.70
antilogarithm of 0.072 1.18
logarithm of 12.1 1.083
log 339 = 2.5301997… = 2.530
antilog (-3.42) = 10-3.42 = 0.0003802 = 3.8x10-4
Logarithms and Antilogarithms
Section R.3
Significant Figures and Calculations
Return to TOC
21Copyright © Cengage Learning. All rights reserved
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?