Measurement and Calculations in Chemistry Review Chapter Measurement and Calculations in Chemistry
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 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 Copyright © Cengage Learning. All rights reserved
Prefixes Used in the SI System Prefixes are used to change the size of the unit. Copyright © Cengage Learning. All rights reserved
Prefixes Used in the SI System 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). 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 Copyright © Cengage Learning. All rights reserved
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
= 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
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
Precision and Accuracy Copyright © Cengage Learning. All rights reserved
Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 3456 has 4 sig figs (significant figures). Copyright © Cengage Learning. All rights reserved
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. Copyright © Cengage Learning. All rights reserved
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). Copyright © Cengage Learning. All rights reserved
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. Copyright © Cengage Learning. All rights reserved
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 = 7.381 7.4 Copyright © Cengage Learning. All rights reserved
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. Copyright © Cengage Learning. All rights reserved
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
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
Logarithms and Antilogarithms 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
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. Copyright © Cengage Learning. All rights reserved
The Organization of Matter Copyright © Cengage Learning. All rights reserved