Chemistry 103 Lecture 2

Outline I. Sig Figs II. Mathematics of Chemistry Identification Rounding Math Operations II. Mathematics of Chemistry Scientific Notation Dimensional Analysis

Periodic Table - Elements to Memorize Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Measured numbers convey Significant Figures Are the digits in any measurement known with certainty, plus one digit that is uncertain. Measured numbers convey *Magnitude *Units *Precision

The Calculator Problem 7.8 3.8

The Calculator Problem 7.8 3.8 Calculator Answer: 2.05263……

Rules for Significant Figures It’s ALL about the ZEROs

Rules for Sig Figs All non-zero numbers in a measurement are significant. 4573 4573 has 4 sig figs

Rules for Sig Figs All zeros between sig figs are significant. 23007 23007 has 5 sig figs

Rules for Sig Figs In a number less than 1, zeros used to fix the position of the decimal are not significant. 0.00021 0.00021 has 2 sig figs

Rules for Sig Figs When a number has a decimal point, zeros to the right of the last nonzero digit are significant 0.0002100 0.0002100 has 4 sig figs

Rules for Sig Figs When a number has a decimal point, zeros to the right of the last nonzero digit are significant 3400. 3400. has 4 sig figs

Rules for Sig Figs _ 820000 meters 3 sig figs 820000 When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used. _ 820000 meters 3 sig figs 820000

Practice Identifying Sig Figs

Significant Figures How many assuming all numbers are measured?

Significant Figures How many assuming all numbers are measured? a). 75924 (5 sig figs) b). 30.002 (5 sig figs) c). 0.004320 (4 sig figs) d). 0.000002 (1 sig fig) e). 46,000 (2 sig figs)

Rounding off Numbers The number of significant figures in measurements affects any calculations done with these measurements Your calculated answer can only be as certain as the numbers used in the calculation

Calculator: Friend or Foe? Sometimes, the calculator will show more (or fewer) significant digits than it should If the first digit to be deleted is 4 or less, simply drop it and all the following digits If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one

Sig Fig Rounding Example: Round the following measured number to 4 sig figs: 82.56702

Sig Fig Rounding Example Round the following measured number to 4 sig figs: 82.56702

Sig Fig Rounding Example Round the following measured number to 4 sig figs: 82.56702 ANSWER: 82.57

Adding Significant Zeros Sometimes a calculated answer requires more significant digits. Then one or more zeros are added. Calculated Answer Zeros Added to Give 3 Significant Figures 4 4.00 1.5 1.50 0.2 0.200 12 12.0

Practice Rounding Numbers

Significant Figures Round each to 3 sig figs b). 0.000230600 c). 2568 d). 2562 e). 8

Significant Figures Round each to 3 sig figs a). 28.394 ANSWER: 28.4 b). 0.000230600 ANSWER: 0.000231 c). 2568 ANSWER: 2570 d). 2562 ANSWER: 2560 e). 8 ANSWER: 8.00

Math Operations & Sig Figs

Multiplication and Division When multiplying or dividing, use The same number of significant figures in your final answer as the measurement with the fewest significant figures. Rounding rules to obtain the correct number of significant figures. Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF

Addition and Subtraction When adding or subtracting, use The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement). Use rounding rules to adjust the number of digits in the answer. 25.2 one decimal place + 1.34 two decimal places 26.54 calculated answer 26.5 answer with one decimal place

Report Answer with Correct Number of Sig Figs A). 124.54 x 2.2 = B). 3420. + 2400. + 1095 = C). 98.5564 = 45.68

When Math Operations Are Mixed If you have both addition/subtraction and multiplication/division in a formula, carry out the operations in parenthesis first, and round according to the rules for that type of operation. -complete the calculation by rounding according to the rules for the final type of operation.

When Math Operations Are Mixed _____5.681g_____ = (52.15ml - 32.4ml)

When Math Operations Are Mixed _____5.681g_____ = (52.15ml - 32.4ml) carry out the operations in parenthesis first, and round according to the rules for that type of operation.

When Math Operations Are Mixed _____5.681g_____ = 5.681g (52.15ml - 32.4ml) 19.8ml

When Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs) (52.15ml - 32.4ml) 19.8ml (3 sig figs) -complete the calculation by rounding according to the rules for the final type of operation.

When Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs) (52.15ml - 32.4ml) 19.8ml (3 sig figs) ANSWER: 0.287g/ml -complete the calculation by rounding according to the rules for the final type of operation.

Mixed Operations and Significant Figures What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured. (179.8) x (24.4 - 23.1)

Scientific Notation Scientific notation Is used to write very large or very small numbers For the width of a human hair of 0.000 008 m is written as: 8 x 10-6 m Of a large number such as 2 500 000 s is written as: 2.5 x 106 s Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

2.2 Scientific Notation A number in scientific notation contains a coefficient (1 or greater, less than 10) and a power of 10. 150 0.000735 coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4 To write a number in scientific notation, the decimal point is moved after the first digit. The spaces moved are shown as a power of ten. 52 000 = 5.2 x 104 0.00378 = 3.78 x 10-3

Comparing Numbers in Standard and Scientific Notation Standard Format Scientific Notation Diameter of Earth 12 800 000 m 1.28 x 107 m Mass of a human 68 kg 6.8 x 101 kg Length of a pox virus 0.000 03 cm 3 x 10-5 cm

Comparing Numbers in Standard and Scientific Notation Standard Format Scientific Notation Diameter of Earth 12 800 000 m 1.28 x 107 m (3 sig figs) Mass of a human 68 kg 6.8 x 101 kg (2 sig figs) Length of a pox virus 0.000 03 cm 3 x 10-5 cm (1 sig fig) NOTE: The Coefficient is used to identify the number of significant figures in the measurement.

Defining Conversion Factors Dimensional Analysis Defining Conversion Factors

Conversion Factors Conversion factors A ratio that specifies how one unit of measurement is related to another Creating conversion factors from equalities 12 in.= 1 ft I L = 1000 mL

Dimensional Analysis How many seconds are in 2 minutes? 2 minutes x 60 seconds = 1 minute 120 seconds (exactly)

Dimensional Analysis If we assume there are exactly 365 days in a year, how many seconds are in one year?

Dimensional Analysis A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations. Conversion Factor

Exact vs Measured Relationships Metric to Metric – exact English to English – exact Metric to English – typically measured (must consider sig figs)

English to Metric Conversion Factors

Dimensional Analysis What is 165 lb in kg? STEP 1 Given: 165 lb Need: kg STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.205 lb 2.205 lb and 1 kg 1 kg 2.205 lb STEP 4 Set Up Problem

Practice Problem On a recent trip to Ireland, my average cost per day was 250. Euro. What was my average cost in U.S. Dollars? (1 Euro = 1.36 U.S. Dollars)

Learning Check A rattlesnake is 2.44 m long. How many centimeters long is the snake? A) 2440 cm B) 244 cm C) 24.4 cm

Learning Check If a ski pole is 3.0 feet in length, how long is the ski pole in mm? (1000mm = 1m, 12 inches=1ft, 1m=39.37inches) 0.910 mm 91 mm 910 mm