Practice Quiz Put the following in order from smallest to largest. 1.8x10-5 8.7x1024 0.7x10-3 1.4x1040

Answers Smallest Largest 1.8x10-5 0.7x10-3 8.7x1024 1.4x1040

Scientists (and those studying science) frequently must deal with numbers that are very large or very small.

Instead of wasting time by writing many zeros before and after numbers, a method of writing very large and very small numbers was invented. It is called scientific notation.

Rules The first figure is a number from 1 to 9. The first figure is followed by a decimal point and then the rest of the figures. Then multiply by the appropriate power of 10.

Examples 425=4.25x102 (102 is the same as 100, so you are really multiplying 4.25 by 100) 0.00098=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)

Practice Write the following in scientific notation: 36000 0.0135

Try These Try to guess the answer without using your calculator. 4.2x104kg + 7.9x103kg= 5.23x106mm x 7.1x10-2mm= 5.44x107g/8.1x104mol=

4.99x104kg 3.7x105mm2 6.72x102g/mol

Metric System

Metric System Every measurement has two parts Number Scale (unit) SI system (le Systeme International) based on the metric system Prefix + base unit Prefix tells you the power of 10 to multiply by - decimal system -easy conversions

The Fundamental SI Units Copyright © Houghton Mifflin Company. All rights reserved.

Prefixes giga- G 1,000,000,000 109 mega - M 1,000,000 106 kilo - k 1,000 103 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- m 0.000001 10-6 nano- n 0.000000001 10-9

The Prefixes Used in the SI System Copyright © Houghton Mifflin Company. All rights reserved.

Some Examples of Commonly Used Units Copyright © Houghton Mifflin Company. All rights reserved.

Deriving the Liter gram is the mass of 1 cm3 Liter is defined as the volume of 1 dm3 gram is the mass of 1 cm3

Measurement of Volume Copyright © Houghton Mifflin Company. All rights reserved.

Soda is Sold in 2-Liter Bottles- an Example of SI Units in Everyday Life Copyright © Houghton Mifflin Company. All rights reserved.

Figure 1.7 Common Types of Laboratory Equipment Used to Measure Liquid Volume Copyright © Houghton Mifflin Company. All rights reserved.

Measurement of Volume Using a Buret Copyright © Houghton Mifflin Company. All rights reserved.

Mass and Weight Mass is measure of resistance to change in motion Weight is force of gravity. Sometimes used interchangeably Mass can’t change, weight can

Figure 1.8 An Electronic Analytic Balance Copyright © Houghton Mifflin Company. All rights reserved.

Significant Figures

Uncertainty Basis for significant figures All measurements are uncertain to some degree Precision- how repeatable Accuracy- how correct - closeness to true value. Random error - equal chance of being high or low- addressed by averaging measurements - expected

Figure 1.10 The Results of Several Dart Throws Show the Difference Between Precise and Accurate Neither accurate nor precise Precise but not accurate Both precise and accurate (large random error) (small random error, (small random error, large systematic error) no systematic error) Copyright © Houghton Mifflin Company. All rights reserved.

Uncertainty Systematic error- same direction each time Want to avoid this Better precision implies better accuracy you can have precision without accuracy You can’t have accuracy without precision

Significant figures Meaningful digits in a MEASUREMENT Exact numbers are counted, have unlimited significant figures If it is measured or estimated, it has sig figs. If not it is exact. All numbers except zero are significant. Some zeros are, some aren’t

Rules All non zero digits are significant Ex: 127 Zeros between significant digits are always significant Ex: 106 Leading zeros are never significant Ex: 0.005 Trailing zeros are significant only if there is a decimal Ex: 25.30

Copy the examples below and write the number of significant figures 7623142516 7084 0.00761 421.00 0.538 5000 5x103 5.0 x103 5000. 5120

Copy the examples below and write the number of significant figures 7623142516 10 7084 4 0.00761 3 421.00 5 0.538 3 5000 1 5x103 1 5.0 x103 2 5000. 4 5120 3

Which zeroes count? In between other sig figs does Before the first number doesn’t After the last number counts iff it is after the decimal point the decimal point is written in 3200 2 sig figs 3200. 4 sig figs

Multiplication and Division The final answer should have the same number of sig figs as the measurement having the smallest number of sig figs Ex: 10.305g x 0.00320g= Ex: 3.64928g/5.2mL=

Addition and Subtraction Line the numbers up in column form Ex: 3.461728+14.91+0.98001+5.2631= Ex: 467.384-2.384= Ex: 564321-264321=

Doing the math Multiplication and division, same number of sig figs in answer as the least in the problem Addition and subtraction, same number of decimal places in answer as least in problem.

Rounding Numbers Copyright © Houghton Mifflin Company. All rights reserved.

Significant Figures Song To the tune of Three Blind Mice

Verse 1 Addition and Subtraction line numbers up in columns (Repeat) Make sure the decimals are aligned right, Take off the numbers that are on the right To get the sig figs (Repeat)

Verse 2 Multiplication and division count the numbers (Repeat) Find the one that is the least That’s the number, the rest will cease To get the sig figs (Repeat)

Temperature

Temperature A measure of the average kinetic energy Different temperature scales, all are talking about the same height of mercury. Derive a equation for converting ºF toºC

0ºC = 32ºF 32ºF 0ºC

(0,32)= (C1,F1) ºF ºC

100ºC = 212ºF 0ºC = 32ºF 0ºC 100ºC 212ºF 32ºF

(0,32) = (C1,F1) (120,212) = (C2,F2) ºF ºC

100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF 0ºC 100ºC 212ºF 32ºF

100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF 1ºC = (180/100)ºF 1ºC = 9/5ºF 0ºC 100ºC 212ºF 32ºF

Figure 1.11 The Three Major Temperature Scales Copyright © Houghton Mifflin Company. All rights reserved.

Figure 1.12 Normal Body Temperature Copyright © Houghton Mifflin Company. All rights reserved.

Equations F=1.80(C)+32 C=(F-32)/1.80

Using the units to solve problems Dimensional Analysis Using the units to solve problems

Dimensional Analysis Use conversion factors to change the units 1 foot = 12 inches (equivalence statement) 12 in = 1 = 1 ft. 1 ft. 12 in 2 conversion factors multiply by the one that will give you the correct units in your answer.

Examples #1,2 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers? A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Example #3 Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots? Warp 1.71 = 5.00 times the speed of light speed of light = 3.00 x 108 m/s 1 knot = 2000 yd/h exactly

Example #4 Apothecaries (druggists) use the following set of measures in the English system: 20 grains ap = 1 scruple (exact) 3 scruples = 1 dram ap (exact) 8 dram ap = 1 oz. ap (exact) 1 dram ap = 3.888 g 1 oz. ap = ? oz. troy What is the mass of 1 scruple in grams?

Example #5 The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?

Group Practice

Group Practice-no flashcards 1) Convert 0.049kg of sulfur to grams. 2) Convert 3µL of saline solution to liters. 3) Convert 150mg of aspirin to grams. 4) Convert 1.18dm3 to mL. 5) Convert 5230000nL of water to grams. 6) Convert 4.19L to cubic centimeters 7) Convert 310000cm3 of concrete to cubic meters

Complex Conversion Problems

#1 A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)

#1 Answer 4.7x103 kcal/h

#3 At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?

#3 Answer 1670km/hr 4.02x104 km/d

#2 A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?

#2 Answer 34L/yr

Density

Density Ratio of mass to volume D = m/V Useful for identifying a compound Useful for predicting weight An intrinsic property- does not depend on what the material is

Formula Density=Mass/Volume D=m/V If you know the density triangle, you can get the formulas for m and V. The units of density are always going to have a division sign in them. Ex: g/mL

Densities of Various Common Substances* at 20° C Copyright © Houghton Mifflin Company. All rights reserved.

Example #1 An empty container weighs 121.3 g. Filled with carbon tetrachloride (density 1.53 g/cm3 ) the container weighs 283.2 g. What is the volume of the container?

Example #2 A 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol? density 0.789 g/cm3 1 gal = 3.78 L 1 lb = 454 g

Examples #3, 4, and 5 (on your own) 3) Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal? 4) Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid? 5) A beaker contains 725mL of water. The density of water is 1.00g/mL. Calculate the volume and mass of the water.

Answers 3) 16.5mL 4) 31.8mL 5) 0.725L, 0.725g