Hippo Nation Pre-AP Chemistry Summer Assignment · Hippo Nation Pre-AP Chemistry Summer Assignment...

Name:_____________________________________________________ Teacher______________________________

HippoNationPre-APChemistrySummerAssignmentIhopeyouareexcitedtotakechemistrynextyear,asamveryexcitedtoteachyou!Chemistryisafascinatingsubjectwhereyouwilllearnaboutthebuildingblocksoftheuniverseandhowtheycombineandchangetoformallweseearoundus.Inordertobefullypreparedforthisrigorousandexcitingcourseyouwillneedtocompletethissummerassignment.ItmustbesubmittedONYOURFIRSTDAYOFSCHOOLAugust22,2016.Thiswillcountasatestgradeworth100pointsso make sure you startthe yearoffstrong.Nolateassignmentsw illbeacceptedandyouwillreceiveazeroforyourfirsttestgrade ifitisnotcomplete!Ifyou are have problemscompletingyourpacket,emailmeatCharlene.mercer@huttoisd.netandIwilltrytohelpyouorsendyoutoaresourcethatwillbeabletoassistyoufurther.Good luckwith yourpacketand Ican’twaitto share the incredible journeythatwillbeyournextyearin Pre-APchemistry!***Anystudententeringthe districtafterthe firstdayofschoolisstillaccountable forthe packetwith five daysto completetheassignment.YOURSUMMERASSIGNMENTHASMULTIPLEPARTS.BESURETOCOMPLETETHEMALL!!!!

A.ElementandPolyatomicflashcards 10ptsB.AtomicStructureWorksheet 10ptsC.ScientificMethodworksheet 10ptsD.RealWorldExamples 10ptsE.Measurement–MetricSystem 10ptsF.SignificantFigures 10ptsG.Scientific/Exponentialnotation 10ptsH.SolvingforVariables 10ptsI.ScientificGraphing 10ptsJ.Logarithms 10pts

100pts(MajorGrade)

Chemistry isa difficultcourse formany students.Itisjustlikelearninganewlanguage.Ineachunityouwilllearnskillsandcontentthatw illbeusedinthenextunit.Chemistryistheonlysciencecoursethatw illusepreviousknowledgetomasterthenextunitandthefollowingunits.Itiscriticaltomastermaterialinordertobesuccessfulthoughouttheyear.Itisimportantthatstudentsandparentsfam iliarizethemselvesw iththemodelofa“flippedclassroom”aswellashowtotakeCornellNotes.Studentsneedtosubscribetothe“HippoNationChemistry”YouTubechannelinordertofind therequiredinstructionalvideostotake notesusingthe“CornellNotes”methodpriortothelessonforeachunit!Watchthe“HowtotakeCornellNotes”videoontheHippoNationYouTubechanneltolearnthepropernotetakingskillforthisyear.Thenyouwillneedtowatchthe informationalvideoonthe“FlippedClassroom”model(websitelinkbelow)andtakeyourfirstpageofCornellNotes.Eachstudentwillneedacompositionbookforyournotesfortheyear.Iexpectyoutohavethisfirstpage ofnotesaboutthe“TheFlippedC lassroom Model”donethefirstdayofclassalongwiththispacket.https://youtu.be/qdKzSq_t8k8 DO YOURBEST!!! CHEMISTRY!!

A)ElementandPolyatomicflashcards

Youwillbemaking36Flashcardstohelpyoutolearnsomeofthecommonelementsandpolyatomicionsthatyouwillbeusing throughouttheyear.Onesetwillbemadeforthefirst36elementsandtheotherforpolyatomicions..

Use3X5notecardstomakeyourflashcards.

***UsethesetoSTUDY!!!Youwillbetestedonthesethefirstweekofschool!.

Youwillberesponsibleforlearningthenamesandsymbolsfortheseelements.Notethatthechemicalsymbolsforanelementarecomposedofoneortwoletters.Thefirstletterisalwayscapitalizedandthesecondletterifpresentisalwayslowercase.Symbolsmustbeprinted,notwrittenincursivehandwriting.Thespellingoftheelementnamesmustalsobecorrect.Set1:ELEMENTNAMESANDSYMBOLSDirections:WritetheelementSymbolononesideofyourcardandtheelementNameandAtomicnumberontheotherside.Spellingcountssobecareful!!!

ExampleFlashcard

24Chromium

Cr

(Front)(Back)

Name Symbol Name Symbol Name Symbol1Hydrogen H 13Aluminum Al 25Manganese Mn2Helium He 14Silicon Si 26Iron Fe3Lithium Li 15Phosphorus P 27Cobalt Co4Beryllium Be 16Sulfur S 28Nickel Ni5Boron B 17Chlorine Cl 29Copper Cu6Carbon C 18Argon Ar 30Zinc Zn7Nitrogen N 19Potassium K 31Gallium Ga8Oxygen O 20Calcium Ca 32Germanium Ge9Fluorine F 21Scandium Sc 33Arsenic As10Neon Ne 22Titanium Ti 34Selenium Se11Sodium Na 23Vanadium V 35Bromine Br

12Magnesium Mg 24Chromium Cr 36Krypton Kr

Set2:PolyatomicIonsandNamesDirections:Writethepolyatomicformulaandchargeononesideofyourcardandthepolyatomicionnameontheotherside.Spellingcountssobecareful!!!Youwillberesponsibleforlearningthenamesandformulasfor20polyatomicions.Apolyatomicionisachargedchemicalspeciescomposedofmorethanoneatom.Example:NO2

-1isNitritethatiscomposedofoneNitrogenatomandtwoOxygenatoms.Itcarriesachargeof-1.Thechargeiswrittenasasuperscriptsoputthechargeinthecorrectplaceafterthesymbol!Thespellingofthepolyatomicnamesmustbecorrect.

Onthefollowingpagesarepracticeproblemsyouwillseethroughouttheyear.UsethestudynotesonthelefthandsideofmostpagesandyourSTAARreferencematerialtoassistyou.Thereisanextrapieceofscratchpaperforyoutouse.Allscratchpapermustbeturnedinwithyourpacket.****Itisimportantthatyoushowallyourwork! ****

Formula&charge Name Formula&charge NameNH4+1 Ammonium OH-1 HydroxideC2H3O2-1 Acetate NO3-1 NitrateHCO3-1 HydrogenCarbonate NO2-1 NitriteCO3-1 Carbonate CN-1 CyanideClO4-1 Perchlorate MnO4 -1 PermanganateClO3-1 Chlorate PO4-3 PhosphateClO2-1 Chlorite PO3-3 PhosphiteClO-1 Hypochlorite HSO4-1 HydrogenSulfateCr2O7-2 Dichromate SO4-2 SulfateCrO4-2 Chromate SO3-2 Sulfite

B)

Atomic Structure Worksheet

1. Name the three particles of the atom and their respective charges:

a.

b.

c.

2. The number of protons in one atom of an element determines the atom’s_ , and the number of

electrons determines of an element.

3. The atomic number tells you the number of in one atom of an element. It

also tells you the number of in a neutral atom of that element. The atomic number

gives the “identity “ of an element as well as its location on the Periodic Table. No two elements will have the

atomic number.

4. The of an element is the average mass of an element’s naturally occurring

atoms, or isotopes, taking into account the of each isotope.

5. The of an element is the total number of protons and neutrons in the

of the atom.

6. The mass number is used to calculate the number of in one atom of an element. In

order to calculate the number of neutrons you must subtract the from the

.

7. Give the symbol and number of protons in one atom of:

Lithium Bromine

Iron Copper

Oxygen _________ Mercury

Arsenic _______ Helium

8. Give the symbol and number of electrons in a neutral atom of: Uranium Chlorine

Boron _______ Iodine _______

Antimony Argon _______

9. An isotope is the same element with a different mass. It is not unlike a room full of people with different weights. When writing the symbol for an isotope the element symbol is written with the mass at the top and the atomic

number at the bottom. Example Give the isotope symbol and number of neutrons in one atom of the following elements. Show your calculations.

Barium – 138 Sulfur – 32

Carbon – 12 Hydrogen – 1 ________

Fluorine – 19 Magnesium – 24

Silicon - 28 _______ Mercury – 202 _______

10. Name the element which has the following numbers of particles. Be specific. (Include charges and mass numbers where possible.)

26 electrons, 29 neutrons, 26 protons ______________

53 protons, 74 neutrons

2 electrons (neutral atom) _______

20 protons

86 electrons, 125 neutrons, 82 protons (charged atom) _____________

0 neutrons

11. If you know ONLY the following information can you always determine what the element is? (Yes/No). number of protons

number of neutrons

number of electrons in a neutral atom

number of electrons

Name

© Carson-Dellosa • CD-104644 27

Atomic StructureAn atom is made up of protons and neutrons (both found in the nucleus) and electrons (in the surrounding electron cloud). The atomic number is equal to the number of protons. The mass number is equal to the number of protons plus neutrons.

In a neutral atom, the number of protons equals the number of electrons. The charge on an ion indicates an imbalance between protons and electrons. Too many electrons produce a negative charge. Too few electrons produce a positive charge.

This structure can be written as part of a chemical symbol. 7 protons 8 neutrons (15 – 7) 4 electrons

Complete the chart.

Element/Ion

Atomic Number Atomic Mass Mass

Number Protons Neutrons Electrons

H

H+

126C

73Li+

3517Cl–

3919 K

2412Mg2+

As3–

Ag

Ag1+

S2–

U

Element SymbolsAn element symbol can stand for one atom of the element or one mole of atoms of the element. (One mole = 6.02 × 1023 atoms of an element.)

Write the symbol for each element.

massnumber

atomicnumber

charge157N

3+

CD_104644_100+ SCIENCE_CHEMISTRY.indd 27 1/23/15 9:05 AM

C) Scientific Method Review Directions: Complete the following problems using resources (Ex. Computer) for help. These are topics that will be on the test and it is important that you answer them correctly and study this often! 1. Define the Scientific Method: __________________________________________________________________________________________________ 2. Put the steps of the Scientific Method in the correct order: Some resources will give you anywhere from 5-7 steps. Either is fine as long as they are in order. 1. 2. 3. 4. 5. 6. 7. 4. Define Hypothesis: ___________________________________________________________ 5. An independent variable is the thing that ________________________________________ 6. A dependent variable is the thing that ___________________________________________ 7. A controlled variable is the thing that ___________________________________________ 8. Underline the independent variable, and circle the dependent variable: a. If Mr. Hasson takes a vitamin pill every day, then he won’t get sick for an entire year. b. If Mrs. Piper waters her garden two times a day, then all of the plants will grow three inches in two weeks. c. If Mr. Monahan runs three miles every morning, then he will lose seven pounds in a month.

9. An experiment is ___________________________________________________________ 10. How many things should be changed during an experiment? ______________________ 11. How can a scientist make sure that the results of an experiment are not a mistake? 12. Name three tools that can be used to collect data: a. b. c. 13. Name two things that should be used to analyze data: a. b. 14. To make a conclusion, you should compare your ___________ to your _______________ a. What happens if they match? ____________________________________________ ________________________________________________________________________ b. What should you do if they do not match? _________________________________ ________________________________________________________________________ 15. Define Observation: _________________________________________________________ a. A ______________________ observation is when you describe something. b. A ______________________ observation is when you count something.

16. Write “QL” for Qualitative and “QT” for Quantitative a. ________ The sky is blue. b. ________ There are 13 clouds in the sky. c. ________ Mr. Hasson’s tie is smooth. d. ________ The guinea pig smells bad. e. ________ There are 20 students in the class. 17. An ________________ is your best guess as to what caused the thing that you observed. 18. Write “I” for Inference or “O” for Observation a. _________ When I rang the doorbell, no one answered. b. _________ The hamburger was hot. c. _________ Jamal must be very popular. d. _________ The sun set at 7:18 pm. e. _________ That sounded like a mean dog.

Name

2 © Carson-Dellosa • CD-104644

Laboratory EquipmentLabel the lab equipment.


Name

Laboratory Dos And Don'tsIdentify what is wrong in each laboratory activity.

1.

________________________________________ ________________________________________ ________________________________________

2.

________________________________________ ________________________________________ ________________________________________

3.

________________________________________ ________________________________________ ________________________________________

4.

________________________________________ ________________________________________ ________________________________________

5.

________________________________________ ________________________________________ ________________________________________

6.

________________________________________ ________________________________________ ________________________________________


4. 4.


D) For each topic in the space provided to the right, determine a real world example and how that topic relates to your every day life.

Topics Covered Real World Examples Measurement & Metric System Classification of Matter States and Changes in Matter Thermochemistry - Energy Atomic Structure Nuclear Chemistry – Nucleus Electrons Periodic Table Chemical Bonding Organic Chemistry Chemical Reactions Mole Stoichiometry Gas Laws Aqueous Solutions Acids/Bases/Salts

E) Measurement, the metric system and conversions Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the page.

In science, it is very important to make measurements to describe the observations that you make. Quantitative observations help us make use of our observations by making sense out of the patterns that we see. It is also very important to have a common system of measurement for the collaboration of people from around the world.

The metric system is an internationally agreed decimal system of measurement that was originally based on the mètre des archives and the kilogramme des archives introduced by France in 1799. Over the years, the definitions of the meter and kilogram have been refined and the metric system has been extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries, the term is now often used as a synonym for "SI" or the "International System of Units"—the official system of measurement in almost every country in the world.

The variation of the metric system we use is the “MKS” which stands for Meter, Kilogram and Second

• m; the meter for length • kg; the kilogram for mass • s; the second for time

along with;

• A; the ampere for electric current • K; the Kelvin for temperature • mol; the mole for amount of substance • cd; the candela for luminous intensity

Unfortunately, the United States is one of the few countries in the world that do not use the metric system. This means that you must be able to make conversions from the English system to the SI system. Common English to metric conversion factors.

• 1 ft (foot) = 0.305 m • 1 mi (mile) = 1.61 km (kilometers) • 1 lb (pound) = 0.45 kg • Degrees Celsius (°C) = (°F – 32) x 5/9 • Kelvins (K) = °C + 273 • 1 gallon (gal) = 4.55 L (liter) • 1 L = 1000 mL = 1000 cc (cubic centimeters)

1) What unit would be used to measure each of the following:

a) The distance from your home to school: b) How much you gained after eating thanksgiving dinner: c) Describing how long it would take you to get ready in the morning: d) Describing how hot or cold it is on a warm summer day: e) Explaining how many molecules there are in a gallon of gasoline:

2) Using the conversion table/facts, convert the following measurements;

a) 6 foot tall person in meters.

6𝑓𝑡1 𝑥 �0.305 𝑚

1 𝑓𝑡 � = 1.83 𝑚𝑒𝑡𝑒𝑟𝑠

b) A 26.2 mile marathon in kilometers. c) Your weight in pounds in kilograms. d) A 20 gallon gas tank in liters. e) A warm summer day (90°F ) in Kelvins. f) 55 miles per hour in kilometers per hour

Name


Metrics And MeasurementsIn the chemistry classroom and lab, the metric system of measurement is used. It is important to be able to convert from one unit to another.

mega- kilo- hecto- deca- Basic Unitsgram (g)liter (L)

meter (m)

deci- centi- milli- micro-(M) (k) (h) (da) (d) (c) (m) (µ)

1,000,000 1,000 100 10 0.1 0.01 0.001 0.000001106 103 102 101 10-1 10-2 10-3 10-6

Unit Factor Method

l. Write the given number and unit. 2. Set up a conversion factor (fraction used to convert one unit to another).

a. Place the given unit as the denominator of the conversion factor. b. Place the desired unit as the numerator. c. Place a one in front of the larger unit. d. Determine the number of smaller units needed to make one of the larger units.

3. Cancel the units. Solve the problem.

Example 1: 55 mm = m Example 2: 88 km = m 55 mm 1 m = 0.055 m 88 km 1,000 m = 88,000 m1,000 mm 1 km

Example 3: 7,000 cm = hm Example 4: 8 daL = dL7,000 cm 1 m 1 hm = 0.7 hm 8 daL 10 L 100 dL = 800 dL100 cm 10,000 cm 1 daL 1 daL

The unit factor method can be used to solve virtually any problem involving changes in units. It is especially useful in making complex conversions dealing with concentrations and derived units.

Convert each measurement.

l. 35 mL = dL

2. 275 mm = cm

3. 1,000 mL = L

4. 25 cm = mm

5. 0.075 m = cm

6. 950 g = kg

7. 1,000 L = kL

8. 4,500 mg = g

9. 0.005 kg = dag

10. 15 g = mg


Name


Dimensional Analysis (Unit Factor Method)

Solve each problem. Round irrational numbers to the thousandths place.

1. 3 hr. = ____________________ sec.

2. 0.035 mg = ____________________ cg

3. 5.5 kg = ____________________ lb.

4. 2.5 yd. = ____________________ in.

5. l.3 yr. = ____________________ hr.

6. 3 moles = ____________________ molecules (1 mole = 6.02 × 1023 molecules)

7. 2.5 × 1024 molecules = ____________________ moles

8. 5 moles = ____________________ liters (1 mole = 22.4 1iters)

9. 100. liters = ____________________ moles

10. 50. liters = ____________________ molecules

11. 5.0 × 1024 molecules = ____________________ liters

12. 7.5 × 103 mL = ____________________ liters

Using this method, it is possible to solve many problems by using the relationship of one unit to another. For example, 12 inches = one foot. Since these two numbers represent the same value, the fractions 12 in./1 ft. and 1 ft./12 in. are both equal to one. When you multiply another number by the number one, you do not change its value. However, you may change its unit.

Example 1: Convert 2 miles to inches.

2 miles ×5,280 ft.

×12 inches

= 126,720 in.1 mile 1 ft.

Example 2: How many seconds are in 4 days?

4 days ×24 hrs.

×60 min.

×60 sec.

= 345,600 sec.1 day 1 hr. 1 min.


F) Significant digits/figures & rounding

Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the page.

Significant digits/figures are the digits in any measurement that are known with certainty, plus one digit that is uncertain. These digits are based on the precision of the measuring instrument used. Rule 1: In numbers that do not contain zeros, all the digits are significant.

• 3.1428 [5] • 3.14 [3] • 469 [3]

Rule 2: All zeros between significant digits are significant.

• 7.053 [4] • 7053 [4] • 302 [3]

Rule 3: Zeros to the left of the first nonzero digit serve only to fix the position of the decimal point and are not significant.

• 0.0056 [2] • 0.0789 [3] • 0.0000001 [1]

Rule 4: In a number with digits to the right of a decimal point, zeros to the right of the last nonzero digit are significant.

• 43 [2] • 43.0 [3] • 43.00 [4] • 0.00200 [3] • 0.40050 [5]

Rule 5: In a number that has no decimal point, and that ends in zeros (such as 3600), the zeros at the end may or may not be significant (it is ambiguous). To avoid ambiguity express the number in scientific notation showing in the coefficient the number of significant digits.

• 3.6 x 103 contains two significant digits

http://misterguch.brinkster.net/sigfigs.html GENERAL RULES FOR ROUNDING: XY--------> X When Y > 5, increase X by 1 When Y < 5, don’t change X When Y = 5, If X is odd, increase X by 1 If X is even, don’t change X

1) How many significant digits are in each of the following measurements? In second column, make some up of your own. Measurement Sig. fig. Measurement Sig. fig. 26.2 mi 105 °F 0.00538 m 1.00 kg 5.65 x 10-7 nm 6.02 x 1023 atoms

2) Round the number π (3.14159265359) to:

a) 1 sig. fig. = b) 2 sig. fig. = c) 3 sig. fig. = d) 4 sig. fig. = e) 5 sig. fig. = f) 6 sig. fig. =

SIGNIFICANT DIGITS IN OPERATIONS 3) Add or subtract as indicated and state the answer with the correct number of significant digits. (Your answer will have the same number of significant digits to the right of the decimal as the number with the least amount of digits to the right of the decimal.)

a) 85.26 cm + 4.6 cm b) 1.07 m + 0.607 m c) 186.4 g - 57.83 g d) 60.08 s - 12.2 s e) 4,285.75 - 520.1 - 386.255 f) 72.60 m + 0.0950 m

4) Multiply or divide as indicated and state the answer with the correct number of significant digits. (Your answer will have the same number of significant digits as the number with the least amount of digits.)

a) (5.5 m) (4.22 m) = (calc. says 23.210) = 23 b) (0.0167 km) (8.525 km) c) 2.6 kg ÷ 9.42 m3 d) 0.632 m ÷ 3.8 s e) (8.95) (9.162)/(4.25) (6.3) f) 0.0045 mm2 ÷ 0.90 mm

Name


Significant FiguresA measurement can only be as accurate and precise as the instrument that produced it. A scientist must be able to express the accuracy of a number, not just its numerical value. We can determine the accuracy of a number by the number of significant figures it contains.

1. All digits 1–9 inclusive are significant.

Example: 129 has 3 significant figures.

2. Zeros between significant digits are always significant.

Example: 5,007 has 4 significant figures.

3. Trailing zeros in a number are significant only if the number contains a decimal point. Sometimes, a decimal may be added without any number in the tenths place.

Example: 100.0 has 4 significant figures.

100. has 3 significant figures.

100 has 1 significant figure.

4. Zeros in the beginning of a number whose only function is to place the decimal point are not significant.


5. Zeros following a decimal significant figure are significant.


0.47000 has 5 significant figures.

Determine the number of significant figures in each number.

1. 0.02 ____________________

2. 0.020 ____________________

3. 501 ____________________

4. 501.0 ____________________

5. 5,000 ____________________

6. 5,000. ____________________

7. 6,051.00 ____________________

8. 0.0005 ____________________

9. 0.1020 ____________________

10. 10,001 ____________________

Determine the location of the last significant place value by placing a bar over the digit. (Example: 1.700)

11. 8,040 12. 0.90100 13. 3.01 × 1021

14. 0.0300 15. 90,100 16. 0.000410

17. 699.5 18. 4.7 × 10-8

19. 2.000 × 102

20. 10,800,000.0

Scientific NotationScientists very often deal with very small and very large numbers, which can lead to a lot of confusion when counting zeros. We can express these numbers as powers of 10.

Scientific notation takes the form of M × 10n where 1 < M < 10 and n represents the number of decimal places to be moved. Positive n indicates the standard form is a large number. Negative n indicates a number between zero and one.

Example 1: Convert 1,500,000 to scientific notation.

Move the decimal point so that there is only one digit to its left, for a total of 6 places.

1,500,000 = 1.5 × 106

Example 2: Convert 0.000025 to scientific notation.

For this, move the decimal point 5 places to the right.

0.000025 = 2.5 × 10-5

(Note that when a number starts out less than one, the exponent is always negative.)

Convert each number to scientific notation.


Name


Percentage ErrorPercentage error is a way for scientists to express how far off a laboratory value is from the commonly accepted value.

The formula is:

% error =Accepted Value – Experimental Value

× 100Accepted Value

Determine the percentage error in each problem.

1. Experimental value = 1.24 gAccepted value = 1.30 g

2. Experimental value = 1.24 x 10-2 gAccepted value = 9.98 x 10-3 g

3. Experimental value = 252 mLAccepted value = 225 mL

4. Experimental value = 22.2 LAccepted value = 22.4 L

5. Experimental value = 125.2 mgAccepted value = 124.8 mg

Calculations Using Significant FiguresWhen multiplying and dividing, limit and round to the least number of significant figures in any of the factors.

Example 1: 23.0 cm × 432 cm × 19 cm = 188,784 cm3

The answer is expressed as 190,000 cm3 since 19 cm has only two significant figures.

When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer.

Example 2: 123.25 mL + 46.0 mL + 86.257 mL = 255.507 mL

The answer is expressed as 255.5 mL since 46.0 mL has only one decimal place.

Perform each operation, expressing the answer in the correct number of significant figures.

1. 1.35 m × 2.467 m = __________________________

2. 1,035 m2 ÷ 42 m = __________________________

3. 12.01 mL + 35.2 mL + 6 mL = __________________________

4. 55.46 g – 28.9 g = __________________________

5. 0.021 cm × 3.2 cm × 100.1 cm = __________________________

6. 0.15 cm + 1.15 cm + 2.051 cm = __________________________

7. 150 L3 ÷ 4 L = __________________________

8. 505 kg – 450.25 kg = __________________________

9. 1.252 mm × 0.115 mm × 0.012 mm = __________________________

10. 1.278 × 103 m2 ÷ 1.4267 × 102 m = __________________________


G) Scientific/exponential notation Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the page.

Scientific notation is a way of writing numbers

that are too big or too small to be conveniently written in decimal form. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians and engineers.

In scientific notation all numbers are written in the form of a x 10b (a times ten raised to the power of b), where the exponent “b” is an integer, and the coefficient “a” is any real number. Correct scientific notation has only one number to the left of the decimal and retains the proper number of significant figures. Standard decimal notation

Normalized scientific

notation 2.0 2.0 × 100 0.2 2 × 10-1 300 3 × 102

6,720,000,000 6.72 × 109 0.000 000 007 51 7.51 × 10−9

Prefixes Along with the basic units of measurement in the metric system we use prefixes to express very large or very small numbers in science. Some commonly used prefixes in the sciences are listed below. (http://www.unc.edu/~rowlett/units/prefixes.html)

• exa- (E-) 1018 1 quintillion • tera- (T-) 1012 1 trillion • giga- (G-) 109 1 billion • mega- (M-) 106 1 million • kilo- (k-) 103 1 thousand • deci- (d-) 10-1 1 tenth • centi- (c-) 10-2 1 hundredth • milli- (m-) 10-3 1 thousandth • micro- (μ-) 10-6 1 millionth • nano- (n-) 10-9 1 billionth

1) Change the following into or out of scientific notation.

a) 50000 b) 0.000197 c) 5 x 10-6 d) 4 x 103

2) Using the metric prefixes, name the following numbers;

a) 6.02 x 1023 b) 1000 c) 0.036 d) 2.36 x 10-6

3) Using the metric prefixes, change the following numbers appropriately

a) 450mL into L b) 2.8 L into mL c) 26 cm into mm d) 2.3 x 107 nm into mm

Name


Significant FiguresA measurement can only be as accurate and precise as the instrument that produced it. A scientist must be able to express the accuracy of a number, not just its numerical value. We can determine the accuracy of a number by the number of significant figures it contains.

1. All digits 1–9 inclusive are significant.

Example: 129 has 3 significant figures.

2. Zeros between significant digits are always significant.

Example: 5,007 has 4 significant figures.

3. Trailing zeros in a number are significant only if the number contains a decimal point. Sometimes, a decimal may be added without any number in the tenths place.


100. has 3 significant figures.

100 has 1 significant figure.

4. Zeros in the beginning of a number whose only function is to place the decimal point are not significant.


5. Zeros following a decimal significant figure are significant.


0.47000 has 5 significant figures.

Determine the number of significant figures in each number.

Scientific NotationScientists very often deal with very small and very large numbers, which can lead to a lot of confusion when counting zeros. We can express these numbers as powers of 10.

Scientific notation takes the form of M × 10n where 1 < M < 10 and n represents the number of decimal places to be moved. Positive n indicates the standard form is a large number. Negative n indicates a number between zero and one.

Example 1: Convert 1,500,000 to scientific notation.

Move the decimal point so that there is only one digit to its left, for a total of 6 places.

1,500,000 = 1.5 × 106

Example 2: Convert 0.000025 to scientific notation.

For this, move the decimal point 5 places to the right.

0.000025 = 2.5 × 10-5

(Note that when a number starts out less than one, the exponent is always negative.)

Convert each number to scientific notation.

1. 0.005 = ____________________

2. 5,050 = ____________________

3. 0.0008 = ____________________

4. 1,000 = ____________________

5. 1,000,000 = ____________________

6. 0.25 = ____________________

7. 0.025 = ____________________

8. 0.0025 = ____________________

9. 500 = ____________________

10. 5,000 = ____________________

Convert each number to standard notation.

11. 1.5 × 103 = ____________________

12. 1.5 × 10-3 = ____________________

13. 3.75 × 10-2 = ____________________

14. 3.75 × 102 = ____________________

15. 2.2 × 105 = ____________________

16. 3.35 × 10-1 = ____________________

17. 1.2 × 10-4 = ____________________

18. 1 × 104 = ____________________

19. 1 × 10-1 = ____________________

20. 4 × 100 = ____________________


Scientific/exponential notation arithmetic Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the page.

To multiply numbers written in scientific notation, multiply the coefficients (M&N) and add the exponents (A&B).

MA X NB = (MxN)A+B For example, (3x104) x (2x102) = (3x2)x10(4+2) =6 x 106.

To divide numbers written in scientific notation, divide the coefficients (M&N) and subtract the exponent in the denominator from the exponent in the numerator.

𝑀𝐴

𝑁𝐵 = �𝑀𝑁�𝑥 10(𝐴−𝐵) For example, 3.0 𝑥1056.0 𝑥 102=(3.0

6.0) x 10(5-2) =0.5x103=5.0x102

If you want to add or subtract numbers expressed in scientific notation and you are not using a calculator, then the exponents must be the same.

For example, suppose you want to calculate the sum of 5.4 x 103 + 8.0 x 102.

First, rewrite the second number so that the exponent is a 3. (5.4 x 103) + (8.0 x 102→0.80 x 103) Now add the numbers.

(5.4 + 0.80) x 103= 6.2 x 103

Follow the same rule when you subtract numbers expressed in scientific notation.

(3.42 x 10-5) - (2.5 x 10-6) = (3.42 x 10-5) - (2.5 x 10-6→0.25 x 10-5) =

(3.42-0.25) x 10-5 = 3.17 x 10-5

1. Using the rules to the left, complete the following operations and record your answer in proper scientific notation

e) (4.8x102) x (2.101x103) f) (1.260 x 10-3)x (3.32 x 108) g) (2.6 x 105)x (2.1 x 10-1)

h)3.0 𝑥 1056.0 𝑥 102

i) 7.32 𝑥 1071.860 𝑥 10−3

j) 2.48x102 + 9.17x103 k) 4.07x10-5 + 3.966x10-4 l) 7.70x10-9 – 3.95x10-8 m) 3.456x106 – 1.01x107

H) Equations/Solving for variables Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the page.

Many relationships in chemistry can be expressed simple algebraic equations. However, the equation given is note always in the form that is most useful in figuring out a particular problem. In such a case, you must first solve the equation for the unknown quantity; this is done by rearranging the equation so that the unknown is on one side of the equation, and all the known quantities are on the other side.

An equation is solved using the laws of equality.

The laws of equality are summarized as follows: If equals are added to, subtracted from, multiplied by, or divided by equals, the results are equal. In other words, you can perform any of these mathematical operations on an equation and not destroy the equality, as long as you do the same thing to both sides of the equation. The laws of equality apply to any legitimate mathematical operation, including squaring, taking square roots, and taking the logarithm.

Consider the following equation relating the

Kelvin and Celsius temperature scales. K = °C + 273

If we need to solve this equation for °C we need to get °C by itself on one side of the equation. This means we need to move 273 to the other side. To do this we need to do the opposite of the operation that is attaching °C and 273, the opposite of addition is subtraction. So we need to subtract both sides by 273.

K - 273 = °C + 273 – 273 The 273 will cancel on the right side of the equation.

K - 273 = °C + 273 – 273 Leaving:

K - 273 = °C If they were attached by subtraction you would

need to use addition to separate them.

The same thing goes for if the numbers are attached by multiplication.

°F = (1.8 x °C) +32 You would need to subtract both sides by 32

and then divide both sides by 1.8. ℉−321.8 =°C

There is one slight change for division, you need to first move your unknown to the numerator if it is in denominator.

1) Solve the following for x:

a) 14x+12=40

b) 5𝑥+ 8 = 11

c) kx = a + by d) 2y - 2x = 38 e) 5x – 2 = 8

2) Solve the following for x1:

a) 3x1+ 5y1 = 2x2 + 8y2 b) y1x1 - k2 x2: = 0

3) Solve the following equation PV = nRT

a) For P: b) For V: c) For n: d) For R: e) For T:

I) Scientific Graphing

Most scientific graphs are made as line graphs. There may be times when other types would be appropriate, but they are rare.

The lines on scientific graphs are usually drawn either straight or curved. These "smoothed" lines do not have to touch all the data points, but they should at least get close to most of them. They are called best-fit lines.

In general, scientific graphs are not drawn in connect-the-dot fashion. Title, Axis, Interval, Line, Slope statement or TAILS for short. Title The title should represent what is being tested. A small statement consisting of both variables. Axis Axis should always be labeled with the manipulated (independent) variable on the X-axis and the responding (dependent) variable on the Y-axis. Interval Your graph should take up as much of the graph as possible. The scale should use intervals such as 1, 2, 5, 10 units per block. Line of best fit NEVER connect the dots on a scientific graph. Use a ruler to draw a straight line through your data. If the data looks as if it represents a curve, freehand draw a curved line through your data. Slope In the form of y = mx + b where “b” is the y-axis intercept A good graph Website: http://misterguch.brinkster.net/graph.html

Graph 1: Temperature scales Use the following data to draw a graph that shows the relationship between the Fahrenheit and Celsius temperature scales. Temp (°F)

-40

32

68

98.6

212

Temp (°C)

-40

0

20

37

100

Graph 2: Gas Laws The following data shows the conditions a diver experiences as they travel to depths in increments of 10m. This is a representation of one of the gas laws which can be useful to drivers. Use the following data to draw a graph that shows the relationship between the Pressure (units of atm) and Volume (units of L).

Graph 1: Temperature Scales

J) Logarithms (Logs) Directions: Read the information on the left side of the page, and then use it to answer the questions on the right side of the pag

The common logarithm (log) of a number (N) is the exponent (X) to which the base 10 must be raised to yield the number.

If N=10x, then log(N) = x

The use of logarithms allows a large range of values to be conveniently expressed as small, nonexponential numbers.

For example, log (103)= 3 and

log(106)= 6.

Although there is a range of three orders of magnitude (10 x 10 x 10 or 1000) between the numbers 103 and 106, the range of the log values is only 3.

The concentration of hydrogen ions in most aqueous solutions, although small, can vary over many orders of magnitude. Scientists use pH, a logarithmic scale which ranges between 1 and 14, to express the hydrogen ion concentration of a solution. log(6.23 x 10-5) = - 4.21 log(8.65 x 109) = 9.94 ________________________________________

The reverse process of converting a logarithm into a number is referred to as obtaining the antilogarithm.

The antilogarithm of the logarithm of number x is the number x itself.

antilog(log x) = x If log 10-7 = -7, then antilog (-7) = 10-7. Likewise, if log102= 2, then antilog(2) = 102. Antilog(5.64) = 105.64 = 4.37 x 105

1) Change the following values into scientific notation. Then calculate the logarithms.

a) 0.001 b) 100 c) 100000 d) 0.00000001

2) Calculate the logarithms of the following values.

a) 0.000678 b) 4270 c) 1.485 x 106 d) 1x10-12

3) Calculate the antilogarithms of the following values.

a) 2 b) 6.56 c) 12.4 d) 0.123

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