Chapter 1: Chemical Foundations (Topics to Review)resources.seattlecentral.edu/faculty/mvillarba/CHEM161/Chapter01...the least number of significant figures. ... we can count exactly

CHEM161: Chapter 1 – Independent Review page 1 of 12

Chapter 1: Chemical Foundations (Topics to Review) 1.7 THE SCIENTIFIC METHOD The Scientific Method and Scientific Models 1. Perform experiments and record observations on the system studied. 2. Analyze the data, and propose a hypothesis to explain the observations. 3. Conduct additional experiments to test hypothesis. If initial hypothesis holds up to extensive

testing, the hypothesis becomes a theory. theory (or model): a tested explanation of a basic natural phenomenon

If all or part of the hypothesis does not hold up to testing, then it is adjusted or a new hypothesis is proposed to explain the observations.

natural law: a simple statement or equation summarizing observations Note: A natural law summarizes what happens; a theory explains why it happens. 1.8 MAKING MEASUREMENTS AND EXPRESSING THE RESULTS Consider the three rulers below:

Ruler A

Ruler B

0 1 2 3 4 5

0 1 2 3 4 5

Ruler C

4.1 4.2 4.3 4.4

A B C

Measurement

# of sig figs


Thus, when a measurement is recorded, all the numbers known with certainty are given along with the last number, which is estimated. All the digits are significant because removing any of the digits changes the measurement's uncertainty.

Guidelines for Sig Figs (if measurement is given): Count the number of digits in a measurement from left to right: 1. When there is a decimal point: – For measurements greater than 1, count all the digits (even zeros). – 62.4 cm has 3 sig figs, 5.0 m has 2 sig figs, 186.000 g has 6 s.f. – For measurements less than 1, start with the first nonzero digit and count all digits

(even zeros) after it. – 0.011 mL and 0.00022 kg each have 2 sig figs 2. When there is no decimal point: – Count all non-zero digits and zeros between non-zero digits – 125 g has 3 sig figs, 107 mL has 3 sig figs – Placeholder zeros may or may not be significant – 1000 may have 1, 2, 3 or 4 sig figs SCIENTIFIC NOTATION

Some numbers are very large or very small → difficult to express. For example,

Avogadro’s number = 602,200,000,000,000,000,000,000 → 6.022×1023 an electron’s mass = 0.000 000 000 000 000 000 000 000 000 91 kg → 9.1×10-27 kg

Also, it's not clear how many sig figs there are in some measurements, so expressing the final answer in scientific notation can eliminate the ambiguity. For example,

Express 100.0 g to 3 sig figs: ______________________ Express 100.0 g to 2 sig figs: ______________________ Express 100.0 g to 1 sig fig: ______________________


UNBIASED ROUNDING (or ROUND-TO-EVEN METHOD)

How do we eliminate nonsignificant digits?

• If first nonsignificant digit < 5, just drop the nonsignificant digits • If first nonsignificant digit ≥ 6, raise the last sig digit by 1 and drop nonsignificant digits

• If first nonsignificant digit =5 and – nonzero digits follow 5, raise the last sig digit by 1 and drop nonsignificant digits – e.g. 3.14501 ⎯⎯⎯ →⎯ s.f. 3 to 3.15 (since nonsig figs are “501” in 3.14501) – no digits or only zeros follow the 5, leave it alone or raise the last sig digit to get

an even number and drop nonsignificant zeros – e.g. 3.145 or 3.145000 ⎯⎯⎯ →⎯ s.f. 3 to 3.14 (to get last sig fig to be an even number) – e.g. 3.175 or 3.175000 ⎯⎯⎯ →⎯ s.f. 3 to 3.18 (to get last sig fig to be an even number) Express each of the following with the number of sig figs indicated:

a. 648.75 ⎯⎯⎯ →⎯ f. s. 3 to ___________________ d. 0.00123456 ⎯⎯⎯ →⎯ f. s. 3 to _______________

b. 23.6500 ⎯⎯⎯ →⎯ f. s. 3 to __________________ e. 1,234,567 ⎯⎯⎯ →⎯ f. s. 5 to _______________

c. 64.35 ⎯⎯⎯ →⎯ f. s. 3 to ___________________ f. 1975 ⎯⎯⎯ →⎯ s.f. 2 to _______________ Instead of using placeholder zeros (e.g. 100 s, 35000 ft.), express measurements in scientific notation (e.g. 1×102 s, 3.5×105 ft) to clarify the number of sig figs in the measurement. ADDING/SUBTRACTING MEASUREMENTS

When adding and subtracting measurements, your final value is limited by the measurement with the largest uncertainty—i.e. the measurement with the fewest decimal places.

MULTIPLYING/DIVIDING MEASUREMENTS

When multiplying or dividing measurements, the final value is limited by the measurement with the least number of significant figures.

Ex. 1: 7.4333 g + 8.25 g + 10.781 g = ______________________

Ex. 2: 13.55 cm × 7.95 cm × 4.00 cm = ______________________ Ex. 3: 9.75 mL − 7.35 mL = ______________________

Ex. 4: cm 8.50 cm 10.25 cm 25.75

g 101.755 ××

= ______________________


MULTIPLYING/DIVIDING WITH EXPONENTIAL NUMBERS: When multiplying or dividing measurements with exponents, use the digit term (N in “N×10n”) to determine number of sig figs.

Ex. 1: (6.02×1023) (4.155×109) = 2.50131×1033

How do you calculate this using your scientific calculator? Step 1. Enter “6.02 × 1023” by pressing:

6.02 then EE or EXP (which corresponds to “×10”) then 23 → Your calculator display should be as follows: Step 2. Multiply by pressing: × Step 3. Enter “4.155×109” by pressing: 4.155 then EE or EXP then 9 → Your calculator should now read

Step 4. Get the answer by pressing: = → Your calculator should now read: or something similar indicating 2.50131×1033

Thus, the answer with the correct sig figs is 2.50×1033

Be sure you can do exponential calculations with your calculator. Many calculations we do in chemistry involve numbers in scientific notation.

Ex. 2: (3.75×1015) (8.6×104) = 3.225×1020 ⎯⎯⎯⎯⎯⎯ →⎯ figs sig of #correct to ___________________

Ex. 3: 4

15

108.605103.75×

× = 4.357931435×1010 ⎯⎯⎯⎯⎯⎯ →⎯ figs sig of #correct to ___________________

EXACT NUMBERS Although measurements can never be exact, we can count an exact number of items. For example, we can count exactly how many students are present in a classroom, how many M&Ms are in a bowl, how many apples in a barrel. We say that exact numbers of objects have an infinite number of significant figures.

6.02 ×1023

4.155 ×1009

2.501313 ×1033


1.9 UNIT CONVERSIONS AND DIMENSIONAL ANALYSIS UNIT EQUATIONS AND UNIT FACTORS Unit equation: Simple statement of two equivalent values Unit conversion factor = unit factor = equivalents: - Ratio of two equivalent quantities Unit equation Unit factor

1 dollar = 10 dimes dollar 1dimes 10 or

dimes 10dollar 1

Equivalents are exact if we can count the number of units equal to another or the units are in the same system (metric or English). For example, the following unit factors and unit equations are exact:

cm 100m 1

foot 1in. 12

hours 24day 1

year1days 365.25 and 1 yard ≡ 3 feet

Exact equivalents have an infinite number of sig figs → never limit number of sig figs!

Note: When the relationship between two units or items is exact, the “≡” (meaning “equals exactly”) is used instead of the basic “=” sign.

Equivalents based on measurements or relating measurements from two different systems are inexact or approximate because they contain uncertainty, such as

sm 102.998

hourmi 65

mile 1km 1.61 8×

Approximate equivalents do limit the sig figs for the final answer. LENGTH, MASS, WEIGHT, VOLUME AND TEMPERATURE LENGTH – generally reported in meters, centimeters, millimeters, kilometers, inches, feet, miles – Know the following English-English conversions:

1 foot ≡ 12 inches 1 yard ≡ 3 feet (These are both exact!)


MASS: A measure of the amount of matter an object possesses. – generally reported in grams, kilograms, or milligrams – measured with a balance and NOT AFFECTED by gravity

MASS ≠ WEIGHT = MASS × Acceleration due to gravity

Mass is not affected by gravity!

VOLUME: Amount of space occupied by a solid, gas, or liquid. – generally in units of liters (L), milliliters (mL), or cubic centimeters (cm3)

– Know the following: 1 L ≡ 1 dm3 1 mL ≡ 1 cm3 (These are both exact!)

Determining Volume – Volume is determined in three principal ways: 1. The volume of any liquid can be measured directly using calibrated glassware in

the laboratory (e.g. graduated cylinder, pipets, burets, etc.) 2. The volume of a solid with a regular shape (rectangular, cylindrical, uniformly

spherical or cubic, etc.) can be determined by calculation. – e.g. volume of rectangular solid = length × width × thickness

volume of a sphere = 34

πr3

3. Volume of solid with an irregular shape can be found indirectly by the amount of liquid it displaces. This technique is called volume by displacement.

Volume By Displacement

a. Fill a graduated cylinder halfway with water, and record the initial volume.

b. Carefully place the object into the graduated cylinder so as not to splash or lose any water.

c. Record the final volume.

d. Volume of object = final volume – initial volume


Ex. 1: What is the volume of the piece of green jade in the figure below?

Ex. 2: A metal rod is placed into a 10-mL graduated cylinder with 5.25 mL of water causing

the water level to rise to 8.75 mL of water. What is the volume of the metal rod? 1.3 UNITS OF MEASUREMENT SI Units (from French "le Système International d’Unités") – standard units for measurement Metric system: A unified decimal system of measurement with a basic unit for each type of

measurement

quantity basic unit symbol

length meter m

mass gram g

volume liter L

time second s


Metric Prefixes Multiples or fractions of a basic unit are expressed as a prefix → Each prefix = power of 10 → The prefix increases or decreases the base unit by a power of 10.

Prefix Symbol Multiple/Fraction

tera T 1,000,000,000,000 ≡ 1012

giga G 1,000,000,000 ≡ 109

mega M 1,000,000 ≡ 106

kilo k 1000 ≡ 103

deci d 0.1 ≡ 10

1 ≡ 10-1

centi c 0.01 ≡ 100

1 ≡ 10-2

milli m 0.001 ≡ 1000

1 ≡ 10-3

micro μ (Greek “mu”) 10–6

nano n 10–9

pico p 10–12

femto f 10–15

KNOW the metric units above (included in Table 1.2 on p. 9)! Metric-English Conversions English system (also called USCS): our general system of measurement, also called the United States Customary System (USCS). Scientific measurements are exclusively metric. However, most Americans are more familiar with inches, pounds, quarts, and other English units. → Conversion between the two systems is necessary.

Quantity English unit Metric unit English–Metric conversion length 1 inch (in) 1 cm 1 in. ≡ 2.54 cm (exact) mass 1 pound (lb) 1 g 1 lb = 453.6 g (approximate)

volume 1 quart (qt) 1 mL 1 qt = 946 mL (approximate)

These and all metric-English conversions will be given on quizzes and exams.


1.8 DENSITY: The amount of mass in a unit volume of matter

Vmd

volumemassdensity =or = generally in units of g/cm3 or g/mL

For water: 1.00 g of water occupies a volume of 1.00 cm3

d =

mV =

1.00 g

1 . 00 cm3 = 1 . 00 g / cm 3

Density also expresses the concentration of mass – i.e., the more concentrated the mass in an object → the heavier the object → the higher its density Sink or Float

Note how some objects float on water (e.g. a cork), but others sink (e.g. a penny). That's because objects that have a higher density than a liquid will sink in the liquid, but those with a lower density than the liquid will float. Since water's density is about 1.00 g/cm3, cork's density must be less than 1.00 g/cm3, and a penny's density must be greater than 1.00 g/cm3. Ex.: Consider the figure at the right and the following solids and liquids and their densities: ice (d=0.917 g/cm3) honey (d=1.50 g/cm3) iron cube (7.87 g/cm3) hexane (d=0.65 g/cm3) rubber cube (d=1.19 g/cm3) Identify L1, L2, S1, and S2 by filling in the blanks below: L1= ___________________ and L2= ___________________

S1= ___________________ S2= ___________________ and S3= ___________________

Applying Density as a Unit Factor Given the density for any matter, you can always write two unit factors. For example, the density of ice is 0.917 g/cm3.

Two unit factors would be: 0.917g

cm or cm

0.917g 3

3


Solve the following problems using these guidelines for dimensional analysis:

1. Write the units for the answer.

2. Determine what information to start with.

3. Arrange all other unit factors—showing them as fractions—with the correct units in the numerator and denominator, so all units cancel except those needed for the final answer.

4. Check for the correct units and the correct number of sig figs in the final answer. Ex. 1 A piece of silver metal weighing 194.3 g is placed in a graduated cylinder containing

42.0 mL of water. The volume of water now reads 60.5 mL. Calculate the density of silver.

Ex. 3 In the opening sequence of “Raiders of the Lost Ark,” Indiana Jones steals a gold

statue by replacing it with a bag of sand. If the statue has a volume of about 1.5 L and gold has a density of 19.3 g/cm3, how much does the statue weigh in pounds?

Ex. 4 The average density of the Earth is 5,515 kg/m3. What is its density in grams per cubic

centimeter?


1.10 TESTING A HYPOTHESIS: THE BIG BANG REVISITED Temperature: – A measure of the average energy of a single particle in a system.

The instrument for measuring temperature is a thermometer. Temperature is generally measured with these units:

References Fahrenheit scale (°F)

English system Celsius scale (°C)

Metric system freezing point for water 32°F 0°C

boiling point for water 212°F 100°C

Nice summer day in Seattle 77°F 25°C

Conversion between Fahrenheit and Celsius scales:

°C = (°F - 32)

1.8 °F = (°C ×1.8) + 32

Kelvin Temperature Scale – There is a third scale for measuring temperature: the Kelvin scale. – The unit for temperature in the Kelvin scale is Kelvin (K, NOT °K!). – The Kelvin scale assigns a value of zero kelvins (0 K) to the lowest possible temperature, which we call absolute zero and corresponds to –273.15°C. – The term absolute zero is used to indicate the theoretical lowest temperature. Conversion between °C and K: K = ˚C + 273.15 C = K – 273.15

Example: Liquid nitrogen boils at 77K. What is this temperature in ˚C and in ˚F? PERCENTAGES

Percent: Ratio of parts per 100 parts → 10% is 10010 , 25% is

10025 , etc.

To calculate percent, divide one quantity by the total of all quantities in sample:

Percentage = sample total

part one ×100%


Ex. 1 In a chemistry class with 25 women and 20 men. What percentage of the class is female? What percentage is male? (Express your answers to 3 sig figs.)

Writing out Percentage as Unit Factors Example: A 1968 penny was cast from a mixture of 95.0% copper and 5.0% zinc by

mass. Write four unit factors using this information. Percentage Practice Problems

Ex. 1 Steel is an alloy of iron mixed with elements like carbon and chromium. If high carbon steel is 1.35% carbon by mass, what mass of the steel contains 3.50 g of carbon?

Ex. 2 How many kilograms of copper are present in 100.0 lbs of 1968 pennies.

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Chapter 1: Chemical Foundations (Topics to Review)resources.seattlecentral.edu/faculty/mvillarba/CHEM161/Chapter01...the least number of significant figures. ... we can count exactly