Chapter 2 Scientific Measurement. Chapter 2 Goals – Scientific Measurement Calculate values from...

Chapter 2Chapter 2

Scientific MeasurementScientific Measurement

Chapter 2 Goals – Scientific Chapter 2 Goals – Scientific MeasurementMeasurement

Calculate values from measurements using Calculate values from measurements using the correct number of significant figures.the correct number of significant figures.

List common SI units of measurement and List common SI units of measurement and common prefixes used in the SI system.common prefixes used in the SI system.

Distinguish mass, volume, density, and Distinguish mass, volume, density, and specific gravity from one another.specific gravity from one another.

Evaluate the accuracy of measurements Evaluate the accuracy of measurements using appropriate methods.using appropriate methods.

IntroductionIntroduction

Everyone uses measurements in some formEveryone uses measurements in some form Deciding how to dress based on the Deciding how to dress based on the

temperature; measuring ingredients for a temperature; measuring ingredients for a recipes; construction.recipes; construction.

Measurement is also fundamental in the Measurement is also fundamental in the sciences and for understanding scientific sciences and for understanding scientific conceptsconcepts It is important to be able to take good It is important to be able to take good

measurements and to decide whether a measurements and to decide whether a measurement is good or badmeasurement is good or bad

IntroductionIntroduction

In this class we will make In this class we will make measurements and express their measurements and express their values using the International values using the International System of Units or the System of Units or the SI systemSI system.. All measurements have two parts: a All measurements have two parts: a

numbernumber and a and a unitunit..

2.1 The Importance of 2.1 The Importance of MeasurementMeasurement

QualitativeQualitative versus versus QuantitativeQuantitative MeasurementsMeasurements Qualitative measurementsQualitative measurements give give

results in a descriptive, nonnumeric results in a descriptive, nonnumeric form; can be influenced by individual form; can be influenced by individual perceptionperception

Example: This room feels cold.Example: This room feels cold.

2.1 The Importance of 2.1 The Importance of MeasurementMeasurement

QualitativeQualitative versus versus QuantitativeQuantitative MeasurementsMeasurements Quantitative measurements Quantitative measurements give results in give results in

definite form usually, using numbers; these definite form usually, using numbers; these types of measurements eliminate personal bias types of measurements eliminate personal bias by using measuring instruments.by using measuring instruments.

Example: Using a thermometer, I determined Example: Using a thermometer, I determined that this room is 24°C (~75°F)that this room is 24°C (~75°F)

Measurements can be no more Measurements can be no more reliable than the measuring reliable than the measuring instrument.instrument.

2.1 Concept Practice2.1 Concept Practice1. You measure 1 liter of water by filling an 1. You measure 1 liter of water by filling an

empty 2-liter soda bottle half way. How can you empty 2-liter soda bottle half way. How can you improve the accuracy of this measurement?improve the accuracy of this measurement?

2. Classify each measurement as qualitative or 2. Classify each measurement as qualitative or quantitative.quantitative.a. The basketball is browna. The basketball is brownb. the diameter of the basketball is 31 b. the diameter of the basketball is 31 centimeterscentimetersc. The air pressure in the basketball is 12 lbs/inc. The air pressure in the basketball is 12 lbs/in22

d. The surface of the basketball has indented d. The surface of the basketball has indented seamsseams

2.2 Accuracy and 2.2 Accuracy and PrecisionPrecision

Good measurements in the lab are both Good measurements in the lab are both correct correct (accurate)(accurate) and reproducible and reproducible (precise)(precise) accuracyaccuracy – how close a single measurement – how close a single measurement

comes to the actual dimension or true value comes to the actual dimension or true value of whatever is measuredof whatever is measured

precisionprecision – how close several – how close several measurements are to the same valuemeasurements are to the same value

Example: Figure 2.2, page 29 – Dart Example: Figure 2.2, page 29 – Dart boards….boards….

2.2 Accuracy and 2.2 Accuracy and PrecisionPrecision

All measurements made with instruments All measurements made with instruments are really approximations that depend on are really approximations that depend on the the quality of the instruments (accuracy) and the and the skill of the person doing the skill of the person doing the measurement measurement (precision)(precision)

The precision of the instrument depends The precision of the instrument depends on the how small the scale is on the device. on the how small the scale is on the device. The finer the scale the more precise the The finer the scale the more precise the

instrument.instrument. 2.2 Demo, page 282.2 Demo, page 28

2.2 Concept Practice2.2 Concept Practice3. Which of these synonyms or 3. Which of these synonyms or

characteristics apply to the concept characteristics apply to the concept of accuracy? Which apply to the of accuracy? Which apply to the concept of precision?concept of precision?

a. multiple measurementsa. multiple measurements

b. correctb. correct

c. repeatablec. repeatable

d. reproducibled. reproducible

e. single measuremente. single measurement

f. true valuef. true value

2.2 Concept Practice2.2 Concept Practice

4. Under what circumstances could a 4. Under what circumstances could a series of measurements of the same series of measurements of the same quantity be precise but inaccurate?quantity be precise but inaccurate?

2.3 Scientific Notation2.3 Scientific Notation In chemistry, you will often encounter In chemistry, you will often encounter

numbers that are very large or very smallnumbers that are very large or very small One atom of gold = One atom of gold =

0.000000000000000000000327g0.000000000000000000000327g One gram of H = One gram of H =

301,000,000,000,000,000,000,000 H molecules301,000,000,000,000,000,000,000 H molecules Writing and using numbers this large or Writing and using numbers this large or

small is calculations can be difficultsmall is calculations can be difficult It is easier to work with these numbers by It is easier to work with these numbers by

writing them in writing them in exponentialexponential or or scientific scientific notationnotation

2.3 Scientific Notation2.3 Scientific Notation scientific notationscientific notation – a number is – a number is

written as the product of two numbers: a written as the product of two numbers: a coefficient and a power of tencoefficient and a power of ten

Example: 36,000 is written in scientific Example: 36,000 is written in scientific notation as 3.6 x 10notation as 3.6 x 1044 or 3.6e4 or 3.6e4 Coefficient = 3.6 → a number greater than Coefficient = 3.6 → a number greater than

or equal to 1 and less than 10.or equal to 1 and less than 10. Power of ten / exponent = 4Power of ten / exponent = 4 3.6 x 103.6 x 1044 = 3.6 x 10 x 10 x 10 x 10 = 36,000 = 3.6 x 10 x 10 x 10 x 10 = 36,000

2.3 Scientific Notation2.3 Scientific Notation

When writing numbers greater than When writing numbers greater than ten in scientific notation ten in scientific notation the the exponent is positive and equal to exponent is positive and equal to the number of places that the the number of places that the exponent has been moved to the exponent has been moved to the leftleft..


Numbers less than one have a Numbers less than one have a negative negative exponentexponent when written in scientific when written in scientific notation.notation. Example: 0.0081 is written in scientific Example: 0.0081 is written in scientific

notation as 8.1 x 10notation as 8.1 x 10-3-3

8.1 x 108.1 x 10-3-3 = 8.1/(10 x 10 x 10) = 0.0081 = 8.1/(10 x 10 x 10) = 0.0081 When writing a number less than one in When writing a number less than one in

scientific notation, scientific notation, the value of the the value of the exponent equals the number of exponent equals the number of places you move the decimal to the places you move the decimal to the rightright..

2.3 Scientific Notation2.3 Scientific Notation To To multiplymultiply numbers written in scientific numbers written in scientific

notation, notation, multiply the coefficients and multiply the coefficients and add the exponentsadd the exponents.. (3 x 10(3 x 1044) x (2 x 10) x (2 x 1022) = (3 x 2) x 10) = (3 x 2) x 104+24+2 = 6 x 10 = 6 x 1066

To To dividedivide numbers written in scientific numbers written in scientific notation, notation, divide the coefficients and divide the coefficients and subtract the exponent in the subtract the exponent in the denominator (bottom) from the denominator (bottom) from the exponent in the numerator (top)exponent in the numerator (top).. (6 x 10(6 x 1033)/(2 x 10)/(2 x 1022) = (6/2) x 10) = (6/2) x 103-23-2 = 3 x 10 = 3 x 1011


Before numbers written in scientific Before numbers written in scientific notation are notation are addedadded or or subtractedsubtracted, , the exponents must be made the the exponents must be made the same same (as a part of aligning the (as a part of aligning the decimal points).decimal points). (5.4 x 10(5.4 x 1033)+(6 x 10)+(6 x 1022) = (5.4 x 10) = (5.4 x 1033)+(0.6 )+(0.6

x 10x 1033) )

= (5.4 + 0.60) x 10= (5.4 + 0.60) x 1033 = 6.0 x 10 = 6.0 x 1033


5. Write the two measurements given 5. Write the two measurements given in the first paragraph of this section in the first paragraph of this section in scientific notation.in scientific notation.

a. mass of a gold atom = a. mass of a gold atom = 0.000000000000000000000327g0.000000000000000000000327g

b. molecules of hydrogen =b. molecules of hydrogen =

301,000,000,000,000,000,000,000 H 301,000,000,000,000,000,000,000 H moleculesmolecules

2.3 Concept Practice2.3 Concept Practice6. Write these measurements in scientific 6. Write these measurements in scientific

notation. The abbreviation m stands for notation. The abbreviation m stands for meter, a unit of length.meter, a unit of length.a. The length of a football field, 91.4 m a. The length of a football field, 91.4 m b. The diameter of a carbon atom, b. The diameter of a carbon atom, 0.000000000154 m0.000000000154 m c. The radius of the Earth, 6,378,000 mc. The radius of the Earth, 6,378,000 md. The diameter of a human hair, 0.000008 d. The diameter of a human hair, 0.000008 m m e. The average distance between the e. The average distance between the centers of the sun and the Earth, centers of the sun and the Earth, 149,600,000,000 m149,600,000,000 m

2.4 Significant Figures in 2.4 Significant Figures in MeasurementMeasurement

The The significant figuressignificant figures in a in a measurement include measurement include all the digits all the digits that are known precisely plus one that are known precisely plus one last digit that is estimatedlast digit that is estimated.. Example: With a thermometer that has 1° Example: With a thermometer that has 1°

intervals, you may determine that the intervals, you may determine that the temperature is between 24°C and 25°C and temperature is between 24°C and 25°C and estimate it to be 24.3°C.estimate it to be 24.3°C. You know the first two digits (2 and 4) with You know the first two digits (2 and 4) with

certainty, and the third digit (3) is a “best guest”certainty, and the third digit (3) is a “best guest” By estimating the last digit, you get By estimating the last digit, you get

additional information additional information

RulesRules

1. Every nonzero digit in a recorded 1. Every nonzero digit in a recorded measurement measurement is significantis significant..- Example: 24.7 m, 0.743 m, and 714 m all - Example: 24.7 m, 0.743 m, and 714 m all have three sig. figs.have three sig. figs.

2. Zeros appearing between nonzero digits 2. Zeros appearing between nonzero digits are are significantsignificant..

- Example: 7003 m, 40.79 m, and 1.503 m all - Example: 7003 m, 40.79 m, and 1.503 m all have 4 sig. figs.have 4 sig. figs.

RulesRules

3. Zeros appearing in front of all nonzero digits 3. Zeros appearing in front of all nonzero digits are not significantare not significant; they act as placeholders ; they act as placeholders and cannot arbitrarily be dropped (you can get and cannot arbitrarily be dropped (you can get rid of them by writing the number in scientific rid of them by writing the number in scientific notation).notation).- Example: 0.0071 m has two sig. figs. And can - Example: 0.0071 m has two sig. figs. And can be written as 7.1 x 10be written as 7.1 x 10-3-3

4. Zeros at the end of the number and to 4. Zeros at the end of the number and to the right of a decimal point the right of a decimal point are always are always significantsignificant..- Example: 43.00 m, 1.010 m, and 9.000 - Example: 43.00 m, 1.010 m, and 9.000 all have 4 sig. figs.all have 4 sig. figs.

RulesRules

5. Zeros at the end of a measurement and 5. Zeros at the end of a measurement and to the left of the decimal point to the left of the decimal point are not are not significant unless they are significant unless they are measured valuesmeasured values (then they are (then they are significant). Numbers can be written in significant). Numbers can be written in scientific notation to remove ambiguity.scientific notation to remove ambiguity.

- Example: 7000 m has 1 sig. fig.; if - Example: 7000 m has 1 sig. fig.; if those zeros were measured it could be those zeros were measured it could be written as 7.000 x 10written as 7.000 x 1033

RulesRules

6. Measurements 6. Measurements have an unlimited have an unlimited number of significant figuresnumber of significant figures when when they they are counted or if they are are counted or if they are exactly defined quantitiesexactly defined quantities..

- Example: 23 people or 60 minutes = - Example: 23 people or 60 minutes = 1 hour1 hour

* You must recognize exact values to * You must recognize exact values to round of answers correctly in round of answers correctly in calculations involving measurements.calculations involving measurements.

Significant Figures – Significant Figures – Example 1Example 1

How many significant figures are in How many significant figures are in each of the following measurements?each of the following measurements?a. 123 ma. 123 m

b. 0.123 cmb. 0.123 cm

c. 40506 mmc. 40506 mm

d. 9.8000 x 10d. 9.8000 x 1044 m m

e. 4.5600 me. 4.5600 m

f. 22 meter sticksf. 22 meter sticks

g. 0.07080 mg. 0.07080 m

h. 98000 mh. 98000 m


7. Write each measurement in scientific 7. Write each measurement in scientific notation and determine the number of notation and determine the number of significant figures in each.significant figures in each.

a. 0.05730 ma. 0.05730 m

b. 8765 dmb. 8765 dm

c. 0.00073 mmc. 0.00073 mm

d. 12 basketball playersd. 12 basketball players

e. 0.010 kme. 0.010 km

f. 507 thumbtacksf. 507 thumbtacks

Significant Figures in Significant Figures in CalculationsCalculations

The number of significant figures in a The number of significant figures in a measurement refers to the precision of measurement refers to the precision of a measurement; a measurement; an answer cannot be an answer cannot be more precise than the least precise more precise than the least precise measurement from which it was measurement from which it was calculated.calculated. Example: The area of a room that measures Example: The area of a room that measures

7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is 7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be 41.58 mcalculated to be 41.58 m2 2 (4 sig. figs.) – you (4 sig. figs.) – you must round the answer to 42 mmust round the answer to 42 m22

Rounding – The Rule of 5Rounding – The Rule of 5

If the digit to the right of the last sig. fig If the digit to the right of the last sig. fig is less than 5, all the digits after the last is less than 5, all the digits after the last sig. fig. are dropped.sig. fig. are dropped. Example: 56.212 m rounds to 56.21 m (for 4 Example: 56.212 m rounds to 56.21 m (for 4

sig. figs.)sig. figs.)

If the digit to the right is 5 or greater, the If the digit to the right is 5 or greater, the value of the last sig. fig. is increased by 1.value of the last sig. fig. is increased by 1. Example: 56.216 m rounds to 56.22 m (for 4 Example: 56.216 m rounds to 56.22 m (for 4

sig. figs.)sig. figs.)

Rounding – Example 2Rounding – Example 2

Addition and SubtractionAddition and Subtraction

The answer to an addition or The answer to an addition or subtraction problem subtraction problem should be should be rounded to have the same number rounded to have the same number of decimal places as the of decimal places as the measurement with the least number measurement with the least number of decimal places.of decimal places.

Multiplication and Multiplication and DivisionDivision

In calculations involving multiplication and In calculations involving multiplication and division, the answer is rounded off to the division, the answer is rounded off to the number of significant figures in the least number of significant figures in the least precise term (least number of sig. figs.) in precise term (least number of sig. figs.) in the calculationsthe calculations

2.6 SI Units2.6 SI Units

The International System of Units, SI, is The International System of Units, SI, is a revised version of the metric systema revised version of the metric system

Correct units along with numerical Correct units along with numerical values are critical when communicating values are critical when communicating measurements.measurements.

The are seven base SI units (Table 2.1) The are seven base SI units (Table 2.1) of which other SI units are derived.of which other SI units are derived. Sometimes non-SI units are preferred for Sometimes non-SI units are preferred for

convenience or practical reasonsconvenience or practical reasons

2.6 SI Units – Table 2.22.6 SI Units – Table 2.2QuantityQuantity SI Base or Derived SI Base or Derived

UnitUnitNon-SI UnitNon-SI Unit

LengthLength meter (m)meter (m)

VolumeVolume cubic meter (mcubic meter (m33)) literliter

MassMass kilogram (kg)kilogram (kg)

DensityDensity grams per cubic grams per cubic centimeter (g/cmcentimeter (g/cm33); ); grams per mililiter grams per mililiter (g/mL)(g/mL)

TemperatTemperatureure

kelvin (K)kelvin (K) degree Celcius (°C) degree Celcius (°C)

TimeTime second (s)second (s)

PressurePressure Pascal (Pa)Pascal (Pa) atmosphere (atm); atmosphere (atm); milimeter of mercury milimeter of mercury (mm Hg)(mm Hg)

EnergyEnergy joule (J)joule (J) calorie (cal)calorie (cal)

Common SI Prefixes Common SI Prefixes

Units larger than the base unitUnits larger than the base unit

TeraTera TT ee-12-12 = = 0.0000000000010.000000000001

terameter terameter (Tm)(Tm)

GigaGiga GG ee-9 -9 = = 0.0000000010.000000001

gigameter gigameter (Gm)(Gm)

MegaMega MM ee-6 -6 = 0.000001= 0.000001 megameter megameter (Mm)(Mm)

KiloKilo kk ee-3 -3 = 0.001= 0.001 kilometer kilometer (km)(km)

HectHectoo

hh ee-2 -2 = 0.01= 0.01 hectometer hectometer (hm)(hm)

DekaDeka dada ee-1 -1 = 0.1= 0.1 decameter decameter (dam)(dam)

Base Base UnitUnit

ee0 0 = 1= 1 meter (m)meter (m)

Common SI PrefixesCommon SI Prefixes

Units smaller than the base unit Units smaller than the base unit

Base Base UnitUnit

ee0 0 = 1= 1 meter (m)meter (m)

DeciDeci dd ee1 1 = 10= 10 decimeter decimeter (dm)(dm)

CentiCenti cc ee2 2 = 100= 100 centimeter centimeter (cm)(cm)

MilliMilli mm ee3 3 = 1000= 1000 millimeter millimeter (mm)(mm)

MicroMicro μμ ee6 6 = 1,000,000= 1,000,000 micrometer micrometer ((μμm)m)

NanoNano nn ee9 9 = = 1,000,000,0001,000,000,000

Nanometer Nanometer (nm)(nm)

PicoPico pp ee12 12 = = 1,000,000,000,001,000,000,000,0000

picometer picometer (pm)(pm)

Common SI PrefixesCommon SI Prefixes

A mnemonic device can be used to A mnemonic device can be used to memorize these common prefixes in memorize these common prefixes in the correct order:the correct order: TThe he GGreat reat MMonarch onarch KKing ing HHenry enry DDied ied

BBy y DDrinking rinking CChocolate hocolate MMocha ocha MMilk ilk NNot ot PPilsnerilsner

2.7 Units of Length2.7 Units of Length

The basic unit of length is the The basic unit of length is the metermeter Prefixes can be used with the base Prefixes can be used with the base

unit to more easily represent small unit to more easily represent small or large measurementsor large measurements Example: A hyphen (12 point font) Example: A hyphen (12 point font)

measures about 0.001 m or 1 mm.measures about 0.001 m or 1 mm. Example: A marathon race is Example: A marathon race is

approximately approximately

42,000 m or 42 km.42,000 m or 42 km.


15. Use the tables in the text to order 15. Use the tables in the text to order these lengths from smallest to these lengths from smallest to largest.largest.

a. centimetera. centimeter

b. micrometerb. micrometer

c. kilometerc. kilometer

d. millimeterd. millimeter

e. metere. meter

f. decimeterf. decimeter

2.8 Units of Volume2.8 Units of Volume

The space occupied by any sample of The space occupied by any sample of matter is called its matter is called its volumevolume The volume ofThe volume of rectangular solids rectangular solids can can

be calculated by multiplying the be calculated by multiplying the lengthlength by by widthwidth by by heightheight Units are cubed because you are measuring Units are cubed because you are measuring

in 3 dimensionsin 3 dimensions Volume ofVolume of liquids liquids can be measured can be measured

with a with a graduated cylindergraduated cylinder, a , a pipetpipet, a , a buretburet, or a , or a volumetric flaskvolumetric flask


A convenient unit of measurement for A convenient unit of measurement for volume in everyday use is the liter (L)volume in everyday use is the liter (L)

Milliliters (mL) are commonly used for Milliliters (mL) are commonly used for smaller volume measurements and smaller volume measurements and liters (L) for larger measurementsliters (L) for larger measurements 1 mL = 1 cm1 mL = 1 cm33

10 cm x 10 cm x 10 cm = 1000 cm10 cm x 10 cm x 10 cm = 1000 cm33 = 1 L = 1 L


17. From what unit is a measure of 17. From what unit is a measure of volume derived?volume derived?

2.8 Practice2.8 Practice

18. What is the volume of a paperback 18. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 book 21 cm tall, 12 cm wide, and 3.5 cm thick?cm thick?

19. What is the volume of a glass 19. What is the volume of a glass cylinder with an inside diameter of cylinder with an inside diameter of 6.0 cm and a height of 28 cm?6.0 cm and a height of 28 cm?

V=V=ππrr22hh

2.9 Units of Mass2.9 Units of Mass A person on the moon would weigh 1/6 of A person on the moon would weigh 1/6 of

his/her weight on Earth.his/her weight on Earth. This is because the force of gravity on the This is because the force of gravity on the

moon is approximately 1/6 of its force of Earth.moon is approximately 1/6 of its force of Earth. Weight is a forceWeight is a force – it is a measure of the pull – it is a measure of the pull

on a given mass by gravity; it can change by on a given mass by gravity; it can change by location.location.

Mass is the quantity of matter an Mass is the quantity of matter an object containsobject contains Mass remains constant regardless of location.Mass remains constant regardless of location.

Mass v. WeightMass v. Weight

2.9 Units of Mass2.9 Units of Mass

The The kilogramkilogram is the basic SI unit of is the basic SI unit of massmass It is defined as the mass of 1 L of water It is defined as the mass of 1 L of water

at 4°C.at 4°C. A gram, which is a more commonly A gram, which is a more commonly

used unit of mass, is 1/1000 of a used unit of mass, is 1/1000 of a kilogramkilogram 1 gram = the mass of 1 cm1 gram = the mass of 1 cm33 of water at of water at

4°C.4°C.

2.9 Concept Practice2.9 Concept Practice20. As you climbed a mountain and the 20. As you climbed a mountain and the

force of gravity decreased, would your force of gravity decreased, would your weight increase, decrease, or remain weight increase, decrease, or remain constant? How would your mass constant? How would your mass change? Explain.change? Explain.

21. How many grams are in each of 21. How many grams are in each of these quantities?these quantities?

a. 1 cga. 1 cg b. 1 b. 1 μμgg c. 1 kgc. 1 kg d. 1mgd. 1mg

2.10 Density2.10 Density

DensityDensity is the ratio of the is the ratio of the massmass of of an object to its an object to its volumevolume..

Equation →Equation → D = mass/volumeD = mass/volume Common units: g/cmCommon units: g/cm33 or g/mL or g/mL Example: 10.0 cmExample: 10.0 cm33 of lead has a mass of lead has a mass

114 g114 g

Density (of lead) = 114 g / 10.0 cmDensity (of lead) = 114 g / 10.0 cm33 = = 11.4 g/cm11.4 g/cm33

See Table 2.7, page 46See Table 2.7, page 46

2.10 Density2.10 Density

Density determines if an object will Density determines if an object will float in a fluid substance.float in a fluid substance. Examples: Ice in water; hot air risesExamples: Ice in water; hot air rises

Density can be used to identify Density can be used to identify substancessubstances See Table 2.8, page 46See Table 2.8, page 46


22. The density of silver is 10.5 g/cm22. The density of silver is 10.5 g/cm33 at 20°C. What happens to the at 20°C. What happens to the density of a 68-g bar of silver that is density of a 68-g bar of silver that is cut in half?cut in half?


23. A student finds a shiny piece of metal 23. A student finds a shiny piece of metal that she thinks is aluminum. In the lab, that she thinks is aluminum. In the lab, she determines that the metal has a she determines that the metal has a volume of 245 cmvolume of 245 cm33 and a mass of 612 g. and a mass of 612 g. Is the metal aluminum?Is the metal aluminum?

24. A plastic ball with a volume of 19.7 24. A plastic ball with a volume of 19.7 cmcm33 has a mass of 15.8 g. Would this ball has a mass of 15.8 g. Would this ball sink or float in a container of gasoline?sink or float in a container of gasoline?

2.10 Specific Gravity 2.10 Specific Gravity (Relative Density)(Relative Density)

Specific gravitySpecific gravity is a comparison of the is a comparison of the density of a substance to the density of a density of a substance to the density of a reference substance, usually at the same reference substance, usually at the same temperature.temperature. Water at 4°C, which has a density of 1 g/cm3, Water at 4°C, which has a density of 1 g/cm3,

is commonly used as a reference substance.is commonly used as a reference substance.Specific gravity = Specific gravity = density of substance (g/cm3)density of substance (g/cm3)

density of water (g/cm3)density of water (g/cm3) Because units cancel, a measurement of Because units cancel, a measurement of

specific gravity has no unitsspecific gravity has no units A hydrometer can be used to measure the A hydrometer can be used to measure the

specific gravity of a liquid.specific gravity of a liquid.


25. Why doesn’t a measurement of specific 25. Why doesn’t a measurement of specific gravity have a unit?gravity have a unit?

26. Use the values in Table 2.8 to 26. Use the values in Table 2.8 to calculate the specific gravity of the calculate the specific gravity of the following substances.following substances.

a. Aluminuma. Aluminum b. Mercuryb. Mercury c. icec. ice

2.12 Measuring 2.12 Measuring TemperatureTemperature

Temperature determines the direction of Temperature determines the direction of heat transfer between two objects in heat transfer between two objects in contact with each other.contact with each other. Heat moves from the object at the Heat moves from the object at the higher higher

temperaturetemperature to the object at a to the object at a lower lower temperature.temperature.

TemperatureTemperature is a measure of is a measure of the degree the degree of hotness or coldness of an objectof hotness or coldness of an object..

Almost all substances expand with an Almost all substances expand with an increase in temperature and contract with increase in temperature and contract with a decrease in temperaturea decrease in temperature An important exception is waterAn important exception is water


There are various temperature There are various temperature scalesscales

On the On the CelsiusCelsius temperature scale temperature scale the the freezing point of water is freezing point of water is taken as 0°Ctaken as 0°C and the and the boiling point boiling point of water at 100°Cof water at 100°C


The The Kelvin scaleKelvin scale (or absolute scale) is (or absolute scale) is another temperature scale that is usedanother temperature scale that is used On the Kelvin scale the freezing point of On the Kelvin scale the freezing point of

water is water is

273 K273 K and the boiling point is and the boiling point is 373 K373 K (degrees are not used).(degrees are not used).

1°C = 1 Kelvin1°C = 1 Kelvin The zero point (0 K) on the Kelvin scale is The zero point (0 K) on the Kelvin scale is

called called absolute zeroabsolute zero and is equal to -273°C and is equal to -273°C Absolute zero is where all molecular motion stopsAbsolute zero is where all molecular motion stops


Converting Temperatures:Converting Temperatures: K = °C + 273K = °C + 273 °C = K - 273°C = K - 273


27. Surgical Instruments may be 27. Surgical Instruments may be sterilized by heating at 170°C for 1.5 sterilized by heating at 170°C for 1.5 hours. Convert 170°C to kelvins.hours. Convert 170°C to kelvins.

28. The boiling point of the element 28. The boiling point of the element argon is 87 K. What is the boiling argon is 87 K. What is the boiling point of argon in °C?point of argon in °C?

2.13 Evaluating 2.13 Evaluating MeasurementsMeasurements

Accuracy in measurement depends on Accuracy in measurement depends on the the quality of the measuring quality of the measuring instrumentinstrument and the and the skill of the skill of the person using the instrumentperson using the instrument.. Errors in measurement could have various Errors in measurement could have various

causescauses In order to evaluate the accuracy of a In order to evaluate the accuracy of a

measurement, you must be able to measurement, you must be able to compare it to the true or compare it to the true or accepted accepted valuevalue..


accepted valueaccepted value – the true or correct – the true or correct value based or reliable referencesvalue based or reliable references

experimental valueexperimental value – the measured – the measured value determined in the experimentvalue determined in the experiment

The difference between the The difference between the accepted valueaccepted value and the and the experimental valueexperimental value is the is the errorerror.. error = accepted value – experimental error = accepted value – experimental

valuevalue


The The percent errorpercent error is the is the errorerror divided by the divided by the accepted valueaccepted value, , expressed as a percentage of the expressed as a percentage of the accepted value.accepted value.

Percent Error =Percent Error = x 100 x 100

An error can be positive or negative, An error can be positive or negative, but an absolute value of error is used but an absolute value of error is used so that the percentage is positiveso that the percentage is positive

|error||error| AVAV


32. A student estimated the volume of 32. A student estimated the volume of a liquid in a beaker as 208 mL. a liquid in a beaker as 208 mL. When she poured the liquid into a When she poured the liquid into a graduated cylinder she measured graduated cylinder she measured the value as 200 mL. What is the the value as 200 mL. What is the percent error of the estimated percent error of the estimated volume from the beaker, taking the volume from the beaker, taking the graduated cylinder measurement as graduated cylinder measurement as the accepted value?the accepted value?

Chapter 2 Scientific Measurement. Chapter 2 Goals – Scientific Measurement Calculate values from...

Documents

Transcript of Chapter 2 Scientific Measurement. Chapter 2 Goals – Scientific Measurement Calculate values from...