Chapter 3

Scientific Measurement

Measurements are essential !!

• One of your most important skills in chemistry is making measurements



Measurement

Has both a quantity and a unit   Ex. 125.3mL

125.3g

Types of Measurements

• Quantitative measurements- give results in definite form, usually numbers – Ex. A child’s temperature is 101.2

– Ex. A child feels feverish o F • Qualitative measurements – give results in descriptive nonnumeric form

Quantitative or Qualitative?

• The plant is growing fast • John wears a size 8 shoe • The candle weighs 90g • The flame is hot • Wax is soft • The boy grew 12cm • Lead is very dense

When making measurements, you can only estimate 1 digit !!!!!!!!!

Measuring Length

• Length – (meters) – use meter stick or metric ruler.

– Calibrated in cm.

0cm 1cm 2cm

Measuring Mass

• Mass =the amount of matter in a substance • Measured in grams (g) • Use digital balance up to 400 grams • Triple beam balance used for heavier masses

Digital Balance

• Make sure balance is set on

grams

• Place empty container on balance.

• Hit “Tare” or “Zero” button to remove the mass of the container.

• Add chemical to amount needed.

Triple Beam Balance

• Make sure riders are set at zero.

• Start with middle rider. Move until it’s too much, then move back one notch. • Then move back rider. Move until it’s too much, then move back one notch.

• Slide front rider until it balances.

• Add amounts of riders together.

Liquid Volume

• Volume =the amount of space it

takes up.

• Measured in mL.

• Use graduated cylinders.

• Read bottom of meniscus,

upward.

except in liquids like mercury that curve

Solid Volume

• Regular shape – use formula (cm 3 ) – Rectangle or cube = L x W x H – Cylinder = πr

2 x H

– Cone = 1/3 x πr

2 x H

– Sphere = 4/3 x πr

3

• Irregular shape – water displacement (mL) – Collect water from overflow can or

measure how much level goes up

1mL = 1 cm

3

* Know this conversion factor !!!!!

Weight

• Weight =the pull of gravity on

an object.

• Measured in newtons.

• Use spring scale.

Density

Density

Density

 Ratio of mass to volume  No set unit, depends of unit of mass and volume  g/cm 3 or g/mL, etc.



Density = mass/volume

Ws. Density Problems ( with answers)  Ws. Density Problems (II)

Indirect Measurement

  Used when matter is too large or too small to measure

Ex. To find the thickness of 1 playing card, find thickness of 100 cards and divided answer by 100.

How could you find the density of a concrete patio?



What is the difference between the terms precision and accuracy?

Accuracy and Precision

 Accuracy - how close the measurement is to accepted value  Precision - how close a series of measurements are to each other.

Three students made multiple weighings of a copper cylinder, each using a different balance. Describe the accuracy and precision of each student’s measurements if the correct mass of the cylinder is 47.32g

Lisa Weighing 1 47.03

Lamont 47.34

Leigh 47.95

Weighing 2 47.94

Weighing 3 46.83

Weighing 4 47.47

Inaccurate & imprecise

47.39

47.31

47.33

47.91

47.90

47.93

Accurate & precise Inaccurate & precise

“Calibrating” an instrument improves it’s accuracy

 

Calculating Error

Ex. Thermometer in pure boiling water reads 99.1

o C (experimental value) Accepted value is 100 o C 

Error = experimental value - accepted value 99.1

o C - 100 o C = -0.9

o C

* Can be a positive or negative number

Percentage Error

error Percentage = error accepted value X 100 = 0.9

o C 100.0

o C X 100 = 0.9%

Ws. Percent Error Problems

 

Scientific Notation

Used to show large or small numbers

602,000,000,000,000,000,000,000 is written 6.02 x 10 23

Coefficient Greater or equal to 1, and less than 10 Shows power of 10 ( number of places decimal was moved)

     If you move the decimal to the left , power is a positive number If you move the decimal to the right , the power is a negative number.

Ex.

0.000 000 000 000 000 000 000 327g Is written: 3.27 x 10 -22

    

Practice Problems

84,000 = 6,300,000 = 0.00025 = 0.000 008 = 0.00736 =

Multiplication with Scientific Notation  Multiply the coefficients and Add the exponents.

(3 x 10 4 ) x ( 2 x 10 2 )= 6 x 10 6 (2.1 x 10 3 ) x (4.0 x 10 -7 ) = 8.4 x 10 -4

Division with scientific notation

Divide the coefficients and Subtract the exponent in denominator by exponent in numerator 3.0 x 10 5 6.0 x 10 2 = 0.5 x 10 3 = 5.0 x 10 2

Addition and Subtraction with Scientific notation   When adding or subtracting the exponents must be the same

Ex. 5.4 x 10 3 and 8.0 x 10 2

Change:

8.0 x 10 2 = 0.80 x 10 3

Then add (or subtract) coefficients:

5.4 x 10 3 + 0.80 x 10 3 = 6.2 x 10 3

Ws. Scientific Notation

Significant Figures

 All measurements must be reported with the correct number of significant figures in order to calculate the answer .

What is a Significant Figure?

  “Sig-Figs” include all the digits known plus the last digit that is estimated

Ex.

 

You use the scale in the produce section of the store to get an approximate weight of your vegetables. The scale is calibrated in 0.1lb intervals Your vegetables are between 2.4 and 2.5lbs.so you estimate its weight to be 2.46lbs.

Your answer has three significant figures

Significant figures  All non-zero numbers are always significant  Zeros are tricky…..

 Leading  Captive zeros NEVER zeros ALWAYS significant (0.005) significant (505)  Trailing zeros SOMETIMES ….

( decimal-yes otherwise no) 5.000 (yes) 5,000 (no)

“Sig-Fig” Rules

1.

All nonzero digits are assumed significant.

Ex. 24.7meters, 7.43meter and 714meters -all have three significant figures

2.

Zeros appearing between nonzero digits are significant.

Ex. 7003 meters 40.79 meters 1.503 meters -all have four significant figures

3.

Leftmost zeros appearing in front of nonzero

digits are NOT significant. (They are placeholders)

Ex. 0.0071 meters 0.42 meters 0.000 099 meters -all have only two “sig-figs”. -You can eliminate the zeros by writing it in scientific notation 7.1 x 10 -3 meter 4.2 x 10 -1 9.9 x 10 -5 meter meter

4. Zeros at the end of a number and to the right of a decimal point are always significant.

Ex. 43.00 meters 1.010 meters 9.000 meters -all have four significant figures

5.

Trailing Zeros at the rightmost end of a measurement are NOT

significant (They are placeholders)

Ex 300m – has 1 “sig-fig” 7000m – has 1 “sig-fig” 27,210m – has 4 “sig-figs”

6.

There are two situations when you have an unlimited number of “sig 1. Counting – Ex. 23 people in the classroom 2. Using exactly defined quantities.

Ex. 60min. = 1 hour 500 pages = 1 ream

How many “Sig-figs” are there?

      123m =

(3)

9.8000 x 10 4

(5)

22 meter sticks = 0.07080 m = 98,000 m =

(4) (5) (unlimited) (2)

Why are Sig-Figs So Important?

© Copyrght, 2001, L. Ladon. Permission is granted to use and duplicate these materials for non-profit educational use, under the following conditions: No changes or modifications will be made without written permission from the author.



Being careless with significant figures may result in dire consequences. The following is a true story told to me by a Baltimore County middle school teacher concerning their mishap resulting from not considering the significance of significant figures:



The science teachers at a Baltimore County middle school wished to acquire a steel cube, one cubic centimeter in size to use as a visual aid to teach the metric system. The machine shop they contacted sent them a work order with instructions to draw the cube and specify its dimensions. On the work order, the science supervisor drew a cube and specified each side to be 1.000 cm. When the machine shop received this job request, they contacted the supervisor to double check that each side was to be one centimeter to four significant figures. The science supervisor, not thinking about the "logistics", verified four significant figures.



When the finished cube arrived approximately one month later, it appeared to be a work of art. The sides were mirror smooth and the edges razor sharp. When they looked at the "bottom line", they were shocked to see the cost of the cube to be $500! Thinking an error was made in billing, they contacted the machine shop to ask if the bill was really $5.00, and not $500. At this time, the machine shop verified that the cube was to be made to four significant figure specifications. It was explained to the school, that in order to make a cube of such a high degree of certainty, in addition to using an expensive alloy with a low coefficient of expansion, many man hours were needed to make the cube. The cube had to be ground down, and measured with calipers to within a certain tolerance. This process was repeated until three sides of the cube were successfully completed. So, "parts and labor" to prepare the cube cost $500. The science budget for the school was wiped out for the entire year. This school now has a steel cube worth its weight in gold, because it is a very certain cubic centimeter in size.

Significant figures  All non-zero numbers are always significant  Zeros are tricky…..

 Leading  Captive zeros NEVER zeros ALWAYS significant (0.005) significant (505)  Trailing zeros SOMETIMES ….

( decimal-yes otherwise no) 5.000 (yes) 5,000 (no)

Use “Oceans” to determine Sig-Figs Pacific Decimal “Present” Atlantic Decimal “Absent”

Start counting with first nonzero number and count all numbers after it.

Using “Sig-Figs” when Calculating

 A calculated answer can not be more precise than the

least

precise measurement used in the calculation For multiplication and division use least # of sig-figs in measurements you are multiplying or dividing

   Try this: 6.9cm x 0.0876cm

Multiply or divide numbers Put into scientific notation Round to the correct # of sig-figs

7.7 meters 5.4 meters 7.7m x 5.4m = 41.58 sq. meters Since measurements only have 2 “sig-figs” then Answer can only have 2 “sig-figs”

Round answer to appropriate number of “sig-figs”

= 4.2 x 10 1 square meters

For addition and subtraction use least number of decimal places in measurements you are adding or subtracting

2.45g + 4.987g = 7.437g

= 7.44g

Take the following answers and round each to the correct number of significant figures. Be sure to include the unit label.

(14.3g ) ÷ (2.03cm

3 ) = 7.0443348g/cm3

7.04g/cm 3

3.004m x 26.4m = 79.3056m

2

7.93 x 10 1 m 2

301.00 L – 99.8643 L = 201.1357L

2.01 x 10 2 L

Math Rules for Sig Fig 

Multiplying and dividing sig fig

 Your answer can only have as many sig fig as the least sig fig in the problem

Math Rules for Sig Fig 

Adding and subtracting

 Your answer can only have as many decimal places as the least in the problem

Rounding Problems

 Round each measurement to the number of “sig-figs” shown in parentheses. Write answers in scientific notation first !!!!

   314.721 meters (four) 0.001 775 meters (two) 8792 meters (two)

= 3.147 x 10 2 = 1.8 x10 -3 = 8.8 x 10 3

Meters, Liters and Grams - YouTube

The International System of Measurement (SI)

• Metric System was developed in France in 1795 • Revised and called International System of Measurements (SI) in 1960 • Based on units of ten

SI Base Units

Quantity SI base unit symbol

Length Meter m Mass Temperature Time Liquid volume Amount of substance gram Kelvin Celsius Second Liter Mole g K o C s L mol

Metric Prefixes and Abbreviations

“Kids haven’t died by doing crazy metric”

kilo hecto deka

basic

deci centi milli

unit (k) (h) (da) (m,L,g) (d) (c ) (m)

Memorize these !!!!!

* “unit” means meter, liter or grams        1 Kilo = 1000 units 1 Hecto = 100 units 1 Deka = 10 units Basic unit = 1 10 deci = 1 unit 100 centi = 1 unit 1000 milli = 1 unit 1Giga(G) =

1 x 10 9 units

1Mega(M) =

1 x 10 6 units

1 x 10 6 1 x 10 9 1 x 10 12 Micro(µ) =

1 unit

Nano(n) =

1 unit

Pico(p) =

1 unit

Conversion factors

 A

ratio

 of equivalent measurements

Ex. 1 dollar = 4 quarters = 10 dimes = 100 pennies

1 dollar 4 quarters or 4 quarters 1 dollar

          

Other Conversion factors

1 week = 7 days 1 year = 365 days 1 decade = 10 years 1 century = 100 years 24 hours = 1 day 1 hour = 60 min.

60 sec = 1 min 1 ft. = 12 in.

1 yd = 36 in 1 yd = 3 ft.

5280 ft = 1 mile

Dimensional Analysis

    A way to solve problems using units, dimensions or measurements

Use “T” boxes

Start with known, work toward unit you want Ex. How many seconds in 8 hours?

Practice problems (use “T” boxes)

     3500 days = ______________ years 4000 days = _______________ decades 83,972.7 minutes = ____________weeks 546 months = _______________ century 5.6 km = _________________ mm

Converting Metric Units to Metric units (2 step-process)  Go from “known” to a basic unit, then basic unit to unit you want.

236.6 kg = __________cg

 Try this one…….

2,998,766 cL = ________________hL

3.9 x 10

14

decigrams = ____ Gigagrams?

  Use “T” boxes convert into basic unit, then to unit needed 3.9 x10 14 dg

g Gg dg g = 3.9 x 10

6

Gg

If two “ knowns ” or “per”……. Use Double “T” box and Fix one at a time.

 If a car is traveling at 65 kilometers per hour, what is its speed in

meters per second?

Writing answers correctly

  Must be in scientific notation Must have correct number of significant figures.   Don’t count the sig-figs in conversion factors Count sig-figs in “known” and put the answer in the same number of sig-figs.

Heat (Thermal Energy)

• The energy in the motion of atoms and molecules

The more heat energy in matter, the faster the atoms or molecules move .

Temperature

- the average kinetic( motion) energy of molecules in a substance.

- measured using a thermometer.

Measuring heat energy

calorie - the amount of heat needed to raise 1 gram of water 1 o C.

1 calorie = 4.18 joules (SI unit of energy) Btu ( British thermal unit) = 252 calories or the amt. of thermal energy to raise 1 pound of water 1 o F

Specific Heat

-different substances absorb different amounts and therefore get “hotter” at different rates.

- Specific heat is the amount of heat needed to raise 1 gram of a substance 1 degree celsius abbreviated “c”

Calculating Heat Change

Heat in calories Change in temperature

Q= mc

DT

Mass in grams Specific heat

Specific Heat Chart

Substance Specific heat

Water Aluminum Iron Copper Zinc Silver Lead 1.0

0.215

0.11

0.092

0.091

0.052

0.04

The Law of Dulong and Petit

Dulong Petit

-they found that s.h. depends on # of atoms/gram.

Heavier atoms = fewer atoms/g = lower s.h.

1 gram Heat up faster (lower s.h.) 1 gram Heat up slower (higher s.h.)

-the less atoms/gram means more energy for each atom and therefore they heat up faster.

Specific Heat Chart

Substance (atomic Mass)

Water (18.0) Aluminum (26.98) Iron (55.85) Copper (63.55) Zinc (65.39) Silver (107.87) Lead (207.2)

Specific heat

1.0

0.215

0.11

0.092

0.091

0.052

0.04

The higher the specific heat, the more heat it needs to raise its temperature.

Ws. Specific Heat Problems

Temperature Scales

Fahrenheit Celsius Kelvin Water Boils

212 o F 100 o C 373K

Water Freezes

32 o F 0 o C 273K

Molecular Motion Stops

-460 o F -273 o C 0K (absolute zero)

Converting between Temperature Scales

From Fahrenheit to Celsius:

o

C = 5/9 (

o

F-32)

Ex. What is the Celsius value for 60.0

o F?

o

o C = 5/9(60-32) o C = 5/9(28) o C = 15.55

C =15.6

( look at Sig-Figs of other temperature reading)

From Celsius to Fahrenheit:

o

F =(9/5 x

o

C) + 32

Ex. What is the Fahrenheit value for 85.0

o C?

o F = (9/5 x 85.0) + 32 o F = (153) + 32 o F = 185

From Celsius to Kelvin:

K =

o

C + 273

Ex. 80.0

o C would be what value on the Kelvin scale?

K = 80 + 273 K = 353

From Kelvin to Celsius:

o

C = K - 273

Ex. 459K would be what value on the Celsius scale?

o C = 459 - 273 o C = 186

From Fahrenheit to Kelvin:

K = 5/9 (

o

F + 460)

Ex. What would 45.0

o F be on the Kelvin scale?

K = 5/9(45 + 460) K = 5/9(505) K = 280.55 = 281

From Kelvin to Fahrenheit:

o

F = (9/5 x K ) - 460

Ex. 690.K would be what value on the Fahrenheit scale?

o F = (9/5 x 690) - 460 o F = (1242) - 460 o F = 782

Liquid Thermometers

-Work on the principle of thermal expansion.

- the expansion of the liquid is proportional to the change in temperature.

-silver- mercury - red- alcohol

Digital thermometers

-measure change in electrical resistance in a wire caused by temperature change.

Liquid Crystal Thermometers

- crystals between thin sheets of plastic change as temperature increases, causing them to change structure and color.

Ws. Temperature Conversions Ws. Temperature Conversions ( word Problems)

 Review for Test Know how to put # into

scientific notation

 Know how to determine

Sig-Figs

in the answer.

and how many should be  Measurements must be in

scientific notation, correct sig-figs and have a unit.

 Be able to convert from unit to another. then= and divide across the bottom Mulitply across top 

Conversion factors

– above and below must be equal. Cross out unit if on top and bottom.



Metric Conversion-

you want unit you have to basic unit to unit

Review for Test  Know the terms accuracy and precision  Know that the density of water is 1g/mL  Know that 1 mL = 1 cm 3  Define temperature  Calculate specific heat problems  Dulong and Petit  Know how water displacement is used to find volume  Know how to manipulate the density equation

Memorize these !!!!!

* “unit” means meter, liter or grams        1 Kilo = 1000 units 1 Hecto = 100 units 1 Deka = 10 units Basic unit = 1 10 deci = 1 unit 100 centi = 1 unit 1000 milli = 1 unit 1Giga(G) =

1 x 10 9 units

1Mega(M) =

1 x 10 6 units

1 x 10 6 1 x 10 9 1 x 10 12 Micro(µ) =

1 unit

Nano(n) =

1 unit

Pico(p) =

1 unit

Formulas You MUST Know     % error = error/ accepted value x 100 Density = mass/volume Specific heat Q=mc ∆T Celsius to Kelvin- add 273 to Celsius temperature

Ws. Problem Solving

Last Hint  Look over all practice worksheets, especially Dimensional analysis problems and metric conversions!!!!!