Chapter 1 (Part 2) Measurements in Chemistry 1.7 … 1 (Part 2) Page 1 of 22 Chapter 1 (Part 2)...

Chapter 1 (Part 2) Page 1 of 22

Chapter 1 (Part 2) Measurements in Chemistry

1.7 Physical Quantities

English Units

Those of us who were raised in the US are very accustomed to these.

Elsewhere in the world, these are very confusing.

Weight: ounce (oz)

pound (lb) [16 ounces = 1 pound]

ton [2000 pounds = 1 ton]

Length: inch (in)

foot (ft) [12 inches = 1 foot]

yard (yd) [3 feet = 1 yard]

mile (mi) [5280 feet = 1 mile]

Volume: teaspoon (tsp)

tablespoon (Tbsp) [3 tsp = 1 Tbsp]

cup [16 Tbsp = 1 cup = 8 oz]

pint (pt) [2 cups = 1 pint = 16 oz]

quart (qt) [4cups = 2 pints = 1 quart = 32 oz]

gallon (gal) [4 quarts = 1 gallon=64oz]

SI Units

− The scientific community has chosen a modified version of the metric system as

the standard for recording and reporting measurements.

− Designated as SI (Systeme International) or International System of Units

Some SI Base Units

Measurement Name of Unit Abbr.

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Amount of substance mole mol

Derived Units

Volume cubic decimeter

= liter

dm3=10

-3m

3

L = dm3

Energy Joule J=kg x m2/sec

2

Notice that the English

system of units uses

ounces to describe both

weight and volume

measurements, which

adds to the confusion.


Unit Prefixes

Selected Prefixes in the Metric System

Prefix Abbr. Means Examples

mega M 106 1 Megawatt = 1,000,000

watts

1,000,000 watt =

1 Mwatt

kilo- k 103 1 kilogram = 1,000

grams 1000g = 1 kg

deci- d 10-1

1 dL = 0.1 liters 10 dL = 1 L

centi- c 10-2

1 cm = 0.01 meters 10

2 or 100 cm = 1 m

milli- m 10-3

1 mg = 0.001 grams 10

3 or 1000 mg = 1 g

micro- µ 10-6

1 microliter = 0.000001 liters 10

6 µL = 1L

nano- n 10-9

1nanometer = 0.00000001

meters

109 nm = 1 m

pico- p 10-12

1 picometer =

0.000000000001 meters

1012

pm= 1 m

Metric System

This is a slight variation on the SI units of measure that is in

common use in most countries other than the United States.

• Unit of mass is the gram (g) rather than the kilogram (1kg =1000g).

• Unit of volume is the liter (L) instead of the cubic meter

(1 m3 = 1000L).

• Unit of temperature is the Celsius degree (°C) rather than the Kelvin.

− Also known as the centigrade degree.

Know

by

heart


1.8 Measuring Mass, Length, & Volume

Mass Measurements

The terms mass and weight are often confused and interchanged.

• Mass - A measure of the amount of matter in an object.

(how much stuff is present)

• Weight - A measure of the gravitational force that the earth

or other large body exerts on an object.

e.g. We “weigh” less on the moon than on earth, but we have the

same mass.

Most useful: 1 lb = 16 oz = 454g

1 kg = 2.205 lb

Length, Area and Volume Measurements

For Length:

Most useful: 1 inch = 2.54 cm exactly

For Areas, that is easy to see:

A square meter (m2) is an area 1 meter on each side.

For volumes this is also true, but the final unit is often given a

new name.

A cubic centimeter (cm3 or cc) is an area 1 cm on each side = 1mL = 1cc

A cubic decimeter (dm3) is an area 1 dm on each side = 1 L


Most useful: 1 L = 1.057 qt

32 oz = 1 qt

1.9 Measurement and Significant Figures

Numbers vs Data – Significant Figures

• In math class

• , numbers are theoretical, exact species.

• In science, most numbers are associated with measurements.

Uncertainty of Data

All measurements contain some uncertainty.

• We make errors

• Tools have limits

We need to be able to show what degree of

confidence we have in a piece of data.

• The value recorded should use all the digits

known with certainty,

plus one estimated digit.


• Significant figures – The number of meaningful digits used

to express a value.

Determining Significant Digits

− Last digit is uncertain

− Non-zero digits are ALWAYS significant.

− Zeros depend on whether they are leading, captive, or trailing

− LEADING zeroes are NEVER significant

− IMBEDDED zeros are ALWAYS significant

− TRAILING zeroes Depend

after a decimal point ARE significant

at the end of a # with no decimal point – we can’t tell

− Numbers with decimal points will be considered to be significant.

(Confusion can be avoided by using scientific notation)

− Numbers that are definitions (e.g. 1 gallon = 4 quarts) have an infinite

number of significant figures.

− Anything that gets counted in integer values is treated as exact.

Problem: How many significant figures are in:

a) 4009

b) 0.0455

c) 2806.0

d) 0.8904

e) 27.401

f) 4200.

g) 4200


1.10 Scientific Notation

Scientific notation is typically used to express very large or very

small numbers or to clarify the number of significant digits present

− Expressed as N x 10n

− N is the digit term and is a number between 1 and 10.

− n is the exponential term.

− In scientific notation, all digits are significant.

− When converting a number to scientific notation:

− For every place you move the decimal to the left, add a power of 10.

Example: 1 2 3 , 0 0 0 , 0 0 0 = 1.23 x 108

(positive powers of 10 are for BIG numbers)

− For every place you move the decimal to the Right, subtract a power

of 10.

Example: 0 . 0 0 0 0 0 0 1 2 3 = 1.23 x 10-7

(negative powers of 10 are for SMALL numbers)


Problem: Write the following in scientific notation:

a) 38666

b) 0.00407

c) 1300 to 2 sf

d) 1300 to 3 sf

e) 0.0000590

We also need to be able to convert values that are shown in

scientific notation back to standard notation.

Problem: Write the following in standard notation:

a) 4.85 x 10-3

b) 3.270 x 103

c) 3.270 x 102

d) 8.819 x 10-6

e) 4.5500 x 103

1.11 Rounding Off Numbers

Calculators often display more digits than are justified by the precision of

the data.

− The last digit to be retained is increased by one if the following digit is

5 or greater. (i.e., 5,6,7,8, or 9)

− Example: 0.57266 rounded to 2 sf =

− The last digit to be retained is left unchanged if the following digit is 4

or less. (i.e., 0,1,2,3, or 4)

− Example: 0.57266 rounded to 3 sf =


Round off the following numbers to the correct number of

significant figures:

Raw # Sig Figs Rounded In sci. not.

1.6753

1.6753

1.6753

1099.7

1099.7

1099.7

In the second example, we cannot tell once the number is rounded,

how many significant figures the number represents.

Scientific Notation (and Sig Figs) on Calculators

When calculators display numbers in scientific notation, the

display may show

• an E followed by a number

• 10x

• simply a number set off to the right side.


To change a value to scientific notation:

Using your calculator, convert the following to scientific notation:

a) 38666 3.8666 x 104

b) 0.00407 4.07 x 10-4

c) 1300 to 2 sf 1.3 x 103

d) 1300 to 3 sf 1.30 x 103

To change a value to standard notation:

Using your calculator, convert the following to standard notation:

a) 4.85 x 10-3

0.00485

b) 3.270 x 103 3270. (decimal is import)

c) 3.270 x 102 327.0 (zero is import)

d) 8.819 x 10-6

0.000008819

e) 4.5500 x 103 4550.0


Calculators do not give us significant figures. We must figure that

part out for ourselves!

Express the following in scientific notation.

a) 21357 2.1357 x 104

b) 0.00374 3.74 x 10-3

c) 238500000 to 4sf 2.385 x 107

d) 238500000 to 7 sf 2.385000 x 107

e) 0.00089700 to 4 sf 8.970 x 10-4

f) 0.00089700 to 2 sf

9.0 x 10-4

Significant Digits in Calculations

The answer to a problem cannot have more significance (accuracy)

than the quantities used to produce it.

− Rule 1: Multiplying or Dividing

The answer should have the same number of significant figures as the

quantity with the fewest significant figures.

Problem: Calculate (3.23 x 0.02704)/(250. x 15) to the correct # of s.f.

• When you have mixed multiplication and division, determine

the # of sig figs in each intermediate result as you go along.

• Do not round any answers until the very end.

Problem: Calculate (3.01-1.2)/(3.56 +9.23) to the correct # of sig figs.

Problem: Calculate 1.68 x 10-1

/ 08.40 x 102 to the correct # of sig figs.


− Rule 2: Adding or Subtracting

The number of decimal places the answer should equal to the number

of decimal places in the number with the fewest decimal places.

Problem: Add 3.295 + 10.2 + 0.00001 to the correct # of sig figs.

Problem:Subtract 4.2 from 15.723 to the correct # of sig figs.

Where do the significant digits that we claim in the previous

exercises come from? – Measurements!!!


Accuracy and Precision These two terms are often confused for being synonymous.

Accuracy vs Precision

− Precision

The precision of a measurement indicates how well several

determinations of the same quantity agree with each other.

− Accuracy

describes how well a measured value agrees with the established

correct value.

Precise Accurate

Both Neither


1.12 Problem Solving: Unit Conversion and Dimensional Analysis

Unit Conversions

• Information is often not given in the units we need or that we

can relate to.

Example Problem: if a horse stands 16 hands tall, the average

person would want to know the height in inches or feet or meters

to better comprehend the information.

• The simplest way to carry out calculations involving different

units is to use the

factor-label method

(aka dimensional analysis or unit cancellation).

To solve the problem above we would need to know that

1 hand = 4 inches

• Units are treated like numbers and can thus be multiplied and

divided.

• Anything divided by itself = 1

• Anything multiplied by 1 = original value (in new units)

• Set up an equation so that all unwanted units cancel.

For above problem:

SOLUTION

Problem : A child is 21.5 inches long at birth. How long is this in

centimeters?


What if units are squares or cubes?

Problem: Convert 24.5 in2 to m

2.

Significant Figures for Unit Conversions

− All English/English conversion factors have unlimited sig figs.

− All Metric/Metric conversion factors have unlimited sig figs.

− All English/Metric conversions have limited sf except 1in=2.54cm.

Problem: (Metric Conversion)

How many centigrams are in a kilogram?

If you are asked to convert from one prefix to another,

remove the first, then add the second.


1.13 Temperature, Heat, & Energy

Energy

− The capacity to do work or supply heat.

Temperature

− The measure of the average kinetic energy (energy of motion) of the

particles.

− Simple definition:

A measure of how hot or cold an object is.

− Temperature – a measure of the heat energy.

Fahrenheit Temperature Scale

− Defined by German scientist

Daniel Gabriel Fahrenheit in

late 1600s or early 1700s.

− Defined by freezing

temperature of saturated salt

solution (intended to be 0°F)

and temperature of the human

body (intended to be 100°F,

turned out to be 98.6°F)

− Current markers are freezing temperature of water (___) and boiling

point of water (____)

− Currently in use primarily only in the United States

Celsius Temperature Scale

− Suggested by Swedish astronomer Anders Celsius in the mid 1700s.

− Sometimes referred to as the _________.


− Defined by freezing temperature of water ( _°°°°C ) and

boiling point of water ( °°°°C)

Kelvin Temperature Scale

− Both Fahrenheit and Celsius temperature scales require the use of

negative numbers.

− However, there is a limit to how low temperature can go.

− This was discovered through hundreds of experiments.

− William Thompson (a.k.a. Lord Kelvin ) suggested in mid to late

1800s a scale that does not use negative numbers.

− The Kelvin scale assigns a value of 0 K to the coldest possible

temperature, __________, which is equal to − 273.15 °C

− It uses the same degree size as the Celsius scale, but starts at absolute

zero, or -273.15°C. (Expressed simply as K not °K)

Temperature Conversions

Conversion Factors

°K = °C + 273.15 °C = °K – 273.15

Problem: If it is 20°F outside, what is the temp. in °C?

Problem: If it is 75°F outside, what is the temp. in K?

)32(9

5FFC °−°=°32*

5

9+

°=° CF


Energy and Heat

Energy

Two basic forms of Energy

Kinetic Energy: The energy of motion.

Potential Energy: Stored Energy

Bouncing ball converts

energy between KE &

PE

Heat

Energy (and heat) are measured in units of

Joules (J) in SI units or calories (cal) in metric.

1 cal = 4.184 J

1 cal = the heat required to raise 1 gram of water 1°C.

1000 cal = 1 kcal = 1 Cal This is the dietary calorie with a capital C!

Specific Heat (c) is the amount of heat required to raise the

temperature of 1 gram of substance 1 degree Celsius.


Substance J/g.°C

Gold 0.126

Copper 0.386

Cast Iron 0.460

Steel 0.490

Granite 0.790

Glass 0.840

Aluminum 0.900

Water 4.186

How much energy in Joules is needed to raise the temperature of 75.0 g aluminum bar from refrigerator temperature 3.0 °C to 13.0°C? In calories?

How much heat (calories) is removed from a 12 oz diet Coke is removed when it is cooled from room temperature (25°C) to 3°C? (Diet coke has the same specific heat as water = =

4.186 ).

[[HINT : 1 oz = 28.35 g]]


1.14 Density and Specific Gravity

Density

Density is the ratio of the mass of an object to its volume.

Mass

Density = ------------

Volume

− Density is a characteristic property of a substance.

− It usually has units of g/cm3 or g/mL.

− Density is stated at a given temperature.

− Density of Water = 1.00 g/ml at 4 degrees C. (It’s maximum density.)

− Substances with lower densities will float on ones with higher

densities.

LP#1. What is the density of 5.00 mL of serum if it has a mass of

5.23 grams?

What would the mass of 1.00 liters of this serum be?


Measuring density of Solids

- Measure the mass of the solid before

submerging it in water to determine its

volume.

Mass =

- Volume displacement is the volume of a

solid calculated from the volume of water

displaced when it is submerged.

- To get the density, divide the mass by the

volume.

Specific Gravity

Specific Gravity is the density of a substance compared to a

reference substance

Density of Substance

Specific Gravity = ----------------------------------------------------------------------

Density of Reference Substance (typically water at 4°C)

• It is a ratio with no units.

At normal temperatures, the specific gravity of a substance is

numerically equal to its density, but has no units.


The specific gravity of a liquid can be measured using an

instrument called a hydrometer.

Hydrometers contain a weighted bulb at the

end of a calibrated glass tube. The depth to

which the hydrometer sinks in the fluid

indicates the fluid's specific gravity.

The lower the hydrometer sinks, the lower the

specific gravity.

Urinometers (a specialized hydrometer) are

used to measure dissolved solids in urine.

Urinometers can help identify dehydration.

Obesity and Body Fat

Body Mass Index

( )270

)(

)()(22

xinheight

lbweight

mheight

kgweightBMI ==

BMI of 25 -30 is considered overweight.

BMI of 30 or above is considered obese.

By these standards, approximately 61% of the U.S.

population is overweight.

The lowest death risk from any cause, including cancer

and heart attack was for BMI 22-24.

By BMI of 29, the risk doubles! (McMurry 7th

Ed.)

Show Galileo

thermometer picture to

class.


Practice Problem for Dimensional Analysis using BMI.

Based on the BMI scale, is a 5’10’ man who weighs 220 lb obese?

Mass =

Height =

BMI =

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