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Chapter 2

- Measurements

Homework

- Do Questions and Problems
- 2.1 through 2.73 (odd)
- Do Understanding the Concepts
- 2.75, 2.79
- Do Additional Questions and Problems
- 2.83 through 2.103 (odd)
- Do Challenge Questions
- 2.105-2.113 (odd)

Measurement

- The most useful tool of the chemist
- Most of the basic concepts of chemistry were

obtained through data compiled by taking

measurements - How much?
- How long?
- How many...?
- These questions cannot be answered without taking

measurements - The concepts of chemistry were discovered as data

was collected and subjected to the scientific

method

Measurement

- The estimation of the magnitude of an object

relative to a unit of measurement - Involves a measuring device
- ie meterstick, scale
- The device is calibrated to compare the object to

some standard (inch/centimeter, pound/kilogram) - Quantitative observation with two parts A

number and a unit - Number tells the total of the quantity measured
- Unit tells the scale (dimensions)

Measurement

- A unit is a standard (accepted) quantity
- Describes what is being added up
- Units are essential to a measurement
- For example, you need six of sugar
- teaspoons?
- ounces?
- cups?
- pounds?

Units of measurement

- Units tells the magnitude of the standard
- Two most commonly used systems of units of

measurement - US system Used in everyday commerce (USA and

Britain) - Metric system Used in everyday commerce and

science (The rest of the world) - SI Units (1960) A modern, revised form of the

metric system set up to create uniformity of

units used worldwide (worlds most widely used)

Metric System

- A decimal system of measurement based on the

meter and the gram - It has a single base unit per physical quantity
- All other units are multiples of 10 of the base

unit - The power (multiple) of 10 is indicated by a

prefix

Metric System

- In the metric system there is one base unit for

each type of measurement - length
- volume
- mass
- The base units multiplied by the appropriate

power of 10 form smaller or larger units - The prefixes are always the same, regardless of

the base unit - milligrams and milliliters both mean 1/1000 of

the base unit

Length

- Meter
- Base unit of length in metric and SI system
- About 3 ½ inches longer than a yard
- 1 m 1.094 yd

Length

- Other units of length are derived from the meter
- Commonly use centimeters (cm)
- 1 m 100 cm
- 1 inch 2.54 cm (exactly)

Volume

Volume side side side

- Measure of the amount of three-dimensional space

occupied by a object - Derived from length
- SI unit cubic meter (m3)
- Metric unit liter (L) or 10 cm3
- Commonly measure smaller volumes in cubic

centimeters (cm3)

Volume side side side

Volume

- Since it is a three-dimensional measure, its

units have been cubed - SI base unit cubic meter (m3)
- This unit is too large for practical use in

chemistry - Take a volume 1000 times smaller than the cubic

meter, 1dm3

Volume

- Metric base unit 1dm3 liter (L)
- 1L 1.057 qt
- Commonly measure smaller volumes in cubic

centimeters (cm3) - Take a volume 1000 times smaller than the cubic

decimeter, 1cm3

Volume

- The most commonly used unit of volume in the

laboratory milliliter (mL) - 1 mL 1 cm3
- 1 L 1 dm3 1000 mL
- 1 m3 1000 dm3 1,000,000 cm3
- Use a graduated cylinder or a pipette to measure

liquids in the lab

Mass

- Measure of the total quantity of matter present

in an object - SI unit (base) kilogram (kg)
- Metric unit (base) gram (g)
- Commonly measure mass in grams (g) or milligrams

(mg) - 1 kg 1000 g
- 1 g 1000 mg
- 1 kg 2.205 pounds
- 1 lb 453.6 g

Temperature

- Measurement of the intensity of heat energy in

matter - Hotness or coldness of an object
- Fahrenheit Scale, F
- Everyday Use in USA
- Not used in science
- Waters freezes at 32F, boils at 212F

Temperature

- Celsius Scale, C
- Metric Unit
- Used in science (USA) and rest of world
- Temperature unit larger than the Fahrenheit unit
- Waters freezes 0C, boils at 100C
- Kelvin Scale, K
- SI Unit
- Used in science
- Temperature unit same size as Celsius unit
- Waters freezes at 273 K, boils 373 K
- Absolute zero is the lowest temperature

theoretically possible

Temperature

- Scales determined by different degree sizes and

different reference points - There are 180 degrees between the freezing and

boiling points on the Fahrenheit scale - The number of degree units between the freezing

and boiling point on the Celsius and Kelvin

scales are the same 100 degrees

A change in 1 C a change in 1 K A change in

1C or 1 K a change of 1.8 F

(No Transcript)

Prefixes and Equalities

- One base unit for each type of measurement
- Length (meter), volume (liter), and mass (gram)
- The base units are then multiplied by the

appropriate power of 10 to form larger or smaller

units

base unit

Prefixes and Equalities (memorize)

base unit

- Mega (M) 1,000,000 106
- Kilo (k) 1,000 103
- Base 1 100
- Deci (d) 0.1 10-1
- Centi (c) 0.01 10-2
- Milli (m) 0.001 10-3
- Micro (µ) 0.000001 10-6
- Nano (n) 0.000000001 10-9

meter

liter

gram

Remembering Metric System

- Keep in mind which unit is larger
- A kilogram is larger than a gram, so there must

be a number of grams in one kilogram - This can help you check if you have the

conversion correct

n

Scientific Notation

- A system in which an ordinary decimal number (m)

is expressed as a product of a number between 1

and 10, multiplied by 10 raised to a power (n) - Used to write very large or very small numbers
- Based on powers of 10

Scientific Notation

- Consists of a number (coefficient) followed by a

power of 10 (x 10n) - Negative exponent Number is less than 1
- Positive exponent Number is greater than 1

exponent

coefficient

exponential term

Scientific Notation

- In an ordinary cup of water there are
- Each molecule has a mass of

7,910,000,000,000,000,000,000,000 molecules

- 0.0000000000000000000000299 gram

In scientific notation 7.91 ? 1024

molecules 2.99 ? 10-23 gram

Writing in Scientific Notation

- For small numbers (
- Locate the decimal point
- Move the decimal point to the right to give a

coefficient between 1 and 10 - The new number is now between 1 and 10
- Add the term x10-n
- where n is the number of places you moved the

decimal point. It has a negative sign - If the decimal point is moved to the right, then

the exponent is a negative number

Writing in Scientific Notation

- For large numbers (1)
- Locate the decimal point
- Move the decimal point to the left to give a

coefficient between 1 and 10 - Add the term x10n
- where n is the number of places you moved the

decimal point. It has a positive sign. - If the decimal point is moved to the left, the

exponent is a positive number

Examples

- Write each of the following in scientific

notation - 12,500
- 0.0202
- 37,400,000
- 0.0000104

Examples

- 12,500
- Decimal place is at the far right
- Move the decimal place to between the 1 and 2

(1.25) - The decimal place was moved 4 places to the left

(large number) so exponent is positive - 1.25x104

Examples

- 0.0202
- Move the decimal place to between the 2 and 0

(2.02) - The decimal place was moved 2 places to the right

(small number) so exponent is negative - 2.02x10-2

Examples

- 37,400,000
- Decimal place is at the far right
- Move the decimal place to between the 3 and 7

(3.74) - The decimal place was moved 7 places to the left

(big number) so exponent is positive - 3.74x107

Examples

- 0.0000104
- Move the decimal place to between the 1 and 0

(1.04) - The decimal place 5 places to the right (small

number) so exponent is negative - 1.04x10-5

Example

- 6.442x105
- 5 is positive, move the decimal 5 places to the

right (to make the number bigger) - 644,200
- 5.583x10-2
- 2 is negative, move the decimal 2 places to the

left (to make the number smaller) - 0.05583

Scientific Notation and Calculators

- Enter the coefficient (number)
- Push the key
- Then enter only the power of 10
- If the exponent is negative, use the key
- DO NOT use the multiplication key
- to express a number in sci. notation

or

EXP

EE

(/-)

X

Converting Back to a Standard Number

- Determine the sign of the exponent, n
- If n is the decimal point will move to the

right (gives a number greater than one) - If n is the decimal point will move to the left

(gives a number less than one) - Determine the value of the exponent of 10
- The power of ten determines the number of

places to move the decimal point

Using Scientific Notation

- To compare numbers written in scientific notation
- First compare the exponents of 10
- The larger the exponent, the larger the number
- If the exponents are the same, then compare

coefficients directly - Which number is larger?

21.8 ? 103 or 2.05 ? 104

2.18 ? 104 2.05 ? 104

Measured Numbers and Significant Figures

- Two kinds of numbers
- Counted (exact)
- Measured

Exact Numbers

- Numbers known with certainty
- Unlimited number of significant figures
- They are either
- counting numbers
- 10 beds, 6 pills, 4 chairs
- defined numbers
- 100 cm 1 m 12 in 1 ft 1 in 2.54 cm
- 1 kg 1000 g 1 lb 16 oz
- 1000 mL 1 L 1 gal 4 qts.
- 1 minute 60 seconds

Measured Numbers

- A measurement always has some amount of

uncertainty - Involves reading a measuring device
- Uncertainty comes from the tool used for

comparison - i.e. Some rulers show smaller divisions

(markings) than others

Measured Numbers

- Always have to estimate the value between the two

smallest divisions on a measuring device - Every person will estimate it slightly

differently, so there is some uncertainty present

as to the true value

2.8 to 2.9 cm

Significant Figures

- To indicate the uncertainty of a single

measurement scientists use a system called

significant figures - Significant figures All digits known with

certainty plus one digit that is uncertain - The last digit written in a measurement is the

number that is considered to be uncertain - Unless stated otherwise, the uncertainty in the

last digit is 1

Counting Significant Figures

- Nonzero integers are always significant
- Zeros (may or may not be significant)
- Leading zeros never count as significant figures
- Captive zeros are always significant
- Trailing zeros are significant if the number has

a decimal point - Exact numbers have an unlimited number of

significant figures

Rounding Off Rules

- If the digit to be removed
- is less than 5, the preceding digit stays the

same - is equal to or greater than 5, the preceding

digit is increased by 1 - In a series of calculations, carry the extra

digits to the final result and then round off

Significant Figures in Calculations

- Calculations cannot improve the precision of

experimental measurements - The number of significant figures in any

mathematical calculation is limited by the least

precise measurement used in the calculation - Two operational rules to ensure no increase in

measurement precision - addition and subtraction
- multiplication and division

Multiplication/Division

- Product or quotient has the same number of

significant figures as the number with the

smallest number of significant figures - Count the number of significant figures in each

number - Round the result so it has the same number of

significant figures as the number with the

smallest number of significant figures

Example

5 SF

3 SF

4 SF

2.1

2 SF

2 SF

- The number with the fewest significant figures is

1.1 so the answer has 2 significant figures

Addition/Subtraction

- Sum or difference is limited by the number with

the smallest number of decimal places - Find number with the fewest decimal places
- Round answer to the same decimal place

Example

2 d.p.

1 d.p.

3 d.p.

236.2

1 d.p.

- The number with the fewest decimal places is

171.5 so the answer should have 1 decimal place

Equalities

- A fixed relationship between two quantities
- Shows the relationship between two units that

measure the same quantity - The relationships are exact, not measured
- 1 min 60 s
- 12 inches 1 ft
- 1 dozen 12 items (units)
- 1L 1000 mL
- 4 quarts 1 gallon
- 1 pound 454 grams

Conversion Factors

- Many problems in chemistry involve a conversion

of units - Conversion factor An equality expressed as a

fraction - Used as a multiplier to convert a quantity in one

unit to its equivalent in another unit - May be exact or measured
- Both parts of the conversion factor should have

the same number of significant figures

Problem Solving Conversion Factors Stated Within

a Problem

- The average person in the U.S. consumes one-half

pound of sugar per day. How many pounds of sugar

would be consumed in one year? - State the initial quantity given (unit)

One year - State the final quantity (unit) Pounds
- Write a sequence of units (plan) which begins

with the initial unit and ends with the desired

unit

year day pounds

Problem SolvingDimensional Analysis Example

- For each unit change,
- State the equalities
- Every equality will have two conversion factors

0.5 lb sugar 1day

365 days 1 year

year day pounds

Problem SolvingDimensional Analysis Example

- State the conversion factors
- Set Up the problem

Guide to Problem Solving when Working

Dimensional Analysis Problems

- Identify the known or given quantity and the

units of the new quantity to be determined - Write out a sequence of units which starts with

your initial units and ends with the desired

units (the unit pathway) - Write out the necessary equalities and conversion

factors - Perform the mathematical operations that connect

the units - Check that the units cancel properly to obtain

the desired unit - Does the answer make sense?

Density

- The ratio of the mass of an object to the volume

occupied by that object - Tells how tightly the matter within an object is

packed together - Units for solids and liquids g/cm3
- 1 cm3 1 mL so also g/mL
- Unit for gases g/L
- Density solids liquids gases

Determining Density

- Weigh the object
- Use a scale
- Determine the volume of the object
- Calculate it if possible (cube)
- Can also calculate volume by determining what

volume of water is displaced by an object

Volume of Water Displaced Volume of Object

Densities of Substances

- Can use density as a conversion factor between

mass and volume - Given in Table 2.9, page 47
- You will be given any densities on tests EXCEPT

water - Density of water is 1.000 g/mL at room

temperature - 1.00 mL of water weighs how much?
- How many mL of water weigh 15 g?

Density Problem

- Iron has a density of 7.87 g/cm3. If 52.4 g of

iron is added to 75.0 mL of water in a graduated

cylinder, to what volume reading will the water

level in the cylinder rise?

Density Problem

Solve for volume of iron

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