1. Chapter 2
Measurements

2. Homework Do “Questions and Problems” Do “Understanding the Concepts”
2.1 through 2.73 (odd)
Do “Understanding the Concepts”
2.75, 2.79
Do “Additional Questions and Problems”
2.83 through (odd)
Do “Challenge Questions”
(odd)

3. 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

4. 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)
Quantitative observation: A numerical measurement of a quantity or value

5. 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?

6. 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 (world’s most widely used)
Common measurements in commerce (gas stations, supermarkets)

7. 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

8. 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

9. Length Meter Base unit of length in metric and SI system
About 3 ½ inches longer than a yard
1 m = yd
Not convenient for description of small things
Can be subdivided or multiplied by use of metric prefixes
The linear extent in space from one end to another

10. Length Other units of length are derived from the meter
Commonly use centimeters (cm)
1 m = 100 cm
1 inch = 2.54 cm (exactly)
Not convenient for description of small things
Can be subdivided or multiplied by use of metric prefixes
The linear extent in space from one end to another

11. 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
No base unit, derived from base unit of length
Cubic meter too large for most lab work so use smaller units such as liter or milliliter

12. 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
No base unit, derived from base unit of length
Cubic meter too large for most lab work so use smaller units such as liter or milliliter

13. 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

14. 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

15. 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

16. 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 = pounds
1 lb = g
See table 2.1 page 21

17. 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
Water’s freezes at 32°F, boils at 212°F
Related to the motion of particles, it is not heat

18. Temperature Celsius Scale, °C Kelvin Scale, K Metric Unit
Used in science (USA) and rest of world
Temperature unit larger than the Fahrenheit unit
Water’s freezes = 0°C, boils at 100°C
Kelvin Scale, K
SI Unit
Used in science
Temperature unit same size as Celsius unit
Water’s freezes at 273 K, boils 373 K
Absolute zero is the lowest temperature theoretically possible

19. 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 1°C or 1 K = a change of 1.8 °F

21. 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
The names of larger and smaller units are made by attaching a prefix to the base unit name. The meaning of the prefix remains constant.
base unit

22. Prefixes and Equalities (memorize)
× base unit
Mega (M) 1,000,
Kilo (k) 1,
Base
Deci (d)
Centi (c)
Milli (m)
Micro (µ)
Nano (n)
meter
liter
gram

23. 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 < µ < m < c < base < k < M

24. Scientific Notation Used to write very large or very small numbers
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

25. 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

26. In 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
gram
In scientific notation:
7.91 х 1024 molecules
2.99 х gram
In scientific work, very large or very small numbers are frequently encountered
The example of one ordinary amount of water (cup)

27. Writing in Scientific Notation
For small numbers (<1):
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

28. 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

29. Examples Write each of the following in scientific notation 12,500
0.0202
37,400,000

30. 12,500 Examples 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

31. 0.0202 Examples 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

32. 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

33. Examples
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

34. 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)

35. 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 EE
EXP
(+/-)
EE key includes the X 10 value X

36. 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

37. 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 х or х 104
2.18 х > х 104

38. Measured Numbers and Significant Figures
Two kinds of numbers
Counted (exact)
Measured
There are two kinds of numbers. Those that are counted and those that are defined. Counted numbers have an exact value, those that are measured can not have an exact value
Counted numbers do not involve a measuring device

39. 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
Exact value is known
Do not affect the number of sig figs in an answer

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. Example
4 SF
5 SF
3 SF
2.1
2 SF
2 SF
The number with the fewest significant figures is 1.1 so the answer has 2 significant figures

48. 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

49. Example
1 d.p.
3 d.p.
2 d.p.
236.2
1 d.p.
The number with the fewest decimal places is so the answer should have 1 decimal place

50. 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
The relationships are exact by definition, whether it measuring length, volume, or mass

51. 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

52. 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 needed (unit): Pounds
Write a sequence of units (plan) which begins with the initial unit and ends with the desired unit:
year day pounds

53. Problem Solving Dimensional Analysis Example
For each unit change,
State the equalities:
Every equality will have two conversion factors
365 days = 1 year
0.5 lb sugar =1day
year day pounds

54. Problem Solving Dimensional Analysis Example
State the conversion factors:
Set Up the problem:

55. 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?

56. 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

57. 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

58. 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 g/mL at room temperature
1.00 mL of water weighs how much?
How many mL of water weigh 15 g?

59. 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?

60. Solve for volume of iron
Density Problem
Solve for volume of iron