UNIT 4: MEASUREMENTS AND SOLVING PROBLEMS

UNIT 4: MEASUREMENTS AND SOLVING PROBLEMS

NOTETAKING GUIDE

I. SI SYSTEM

a. Scientists in Scientists in different parts of the world need to be able to compare measurements

b. Scientists came together in a convention and created a standard system

c. New system is based on a set of standard units used to measure things like mass, volume, temperature, etc

d. Named the system: System International or SI

Quantity Measured

Unit

Symbol

e. Prefixes are used to make units (numbers) bigger or smaller

Prefix

Symbol

Amount

II. FACTOR LABEL METHOD (dimensional analysis)

a. To convert from one factor to another, you must use a conversion factor.

b. The steps involved in the factor label method are:

i. Start with what you know: write the given number and unit.

ii. Draw a “fence” and write the given in the top left

iii. Set up a conversion factor (fraction used to convert one unit to another).

1. Place the given unit as denominator of conversion factor this will allow the “unwanted” units to cancel (think reducing/canceling out like variables). You want to make sure the units you want to end up with are the units that end up on top.

2. You will always place a 1 next to the “prefix” and the number you wrote as that prefix’s meaning next to the base unit. For example 1 cm = 1x10-2m.

iv. Multiply the top of the fence and divide by the bottom.

c. Examples

i. 280 grams equals how many milligrams?

ii. 34 ng = ? grams

iii. 8 Gg = ? grams

iv. 278 Mg = ? pg

v. 62 mg = ? cg

vi. 365 days = ? seconds

III. DERIVED SI UNITS

a. When two or more base units are combined to get a new measurement

Quantity

Symbol

Unit

Unit

Abbreviation

Formula

Area

Volume

Density

Energy

*** Key Fact: 1mL = 1 cm3***

b. The steps involved in with derived SI units

i. Convert each part of the equation to the correct unit using the factor label method.

ii. Plug numbers into the formula and solve

c. Examples

i. Mass is 483 kg. Volume is 2.4 mL. What is density?

ii. What is the density of a 9040 kg sample of an unknown substance that occupies 40.6 cm3?

IV. Scientific Notation

a. All numbers are in the form of M X 10n

i. M is a number from 1 to 10

ii. n is a whole number and may be positive or negative

b. Example: Put 4500 in scientific notation.

i. Step One: Draw in the decimal point if there is not one

already.

4500.

ii. Step Two: Move the decimal point to either the right or

the left until you have created a number that is between 1

and 10.

4.500

iii. Step Three: Count the number of places you moved the

decimal. If you moved the decimal to the left, then n is a

positive number. If you moved the decimal to the right,

then n is a negative number.

n = 3

iv. Step Four: Write the number in the form M X 10n.

4.500 x 103

c. Example 2: Put 0.098 in scientific notation.

d. Example 3: Put 8.9 X 103 in standard notation.

e. Example 4: Put 2.6 X 10-4 in standard notation.

f. Operations with Scientific Notation:

a. Multiplication

i. Rules

1. Example

b. Division

i. Rules

1. Example

c. Addition/Subtraction

i. Rule

1. Example

2. Example

UNIT 4: MEASUREMENTS AND SOLVING PROBLEMS

NOTETAKING GUIDE II

I. Introduction to the Mole

a. A mole measures the number of molecules, or atoms.

b. A mole allows you to relate grams of an element to the number of atoms in that element.

c. Represents a number

d. Defined as the number of atoms in exactly 12 grams of  12C (carbon twelve).

12 donuts = 1 dozen

Atoms moles

e. Like the word "dozen" represents the number 12, so "mole" represents the number 6 x 1023.

a. A mole is 6.02x1023 molecules or atoms.

i. 6.02x1023 = Avogadro’s number

f. Molar Mass:

a. Using Carbon 12 as an example, 12 is the mass number of carbon.

b. one mole of carbon atoms has a mass of 12 grams.

c. The atomic mass of an element expressed in grams is the mass of a mole of the element. The mass of the mole of an element is its molar mass. For carbon, the molar mass is 12.0 g. For atomic hydrogen, the molar mass is 1.0 g.

g. Examples

a. Mole(Gram Conversion

i. What is the mass of 3.50 moles of Cu?

ii. What is the mass of 2.25 moles of Fe?

b. Gram(Mole Conversions

i. If you have 11.9 grams of Al, how many moles do you have?

c. Atom(Mole Conversions

i. How many moles of Ag are in 3.01x1023 atoms of Ag?

d. Mole(Atom Conversions

i. How many atoms of S are in 34 moles of S?

e. Gram(Conversions

i. What is the mass of 1.2x108atoms of Cu?

II. Significant Figures

a. General Rules

a. All non-zero numbers are ALWAYS significant.

987 has ________________

b. Zeroes between nonzero digits are significant:

1002 kg has ____________

3.07 mL has _______________

c. Leftmost zeros between the decimal point and the first nonzero digit are not significant; such zeroes merely indicate the position of the decimal point:

0.001°C has _________________

0.012 g has _________________

d. Zeroes at the end of a non-zero number AND to the right of a decimal point are always significant:

0.0230 mL has ________________

0.20 g has __________________

9.000 m has _________________

e. When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant:

7000 has ___________________

190 miles may be 2 or 3 significant

figures,

50,600 calories may be 3, 4, or 5

significant figures.

The potential ambiguity in the last

rule can be avoided by the use of

standard exponential, or "scientific,"

notation. For example, depending on

whether the number of significant

figures is 3, 4, or 5, we would write

50,600 calories as:

5.06 × 104 calories (____________)

5.060 × 104 calories (____________)

5.0600 × 104 calories (__________)

B. Multiplication/Division

a. Do the Math

b. Count the # of sig figs in each number of the problem

c. Pick the smallest number

d. Round your answer so that it has the number of sig figs determined in above step

e. Example: 25 x 703

f. Example: 21.00 x 0.003

C. Addition/Subtraction

a. Do the Math

b. Count the number of places to the right of the decimal in each number in the problem

c. Pick the smallest number

d. Round your answer so that it has this number of places to the right of the decimal.

e. Example: 23.576 + 8.92

III. Specific Heat

A. Amount of energy needed to raise 1 gram of a substance 1 degree Celsius

B. Q = m c T

C. Example:

a. Specific heat of water is 4.18

Mass of water is 23.5 g

Initial temperature is 58

Final temperature is 90

How much energy is required?

b. Energy is 2098 Joules

Mass of Zn is 88.9 grams

Initial temperature is 21

Final temperature is 23

What is specific heat of Zn?

c. 3500 joules of heat are added to a 28.2 gram sample of iron at 20 degrees Celsius. What is the final temperature of the iron if the specific heat of iron is 0.449?

Law of Conservation of Energy:

Energy can neither be created nor destroyed.

(If one substance gains heat, then another must lose heat)

mcT = mcT

d. 86 grams of lead at 114 degrees Celsius was dropped into 123 grams of some alcohol at 31 degrees Celsius. The final temperature of the system was 48 degrees Celsius. If the specific heat of lead is 0.130, then what is the specific heat of alcohol?

e. 116 grams of Mercury at 161 degrees Celsius was placed into 217 grams of water at 41 degrees Celsius. If the specific heat of Hg is 0.033 and the specific heat of water is 1.0, what would be the final temperature of the mixture?

IV. Accuracy vs. Precision

A. Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured

B. Precision is a measure of how close a series of measurements are to one another

C. Error = experimental error – accepted value

D. Percent error = │error│

x 100%

Accepted value

E. Example: The density of copper is 8.96 g/mL. Group A measures the density of copper in the density lab and finds the density to be 9.02 g/mL. What is group A’s error?

F. Example: In the same density lab, group B measures the density of copper and finds it to be 8.34 g/mL. What is group B’s error?