Chapter 2: Data AnalysisSection 1: Units of measurement

Intro problems: D = m V

• Calculate the density of a piece of bone with a mass of 3.8 g and a volume of 2.0 cm3

• A spoonful of sugar with a mass of 8.8 grams is poured into a 10 mL graduated cylinder. The volume reading is 5.5 mL. What is the density of the sugar?

Not so long ago…….

People used all kinds of units to describe measurements:

Their feet

Sundials

The length of their arm

Needless to say, this led to much confusion!

• Scientist needed a way to report their findings in a way that everyone else understood.

• So, in 1795, the French developed a system of standard units, which was updated in 1960

• The revised system is called the Système Internationale d’Unités, which is abbreviated SI

SI Units

A system of standard measures that every scientist uses

It consists of 7 base units which have real measures in the real world

SI Base

Units

Quantity Base unit

Time second (s)

Length meter (m)

Mass kilogram (kg)

Temperature kelvin (K)Amount of substance mole (mol)

Electric current ampere (A)

Luminous intensity candela (cd)

Time

Base unit for time is the secondIt is based on the frequency of microwave

radiation given off by a cesium-133 atom         

Length

The SI unit for length is the meter (m).

The distance that light travel through a vacuum

Equals 1/300,000,000 of a second

About 39 inches

          

Mass

Base unit for mass is the kilogram (kg)

You may see grams (g) or milligrams (mg)

Defined by a platinum-iridium cylinder stored in a bell jar in France

About 2.2 pounds

Temperature You classify an object as

hot or cold by whether heat flows from you to the object or from the object to you.

Heat flows from hot to cold.

Thermometers are used to measure temp.

SI unit of temp is kelvin (K)

In science, the celsius and kelvin scales are most often used.

To convert from celsius to kelvin: add 273

ex: -39º C + 273 = 234 KTo convert from kelvin to celsius: subtract 273

ex: 332 K – 273 = 59ºC

Temperature

Derived Units Not all quantities can be

measured with base units

Volume—the space occupied by an object

-measured in cubic meters (cm3)

-or liters (L) or milliliters (ml)

Density—a ratio that compares the mass of an object to its volume

--units are grams per cubic centimeter (g/cm3)

D = m V

Derived Units

Density equals mass divided by volume.

Example: If a sample of aluminum has a mass of 13.5g and a volume of 5.0 cm3,

what is its density?

Density = mass

volume D = 13.5 g

5.0 cm3

D = 2.7 g/cm3

Suppose a sample of aluminum is placed in a 25 ml graduated cylinder containing 10.5 ml of water. A piece of aluminum is placed in the cylinder and the level of the water rises to 13.5 ml. The density of aluminum is 2.7 g/cm3. What is the mass of the

aluminum sample?

Practice Problems—pg. 29 # 1, 2, 3

Other Derived Quantities

• Velocity or speed- distance an obj travels over a period of time– V = ∆d/ t – Units: m/s

• Force – push or a pull exerted on an object– F = m*a m= mass a= acceleration– Units: Kg * m/s2 = Newton (N)

Metric Prefixes• To better describe the range of possible

measurements, scientists add prefixes to the base units.

• For example: 3,000 m = 3 km (easier to manage)

• Most common prefixes:– King Henry Died by Drinking Chocolate Milk

• Metric prefixes are based on the decimal system

Converting Between Units• To convert b/w units simply move the decimal

place to the right or left depending on the number of units jumped.

• Ex: K he da base d c m

– 24.56 m = 245.6 dm = 2,4560 mm

• May use power of 10 to multiply or divide– Big units to small units Multiply– Small units to big units divide

Section 2.2

Scientific Notation and Dimensional Analysis

Scientific Notation• A way to handle very large or very small

numbers

• Expresses numbers as a multiple of 10 factors

• Structure: a number between 1 and 10; and ten raised to a power, or exponent– Positive exponents, number is > 1– Negative exponents, number is <1

Ex: 300,000,000,000 written in scientific notation is 3.0 x 10 11

Change the following data into scientific notation.a. The diameter of the sun is 1 392 000 km.b. The density of the sun’s lower atmosphere is 0.000 000 028 g/cm3.

Practice probs. Pg. 32 #12, 13

To add or subtract in scientific notation:+ The exponents must be the same before doing the arithmetic+ Add/Subtract numbers, keep the power of 10.

Ex: To add the numbers

2.70 x 107

15.5 x 106

0.165 x 108

Move the decimal to right (make # bigger): subtract from exponent (exp smaller)

Move the decimal to left (smaller #): add to exponent (bigger exp)

Practice probs. Pg. 32 #14

To multiply or divide numbers in scientific notation:

To multiply: multiply the numbers and ADD the exponents

ex: (2 x 103) x (3 x 102)

2 x 3 = 6

3 + 2 = 5

Answer = 6 x 105

To divide: divide the numbers and SUBTRACT the exponents

ex: (9 x 108) (3 x 10-4)

To multiply or divide numbers in scientific notation:

9 3 = 3 8 – (-4) = 12

Answer = 3 x 1012

Practice probs. Pg. 33 #15, 16

Dimensional Dimensional analysisanalysis

• A method of problem-solving that focuses on the units used to describe matter

• Converts one unit to another using conversion factors in a fraction formatfraction format– 1teaspoon = 5 mL 1 tsp or 5 ml

5 ml 1 tsp– 1 km = 1000 m 1 km or 1000 m

1000 m 1 km

• To use conversion factors simply write:1. What is given with the unit 2. Write times and a line (x ______).

3. Place the unit you want to cancel on the bottom, unit you are converting to on top.

4. Use as many conversion factors until you reach your answer

– ex: Convert 48 km to meters:

Dimensional Dimensional analysis analysis cont….cont….

48 km x 1km

= 48,000 m1000m

Conversion factor 1km = 1000 m

Practice: Convert 360 L to ml and to teaspoons:

1. How many seconds are there in 24 hours?

2. How many seconds are there in 2 years?

Practice probs. Pg. 34 #17, 18

You can convert more than one unit at a time:

What is a speed of 550 meters per second in kilometers per minute?

HINTs:Convert one unit at a time!Units MUST be ACROSS from each

other to cancel out!

Section 2.3

How reliable are measurements:

Sometimes an estimate is acceptable and sometimes it is not.

When you are driving to the beach

Miles per gallon your car gets

Your final grade in Chemistry

Okay?

X

When scientists make measurements, they evaluate

the accuracy and precision of the measurements.Accuracy—how close a measured value

is to an accepted value.

Not accurate

Accurate

Precision—how close a series of measurements are to each other

Not preciseNot precisePrecisePrecise

Density Data collected by 3 different students

Accepted density of Sucrose =1.59 g/cm3

Student A

Student B

Student C

Trial 11.54

g/cm3

1.40 g/cm3

1.70 g/cm3

Trial 21.60

g/cm3

1.68 g/cm3

1.69 g/cm3

Trial 31.57

g/cm3

1.45 g/cm3

1.71 g/cm3

Average1.57

g/cm3

1.51 g/cm3

1.70 g/cm3Which student is the most accurate? Which is most Which student is the most accurate? Which is most

precise? What could cause the differences in data?precise? What could cause the differences in data?

It is important to calculate the difference between an accepted value and an

experimental value.

To do this, you calculate the ERROR in data. (experimental – accepted)

Percent error is the ratio of an error to an accepted valuePercent error = error

accepted value x 100

Calculate the percent error for Student A

TrialDensity

(g/cm3)Accepted

valueError

(g/cm3)

1 1.54 1.59

2 1.60 1.59

3 1.57 1.59

Percent error = error x 100

accepted value

First, you must calculate the error!!

Practice probs. Pg. 38 Practice probs. Pg. 38 #29#29

Significant Figures

Scientists indicate the precision of measurements by the number of digits they report

A value of 3.52 g is more precise than a value of 3.5 g

A reported chemistry test score of 93 is more precise than a score of 90

Include all known digits and one estimated digit.

Rules for significant figures

1. Non-zero numbers are always significant 72.3 g has__ 2. Zeros between non-zero numbers are 60.5 g

has__ significant

3. Leading zeros are NOT significant 0.0253 g

has __

4. Trailing zeros are significant after a 6.20 g has__ decimal point

Trailing zeros

Leading zeros

100 g has__

Determine the number of significant figures in the following masses:a. 0.000 402 30 gb. 405 000 kg

a. 0.000 402 30 g

b. 405 000 kg

5 sig figs

3 sig figs

To check, write the number in scientific notation

Ex: 0.000 402 30 becomes

4.0230 x 10-

4

and has 5 significant figures

Practice probs. Pg. 39 # 31, 32

Rounding to a specific # of sig figs

When rounding to a specific place using sig figs, use the rounding rules you already know.

ex: Round to 4 sig figs: 32.54321. Count to four from left to right:

1 2 3 4

2. Look at the number to the right of the 4th digit and apply rounding rules

32.54

Practice probs. Pg. 41 #34

Practice probs. Pg. 41 # 35, 36pg. 42 #37, 38