Measuring Matter

Measuring Matter in Two Ways

Qualitative Measurements: which are usually descriptive like observations.

Now it is important to start making…

Quantitative Measurements: are in the form of numbers and units.

The Powers of Ten

Picture a microscopic cell.

Picture the galaxy.

Scientific NotationScientists need a way to express extremely LARGE

and extremely SMALL numbers in their quantitative measurement.

Scientific notation shows the product of two numbers:

A coefficient X 10 to some exponent

Scientific NotationRemember that a coefficient is simply a number that you

multiply an expression by.

**In scientific notation1≤ coefficient <10.

Also remember that 10 to some power is simply ten multiplied by itself that many times.

Ex. 103 = 10 x 10 x 10

Also, ten to a minus power is dividing by ten that many times.

Examples of the use of Scientific Notation

I like to run. For every one mile, I have run 1609 meters.

Expressed in scientific notation, this is

1.609 x 103 meters

When you multiply something times ten THREE times, you move the decimal place to the right three times.

More examplesThe diameter of a human hair is 0.000 008

meters.

Expressed in scientific notation that is,

8.0 x 10-6 meters

Note: The negative sign moves the decimal place in the other direction.

Try some on your own…45,700 =

0.009 =

24,200,000 =

0.000665 =

4.57 x 104

9.0 x 10-3

2.42 x 107

6.65 x 10-4

Converting to Expanded Form

Move the decimal place the number of times indicated by the exponent.

To the right if it is positive.

To the left if it is negative.

Example:

4.5 x 10-2 = 0.045

Try some on your own…1.2 x 10-4 =

9.6 x 103 =

8.07 x 102 =

0.00012

9 600

807

Multiplying with Scientific Notation

Multiply the coefficients

Add the exponents

Example:

(2.0 x 103) x (2.0 x 103) = 4.0 x 106

Dividing with Scientific Notation

Divide the coefficients

Subtract the exponent in denominator from the numerator.

Example:

3.0 x 104 ÷ 2.0 x 102 = 1.5 x 104-2 = 1.5 x 102

Adding & Subtracting with Scientific Notation

In order to add numbers written in scientific notation, the exponents must match.

Example

5.40 x 103 + 6.0 x 102 =

Change 6.0 x 102 to 0.60 x 103, then add.

5.40 x 103 + 0.60 x 103 = 6.00 x 103

Try some on your own…(3.95 x 102) ÷ (1.5 x 106)  =

 

               

(3.5 x 102) (6.45 x 1010) =  

(4.44 x 107) ÷ (2.25 x 105)  =

      

(4.50 x 10-12) (3.67 x 10-12) =

2.63 x 10-4

               2.2575 x 1013

1.973 x 102            1.6515 x 10-23

A Short History of Standard Units

Humans did not always have standards by which to measure temperature, time, distance, etc.

It was not until 1790 that France established the first metric system.

The First Metric SystemThe French established that one meter was one ten-millionth of the distance of the from the Equator to the North Pole.

One second was equal to 1/86,400 of the average day.

Today’s StandardsThe techniques used today to establish

standards are much more advanced than in 1790…

One meter is equal to the distance traveled by light in a vacuum in 1/299,792,458 of a second.

One second is defined in terms of the number of cycles of radiation given off by a specific isotope of the element cesium.

S.I. UnitsThe International System of Units is used

ALMOST exclusively worldwide (the U.S. is one the of the exceptions).

ALL science is done using S.I. units.

The United States’ System of Measurement

In 1975, the U.S. government attempted to adopt the metric system with little success.

The U.S. currently uses the English System of Measurement.

Math Quiz

Complete the following:

3 5/6 in. + 8 4/9 in. + 5 2/7 in. =

Math Quiz

Complete the following:

3.83 cm + 8.44 cm + 5.29 cm =

So why S.I.?

So why S.I.?Decimals are more “computationally friendly”

Multiples of ten

Eliminate LARGE numbers by using prefixes

Scientifically based

Measurements and SI Units

Quantitative measurements must include a number AND a unit.

Base units are used with prefixes to indicate fractions or multiples of a unit.

Try to fill in your table.

Base UnitsBase Unit Symbol Measures…

grams g mass

meter m distance

Liter L volume

Kelvin K temperature

degrees Celsius °C temperature

mole mol amount of a substance

second S or sec time

ampere A electric current

candela cd light intensity

Joule J energy

PrefixesPrefixes combine with base units to indicate fractions or multiples of a unit.

PrefixesPrefix Symbol Meaning mega- M 1 000 000 times larger

kilo- K 1 000 times larger

Hecto- H 100 times larger

deca- D 10 times larger than base unit

Base Unit

deci- d 10 times smaller than base unit

centi- c 100 times smaller

milli- m 1 000 times smaller

micro- µ 1 000 000 times smaller

nano- n 1 000 000 000 times smaller

pico- p 1 000 000 000 000 times smaller

femto- f 1 000 000 000 000 000 times smaller

SI Prefixes1 000 000 000 000 000 000 000 0001 000 000 000 000 000 000 0001 000 000 000 000 000 0001 000 000 000 000 0001 000 000 000 0001 000 000 000 1 000 0001 000100100.10.010.0010.000 0010.000 000 0010.000 000 000 0010.000 000 000 000 0010.000 000 000 000 000 0010.000 000 000 000 000 000 0010.000 000 000 000 000 000 000 001

yotta-zetta-exa-peta-tera-giga-mega-kilo-hecto-deca-deci-centi-milli-micro-nano-pico-femto-atto- zepto-yocto-

YZEPTGMkhdadcmµnpfa zy

More Details: Lengthmeters

centimeters (for smaller units of length)

millimeters (very small units of length)

kilometers (for large units of length)

These are the most commonly used.

More details: Massgram

kilogram

Measured using balances.

More details: Volumeliters

milliliters (for small volumes)

microliter (for extremely small volumes)

Measured using a graduated cylinder, pipet or buret (more accurate), volumetric flask or even a syringe.

Volume is a derived units…Some metric units are

derived from S.I. units.

Volume is L x W x H = cm x cm x cm = cm3

One cm3 is the same as one mL.

Also, dm x dm x dm = dm3

One dm3 is the same as one L.

Conversions Using Factor Label Method

Multiplying any number by an equality does NOT change the value.

An equality is two measurements that are equal in amount but have different units and numbers.

Examples:

one dozen bagels = 12 bagels

10 mm = 1 cm

Steps of Factor Label Method

1. Write down the units you are given.

2. Write X and a Line.

3. Write unit you want to cancel on the bottom of the line, the unit you want to keep on the top of the line. Find and plug in your equality. (hint: the larger unit will always get a 1 next to it)

4. Cancel units and do the math.

Let’s do one together…

0.600L = _______mL

0.600L X mLL

10001

= 600 mL

1 L = 1000mL

TRY THE REST ON YOUR OWN !!!!

Temperature ScalesThere are three temperature scales in use in this country that you need to be familiar with.

Temperature:

A measure of the average kinetic energy of the particles in a sample.

Fahrenheit18th-century German

physicist Daniel Gabriel Fahrenheit

Based his scale on an ice-salt mixture and normal body temperature

Freezing point for water = 32°F

Boiling point for water = 212°F

Celsius ScaleSwedish guy,

Anders Celsius in 174

Freezing point at 0°C.

Boiling for water at 100°C.

Below 0 is negative.

Kelvin ScaleEnglish guy, William

Kelvin

Measures molecular movement

Theoretical point of ABSOLUTE ZERO is when all molecular motion stops (no negative numbers)

Divisions (degrees) are the same as in Celsius

Absolute ZeroTheoretical point where there is absolutely no

movement of molecules in matter and a measure of ZERO ENERGY

This is not something that we ever witness, scientists have only theorized this point

Conversion Factors You need to know these conversion factors!

K = °C + 273

°C = K – 273 On Table T

NOT on Table T

Practice Conversion Problems

Room temperature is approximately 23°C. What is this temperature in Kelvin?

Ethanol has a boiling point of 351 K. That won’t help us if we have a thermometer reading degrees Celsius, so convert it.

Uncertainty in Measurement

Uncertainty in Measurement

No measurement can be perfect.

Scientists need to account for some degree of uncertainty in measurements.

Refer to terms accuracy and precision.

An ideal measuring device is accurate and precise and does not have a great deal of uncertainty.

AccuracyAccuracy is when you are close to the actual value of what you are trying to measure (For example you throw three darts and they are all close to the bull’s eye).

PrecisionPrecision is a measure of how close each measurement is to the others. For example if you are at the driving range and all of the golf balls head towards the pond, that is precision (but not accuracy).

Uncertainty in Measurement

Uncertainty occurs in every measurement made and must be accounted for.

In chemistry, we use different tools, each of which has certain limitations. We use the ± to indicate uncertainty in measurement.

Uncertainty EquationYOU MUST MEMORIZE THIS EQUATION AS YOU

WILL PERFORM IT ALMOST DAILY!

ΔF = (δF / δX1) ΔX1 + (δF / δX2) ΔX2 + …(δF / δXn) ΔXn

Just Kidding!However, there is a system we use in chemistry

that helps to minimize uncertainty by only including those values that have certainty and one that is uncertain.

We call them SIGNIFICANT FIGURES!

Using Significant FiguresWhy are significant figures important?

Have you ever multiplied two numbers and come up with a really LONG decimal?

Well, those numbers are INSIGNIFICANT with respect to scientific calculations.

And now for a short story…

Counting Sig FigsThe Atlantic-Pacific Rule

If the decimal is Absent (A), start counting on the Atlantic (right) side. Go to the first NON-zero number and count everything after that.

If the decimal is Present (P), start counting on the Pacific (left) side. Go to the first NON-zero number and count everything after that.

Quick Self-AssessmentHow many sig figs are in each of these

numbers:

98,000 m0.123 L0.00073 L8765 cm40,506 m 20.00 mL

More PracticeRound each number to the number of sig

figs shown in parentheses.

314.721 m (4)

0.001775 m (2)

8792 m (2)

Sig Figs in CalculationsWhen adding or subtracting

measurements, report to the LEAST number of DECIMAL PLACES.

For example:

12.52 + 349.0 + 8.24 = 369.76

You will report this with one decimal place as 369.8.

Sig Figs in CalculationsWhen multiplying or dividing

measurements, you want to report the answer with the same number of sig figs as the measurement with the least number of sig figs.

For example:

7.55 m x 0.34 m = 2.567 square meters

You will report this with 2 sig figs as 2.6 square meters because 0.34 m contains 2 sig figs.

Percent Error in Experimentation

When trying to determine how accurate your experimental value (“what you got in the lab”) is compared with the theoretical (“what it is supposed to be”), we use a simple formula.

experimental – theoretical x 100%

theoretical

Theoretical VS Experimental

Example of Percent ErrorWhen you calculate the density of chemical X

experimentally you get 1.13 g/mL. The actual density according to the literature is 1.16 g.mL. What is your percent error?

% %

DensityDensity is a derived unit which is found by

dividing a substances mass by its volume.

Density Equation

D=M/V

Common Units = g/mL or g/cm3

Density Practice Problems

1. A student measures the mass of a piece of metal to be 4.0g and it has a volume of 1.5mL what is the density of this metal?

2. The Density of CO2 gas is 1.8 grams per liter. What is the mass of 0.2L of CO2 gas?