Chapter 2Measurement and Calculations

Chapter 2Measurement and Calculations

The marshmallow test

The marshmallow test study description and conclusionshttp://www.youtube.com/watch?v=amsqeYOk--w&NR=1

http://youtu.be/QX_oy9614HQ

Observing and Collecting DataQualitative: Use descriptions to

explain dataEx: small, white, puffy, smells good,

quiet, wiggly

Quantitative: Use numbers to describe dataEx: 4 cm, 5.30 grams, 15.65 minutes

2.1 The Scientific Method

System – a specific portion of matter in a given region of space that has been selected for study during an experiment.

2.1

Example: In Marshmallow Test, the system is the child, the marshmallow, the plate, and everything in the room.

Surroundings – everything outside of the system.

Example: In the Marshmallow Test, the surroundings are everything outside of the room.

2.1 The Scientific Method – a review

Formulating HypothesesA hypothesis is a testable statement

(it really is not just an educated guess)

A hypothesis is often written as an if – then statement

2.1

Ex. If phosphorus stimulates plant growth, then plants treated with phosphorus fertilizer should grow faster than plants not treated with phosphorous fertilizer (all other variables held constant).

Sometimes we add more detail to the hypothesis:• Plants that receive more phosphorus should

grow faster than those that receive less phosphorus.

Testing Hypotheses2.1

In Science, there is a commitment to follow the evidence, wherever it leads. If a hypothesis is not supported by data, it must be rejected.

There must also be a willingness to accept that new evidence may require us to modify or change our ideas about what we thought to be true.

So, was the hypothesis about phosphorus fertilizer correct?

Theorizing2.1

In everyday language, the word “theory” is often misused when a more accurate term would be “hypothesis.”

Example: I have a theory that it always rains after I wash my car.

This is really a hypothesis. It has not been, but could be tested. A theory would have already been vigorously tested, generated consistent results, and would offer an explanation of why the event occurs.

Theorizing2.1

A theory is a broad generalization that explains a body of facts or observations.

Theories are well documented and proved beyond reasonable doubt.

Scientists continue to tinker with the component parts of each theory in an attempt to make them more exact. Theories can be tweaked, but they are seldom, if ever, entirely replaced.

The SI Units of Measurement (le Système International, SI)

You do not need to be concerned with Amperes and candelas this year

2.2

Quantitative Measurements

Always contain two partsnumberunit

Both parts must be present for the measurement to be meaningful.

2.2 Units of Measurement

The SI Units of Measurement (le Système International, SI)

Prefixes are added to these base units to show quantities in larger or smaller amounts.

(you will have the ones you need on a handout)

2.2

Here are a few of them:Tera T 1012 1 000 000 000 000Giga G 109 1 000 000 000Mega M 106 1 000 000Milli m 10-3 1/1000Nano n 10-9 1/1 000 000 000

SI Measurement2.2

A quantity is something that has magnitude, size or amount.

The units of measurement must be standardized for the measurement to make sense to everyone. A standardized system of measurement is one in which everyone agrees upon the size of the unit. Early systems of measurement were based upon the size of the king’s foot, or length of arm, for example.

But this type of system has problems:• What happens if you want to communicate

measurements to someone in another country?

• What happens when you get a new king?

2.2

Mass- • a measure of the amount of matter in an object• standard unit is the kilogram (but we often use grams)• not the same as weight

Remember this?Weight is a measure of the pull of gravity on the object, so the stronger the gravitational pull, the higher the weight.

SI Base Units

2.2

Length- • a measure of distance• standard unit is the meter • we often use mm, cm

SI Base Units

2.2

Volume- • the amount of space an object takes up

• standard unit for liquids is the liter (L) but we often use mL (1/1000 of a liter)

• we also use cm3 (for solids)

SI Base Units

It is very helpful to know that 1 mL and 1 cm3 are equal volumes

1 cm3 = 1mL

Used for solids Used for liquids

2.2

2.2 Density

Density = mass divided by volume

Density is a measure of how packed together the molecules are. The more packed together it is, the more dense it is.

Which material below is most dense?A B

DensityDensity - mass per unit volume

(g/cm3 for solids and g/mL for liquids)

D = MV

DM

V

2.2

2.2 Density is a ratio of mass to volume.Does changing the size of the sample (like cutting it in half) change the density?

Example: a 2 cm3 piece of copper weighs 18 g. What is the density of the copper?

Half the size: 9 g 1 cm3

= 9 gcm3

18 g 2 cm3

= 9 gcm3

Density for a material does not depend on the size of the sample!

D = M V

What is the density of a piece of copper that is half the size?

Density Practice Problem 1An object has a volume of 825 cm3 and a

density of 13.6 g/cm3. Find its mass.

GIVEN:V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:M = DVM = (13.6 g ) x (825 cm3)

cm3

M = 11,220 g

DM

V

2.2

Density Practice Problem 2A liquid has a density of 0.87 g/mL.

What volume is occupied by 25 g of the liquid?

GIVEN:D = 0.87 g/mLV = ?M = 25 g

DM

V

WORK:V = M D

V = 25 g 0.87 g/mL

V = 28.73563218 mL

2.2

Density Practice Problem 3You have a sample with a mass of 620 g &

a volume of 753 cm3. Find density.

GIVEN:M = 620 gV = 753 cm3

D = ?

DM

V

WORK:D = M V

D = 620 g 753 cm3

D = 0.823373174 g/cm3

2.2

2.2

Multiplying or dividing SI units creates a “derived unit”

(derived units are generated by calculation, not by a direct measurement)

Derived SI Units

Volume = length x width x height

Volume =__ cm x __cm x __cm Volume = __cm3

Example: measuring the volume of a shoebox

a derived unit that came from a calculation

You measure these directly

How do you find the mass of an object?

How do you find the volume of an object?

Put it on a balance and weigh it!

If it is rectangular, you can multiply length x width x height

For irregular shaped objects, slide it into water and notice how much the water level rises

Lab:

Scientific Notation - a quick review

36 000 = 3.6 x 1040.0081 = 8.1 x 10-3

8.6 x 1018

coefficient

exponent

Scientific notation allows us to talk about numbers that are very, very large or very, very small

(2.3)

Example 1: one electron weighs0.000000000000000000000000009109 grams

(that’s 27 zeros after the decimal point)Its much easier to write the mass of an electronin scientific notation as…9.109 x 10-28 grams

(2.3)

Example 2:12.0 grams of carbon contains 602000000000000000000000 atoms of carbon

That’s…………..6.02 x 1023 atoms

Why do we need scientific notation in chemistry?

Write in Scientific Notation

1) 98,500,000 =

2) 64,100,000,000 = 3) 279,000,000 = 4) 4,200,000 =5) 0.0054 =

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

Note that we put only one digit in front of the decimal. (This makes it a number between 1 and 10)This is proper scientific notation form.

5.4 x 10-3

(2.3)If the number is GREATER than 1, the exponent is POSITIVEIf the number is LESS than 1, the exponent is NEGATIVE

1. 6.27 x 106 =2. 9.01 x 104 =3. 2.65 x 10 -3

=

6,270,00090,1000.00265

Write in Decimal notation(2.3)

If the exponent is +, move the decimal to the RIGHTIf the exponenet is -, move the decimal to the LEFT

What’s wrong with these?

30 x 106

0.1 x 10-3

10.1 x 1012

0.72 x 10-9

Can you fix them?

3.0 x 107

1 x 10-4

1.01 x 1013

7.2 x 10-10

Improper form!

(2.3)

There should be one digit in front of the decimal

Scientific Notation MathMultiplying scientific notation:

1. Multiply the coefficients2. Add the exponents3. Make sure the new coefficient is a

number between 1 and 10(2.5 x 104) x (4.5 x 103)(11.25 x 107)(1.125 x 108)

Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

}

31

Scientific Notation Math

Dividing scientific notation:1. Divide the coefficients2. Subtract the exponents3. Make sure the new coefficient is a

number between 1 and 10(2.5 x 104) ÷ (4.5 x 103)(.5555… x 101)(5.6 x 100)

Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

}

32

Scientific NotationAdding Scientific notation:1. Set both notations to the same exponent.2. Add the coefficients3. Exponent stays the same4. Make sure the new coefficient is a number between 1 and 10

(3.4 x 104) + (5.7 x 107)(3.4 x 104) + (5700.0 x 104)5703.4 x 104

5.7034 x 107

Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

33

Scientific NotationSubtracting Scientific notation:1. Set both notations to the same exponent.2. Subtract the coefficients3. Exponents stay the same4. Make sure the new coefficient is a number

between 1 and 10(3.4 x 104) - (5.7 x 107)(3.4 x 104) - (5700.0 x 104)-5696.6 x 104

-5.6966 x 107

Remember: If you increase the coefficient, you must decrease the exponent. If you decrease the coefficient, you must increase the exponent.

34

Scientific Notation And Your CalculatorTo key in the number 4.2 x 103….

Type 4.2 (the base)Press EE or EXP (this takes care of the x 10 part)Type 3 (the exponent)

Don’tType 4.2 X 10 ^ 3 (don’t use the evil ^ button!)

DON’T hit the x (times button) if you are using the EE or EXP button

(2.3)

Try out your calculator

(3.1 x 103)(4.8 x 102)Answer: 1.488 x 106

calculator may say 1.488 E 6 calculator may say 1.488 6

If you didn’t get these answers, let’s examine your calculator to see what buttons you should press.

It is important to learn how your individual calculator works.

Borrowing a calculator from a friend is not a good idea because you may make input errors if theirs works differently from the one you are used to.

(2.3)

or 1 488 000

Try out your calculator again

(8 x 10-7) x (4 x 10-1) Answer: 3.2 x 10-7

or 0.00000032

calculator may say 3.2 E -7

If you didn’t get this answer, get help NOW!

(2.3)

The videohttp://www.powersof10.com/

Powers of Ten slide showhttp://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Sci notation pracrticehttp://www.aaamath.com/dec71i-dec2sci.html

Sci notation practice with quizhttp://janus.astro.umd.edu/cgi-bin/astro/scinote.pl

For more scientific notation practice:

Quick Tutorial on Scientific Notation:http://www.swtc.edu:8082/mscenter/mthsci/science/1tools/p02csnot.pps

(2.3)

Sci notation practicehttp://janus.astro.umd.edu/astro/scinote/

Scientific notation practice sitehttp://science.widener.edu/svb/tutorial/sigfigurescsn7.html

messing with the exponents in sci notationhttp://www.ucel.ac.uk/rlos/essentialmaths/M1/1E.Int3.htm

decimal sci notation conversionshttp://academic.umf.maine.edu/~magri/tools/DSconversion.html

Scientific Notation Practice Worksheet 1

Scientific Notation Practice Worksheet 2