Fundamentals of Chemistry

Unit OneScientific Method and

Measurement

Scientific Method

Scientific Method: A way to Solve Problems.

Steps of the Scientific MethodStep 1: Identify the problem

To begin the scientific process, a problem must be clearly and specifically identified.

Step 2: Gather InformationBefore setting out to find the answer to

a scientific question, information must be gathered in the form of preliminary research.

Sources such as journals and scientific papers could be checked for existing

information on the problem at hand.Step 3: For m a Hypothesis

Once a problem or question has been recognized, a hypothesis or educated guess is

constructed. In an experiment, hypotheses are not

“correct” or “incorrect”, they are supported or not supported by the data collected.

if a hypothesis has be tested repeatedly and not disproven it is known as a theory or postulate.

Theory answers the question “Why?”

(a theory explains what happened)

A rule of nature is known as a law. Ex. Law of attraction and repulsion, Law of universal gravitation.

Lawanswers the question “what?”(Law tells what happens)

Step 4: Experimentation and Observation – Used to test your hypothesis.

Data collected during this step needs to be organized and analyzed.

-2 types of data: Qualitative & Quantitative.▪Qualitative made using the five

senses▪Quantitative made using instruments

**Think about qualitative as “what” and quantitative as “how much”

A controlled experiment contains only 1 experimental variable.

-Variable any factor affecting the outcome of an experiment.

▪Independent variable is set and controlled by the

experimenter (such as time)

▪Dependent variable changes based on what is done to

the experimental variable.

(such as plant growth)Properly set-up experiments provide a control

group as well as an experimental group.-Control groups are set-up under

“normal” conditions and are used to compare to the experimental groups.

Step 5: Draw Conclusions interpretations of experimental results. reference should be made to the original hypothesis.Questions to think about in the conclusion may include:

*Was the hypothesis supported or not supported by the data?

*What were possible sources of error in the lab?

*What are some ways to improve the experiment?

*What are some questions yet to be addressed?

Important considerations:1) If the data does not support the initial

hypothesis, the experiment was not pointless!

2) If the original hypothesis or problem addressed needs to be modified, the whole process needs to start over.

Sometimes an experiment that “goes wrong” opens

the doorway to a new discovery.

How Much Liquid is in Each Graduated Cylinder?

Significant Figures: a system for representing measured values with the correct degree of accuracy. Its main purpose is to know how much to round off answers calculated from any measurement. A "significant" figure is a figure that is considered accurate.

Significant figures: all of the digits that are known in a measurement plus a last digit that is estimated. Measurements and calculations should ALWAYS be recorded to the correct number of significant figures! Example: Room temperature 25.4ºCSuppose you were given temperature data for various points in Frederick from a variety of sources and the data looked like this: 23.232ºC, 25.2ºC , 26.1746ºC , 27.12ºC. When you calculate the average, how many sig figs should keep?3 significant figures (25.4ºC)

General Rule of Sig FigsAn answer cannot be more precise than the least precise measurement from which it was calculated.

RULES to identifying the number of sig. figs.:1)Every Nonzero digit in a reported

measurement is significant• 56.6, 2.34 and 978 all have 3 sig. figs.

2)Zeroes between nonzeroes are significant.• 6007, 50.89 and 5.708 all have 4 sig. figs.

3)Leading zeros appearing in front of nonzero digits are placeholders and not considered significant.

• 0.000091, 0.042 and 0.42 all have 2 sig.figs.

4) Zeros at the end & to the right of a decimal point are ALWAYS significant.

• 57.00, 2.030 and 7.000 all have 4 sig. figs.

5) Zeros at the end & to the right without a decimal point are NOT significant unless a careful measurement was actually made (which will have a decimal point after - 10.) • 400, 4000 and 30000 all have 1 sig. fig.

When calculating the correct number of sig figs in an answer, perform all of the calculations first then round the final answer.

Summary1. If you are not a zero, you are significant.

2. If you are a sandwiched zero, you are significant. 3. If you are a zero at the end of a number, and there’s a decimal in your number, you are significant. 4. If you are a zero at the end of a number, and there’s NOT a decimal in your number, then you are NOT significant. 5. If you are a zero and you are at the beginning of a number, you are NOT significant.

Adding or subtracting round to the same number of

decimal places as the measurement with the least number of decimal places.

Examples3.451 + 1.41 + 2.072 = 6.933

6.93 (2 dec.)

7.982 + 1.02 + 2.1 = 11.102 11.1 (1 dec. )

3.45 – 1.1 = 2.35 2.4 (1 dec.)

Multiplying or dividinground the answer to the same

number of significant figures as the measurement with the least number of significant figures.

examples:2.1 x 1.301 = 2.7321

2.7 (2 sig figs)4.02 x 2.945 = 11.8389

11.8 (3 sig figs)0.034 x 3.223 = 0.109582

0.11 (2 sig figs)

Scientific Notation ReviewScientific Notation

A number written in scientific notation has two components:

-a coefficient and 10 raised to a power

•Coeffiecient must be greater than or equal to 1

and less than 10. Examples:

2.3 x 103

7.9 x 10-5

What is 540,000 in scientific notation?-Number between 1 & 10 = 5.4-Move the decimal 5 times

5.4 x 105

5.4 x 10 = 5454 x 10 = 540540 x 10 = 5,400 5,400 x 10 = 54,00054,000 x 10 = 540,000 5.4 x 105 = 540,000

Power can be positive or negative positive power of ten, the decimal moves one place to the right.Examples: 4.67 x 103 = 4670 2.71 x 104 = 27100negative power of ten, the

decimal point moves one place to the left.

Examples: 4.5 x 10-6 = 0.0000045 1.21 x 10-3 = 0.00121

*Remember: 10-1 = (1/10) = 0.1 3.2 x 10-1 = (3.2/10) = 0.32

Accuracy & PrecisionCounting is exact!! Ex. 26 students in this classCounted numbers are considered to have infinite precision.Measurements are subject to error. (Errors reflect limitations in the methods used to make the measurement.)

-Examples of error: incorrectly calibrated equipment or uncertainty of equipment or uncontrollable human error If each of the individual measurements in a set of data are close to the average of the set, then they are precise.

PrecisionPrecision of an individual measurement is determined by the markings on the piece of equipment used to take the measurement.REMEMBER: the number of significant figures in a measurement is determined by:

-all of the known digits in the measurement

(indicated by the markings on equipment)

-plus one digit that is estimated (how far in between the markings).

Precision ExampleA thermometer marked in whole ºC and you read it as 25.5ºC .

-you would be estimating 1 decimal place!!-the 25 degrees in known and the .5

is estimated.(It was marked to the whole degree,

so you can only estimate to the tenth.)

**Only estimate 1 place beyond what you can read for sure!!**

AccuracyAccuracy refers to the closeness of the average of the set to the “accepted” value and depends on how carefully the measurement was made.Example: A block of wood has a length of

4.3cm. -Student 1 measures the length of the block and finds it to be 4.4cm. -Student 2 measures the block of wood

and determines its length to be 5.2 cm.*Which measurement is more

accurate?4.4cm

Metal Ruler:

Object is more than 12.3cm and just less than 12.4cm.

The smallest marking represents 0.1cm, so you estimate to the nearest 0.01cm.

The length of the object would be accurately and precisely recorded as 12.39cm.

The last digit is estimated, so, 12.31 – 12.39cm would be acceptable.

Plastic Ruler:

Object is more than 12cm and less than 12.5cm.

The smallest marking represents 0.5cm, so you estimate to the nearest 0.1cm.

The length of the object would be accurately and precisely recorded as 12.4cm.

The last digit is estimated, so, 12.1 –12.4 cm would be acceptable. (Up to 0.5 cm off)

Which ruler is more precise?

How much is the smallest marking worth?0.1 gram (you can read it to the tenth’s place!!)

What are the digits of this mass you know for certain?

200.5 grams(hundreds, tens, ones, tenths marked)

Next you always estimate 1 place beyond.200.53 grams

From 200.51g to 200.57

g

Good or Poor??

Good accuracy

Good precision

Poor accuracy

Good precision

Good or Poor??

Good accuracy (on average)

Poor precision

Poor accuracy

Poor precision

More Examples!!Which number is more precise?(If you were buying a gold nugget, how many decimal places would you want to be sure of??)

A) 3.00g B) 3.000g C) 3gANSWER: B) 3.000g

Which number is a more accurate measure of a 7.00kg block? (accuracy deals with closeness!!)

A) 6.93kg B) 6.9kg C) 8 kgOff by: 0.07kg 0.1kg 1kg

ANSWER: A) 6.93kg

Remember to think about accuracy , precision and significant digits ALL THE TIME!! An answer of 9.067894038399L is not an acceptable answer in lab, test or any other piece of paper that bears the privilege of sporting your signature!!

Percent ErrorA mathematical value representing the difference between the accepted value and the experimental value.

(analyzes the accuracy of the data)Accepted value correct value (what the

data should be – based on reliable research)(What you are told it should be!!)

Experimental value value measured in lab

(what you measure or calculate it to be!!)

Formula:

% Error =

Experimental value – Accepted value x 100%

Accepted value

Negative % error Your answer is lower than it should be.

Positive % error Your answer is higher than it should be.

% Error Example 1A block of wood has a length of 4.3cm. A student measures the length and finds it to be 4.4cm. What is this student’s % error?

Accepted value – experimental value x 100%

Accepted value

Experimental value = 4.4 cm (student measured)

Accepted value = 4.3cm (what you’re told it should be)

4.3cm – 4.4cm x 100% = -2.3 % error

4.3cm

% Error Example 2A block of wood has a length of 15.8cm. A student measures the length and finds it to be 15.7cm. What is this student’s % error?

Accepted value – Experimental value x 100%

Accepted value

Experimental value= 15.7 cm (student measured)

Accepted value= 15.8cm(what you’re told it should be)

15.8cm – 15.7cm x 100% = 0.63 % error 15.8cm

Metric MeasurementsSI (International System of units) system is used worldwide based on units of ten.Base

UnitAbbreviatio

nQuantity Measured

Meter m Length

Second s Time

Kelvin K Temperature

Gram g Mass

Ampere A Electric current

Candela Cd Luminous intensity

Mole Mol Amount of substance

All other units are derived from the seven base units (thus known as derived units).Volume: The amount of space an object occupies.

Can be determined by three methods:

1. Formula: volume=ℓ x w x h (units= cm3)

2. Measuring with a graduated cylinder(units = mL)

3. Determined by water displacement(units = mL = cm3)

Remember that 1 mL = 1 cm3

If a metal block displaces 8.0mL of water, then the block’s volume in cm3 is 8.0cm3.

* What is the volume in cm3 of a metal toy that displaces 7.5mL of water when dropped into a small container?

7.5cm3

Mass A measure of the amount of matter in an object.Measured on a balance. (ex. Triple beam balance, digital or electronic balance)

Weight A measure of the force of gravity acting on an all objects with mass. The product of mass and gravitational force.

Density The amount of mass per unit of volume. formula: density=mass/volume

D = m/V

Temperature A measure of the average kinetic energy of the particles in a sample of matter. The scales are used to measure temperature are Fahrenheit, Celsius and Kelvin. Kelvin is the SI unit for temperature.

Using Prefixes

The distance form Maryland to Utah would be best measured in km.The length of a pencil would be measured in cm.The height of the letter “h” would be measured in mm.

** Different prefixes are used for different amounts**

Prefix Symbol # base units Sci. Notation

Mega M One million 1 x 106

Kilo k One thousand 1 x 103

Hecta h One hundred 1 x 102

Deka dk Ten 1 x 101

Base unit One 1 x 100

Deci d One tenth 1 x 10-1

Centi c One hundredth

1 x 10-2

Milli m One thousandth

1 x 10-3

Micro μ One millionth 1 x 10-6

Nano n One billionth 1 x 10-9

Pico p One trillionth 1 x 10-12

Conversion sTo convert between units, you could move the decimal point. (if factors of ten!!)

_____ ____ ____ 0.4 4 40 400

K h dk U d c m

0.0004 0.004 0.04

5 50 500 5000 _____ ______ _____50000 500000

5000000

Dimensional Analysis (factor-label method)

used to convert from units1) write down what is known (number & unit)2) set up a conversion factor with the target end unit on top and one known unit on the bottom (if unit you are canceling is on top)3) divide the product of the numbers in the numerator by the product of the numbers in the denominator4) make sure that the final answer has the same number of significant figures as the number given.

Examples#1. How many seconds are in 7 minutes?

known = 7 min.

conversion factor = 60 sec. / 1 min.

7 min x 60 sec = 420 sec = 420 sec

1 min 1

Examples#2. How many cm are there in 5.2

meters?

known = 5.2 m

conversion factor = 1 m / 100 cm

5.2 m x 100 cm = 520 cm = 520 cm

1 m 1

Examples#3. How many hours are there in 3

weeks?known = 3 wkconversion factor = 1 wk / 7

days1 day / 24 hr

3 wk x 7 days x 24 hr = 520 hr = 520 hr

1 wk 1 day 1