Ch. 2: Measurements & Calculations

An Introduction to Scientific Investigations

What is Chemistry?

• Chemistry- the study of substances and the changes they can undergo. – EX: a match burning, how bleach removes stains, why

bread dough rises, etc.

• A) The Central Science– Chemicals are everywhere, in everything, and

impact many different aspects of life. Chemistry, therefore, is considered a central science. Life, as we know it, is a product of what Chemistry and Physics has already done.

• (ex. occupations which require chemistry: Engineering, medical professionals, hair stylists, crime labs, cosmetic makers, drug developers, oil companies, Wine makers, Mc Donald’s, Candy makers, Photographers …)

• B) Why Study Chemistry?– To help you understand the physical

world around you. To develop skills for evaluation and critical thinking. Maybe even help prepare you for a job which requires chemistry.

2.1 The Scientific Method

• Scientific Method- an orderly, systematic approach to gather knowledge. It is a way of answering questions about our observable world.

• Steps of the Scientific Method1. Make an observation2. State the question3. Collect information4. State a hypothesis5. Design an experiment6. Make observations 7. Collect, record and study data8. Draw a conclusion

• Making an Observation– Notice a natural event: the ball falls to

the ground, the sky is blue, etc. This observation can be about almost anything! Once you’ve noticed something… form a question.

• Forming a Hypothesis– This should be a possible, logical,

answer to the question about your observation. It is typically expressed in a “cause-and-effect” format. A scientific hypothesis must be one which requires and can be tested by an experiment. If it does not… it is not “scientific”.

• Performing an Experiment– For a hypothesis to be tested

properly, you must design and perform an experiment which examines ONE variable at a time. If you have more than one variable the results will not be conclusive and very little knowledge will be gained.

• Interpreting the Results– Once the experiment is complete…

you look at your data and the observations you made interpret what they tell you. Did you prove your hypothesis wrong? Did you learn anything new? (Experimental control)

Quantitative- numerical values

Qualitative- “descriptive” i.e. color, shape, ect.

• Laws and Theories– Law- a statement of fact meant to explain, in

concise terms, an action or set of actions. It is generally accepted to be true and universal, and can sometimes be expressed in terms of a single mathematical equation. THEY TELL WHAT HAPPENED.

– Theory- an explanation of a set of related observations or events based upon proven hypotheses and verified multiple times by detached groups of researchers. One scientist cannot create a theory; he can only create a hypothesis. THEY EXPLAIN AND PREDICT EVENTS.

Lab Safety

• Video

• http://www.youtube.com/watch?v=VRWRmIEHr3A

2.2 Units of Measurement

• The International System of Units

– In 1960, at a scientific conference on units held in France, the SI system of units were internationally accepted for the scientific community. The SI system is based on the metric system and we refer to these as base units.

BASE UNITS

Mass kilogram kg

Length meter m

Time seconds s

Count quantity mole mol

Temperature kelvin K

Electric current ampere A

Luminous intensity candela cd

• Meter- defined as the distance that light travels in a vacuum during a time interval of 1/299,792,458 of a second.

• Mass- amount of matter in an object. 1 kg = 2.2 lbs (on earth).

• Weight - equals the force of gravity pulling on the object. – ?? What changes in outer space… weight or

mass??

• Derived units - a combination of 2(+) base units =a new unit.

DERIVED UNITS

Area Square meter m2

Volume Cubic meter m3

Force Newton N

Pressure Pascal Pa

Energy Joule J

Power Watt W

Voltage Volt V

Frequency Hertz Hz

Electric charge Coulomb C

Area- length X width = m X m= m2

Volume- the amount of space that an object occupies.

Length X width X height = m X m X m= m3

EXCEPTIONS…

The liter (L)- the common unit for volume. 1mL= 1cm3

Celsius (C)- common unit for temperature

1K = (273 + C)

• Metric Prefixes– Prefix- a word attached to the front of

the base unit. • The SI prefixes are base 10 and,

therefore, increase and decrease by 10’s.

Prefix Abbreviation # Power of 10

mega- M 1,000,000 106

kilo- k 1,000 103

hecto- h 100 102

deca- da 10 101

Base 1 100

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- 0.000001 10-6

nano- n 0.000000001 10-9

Converting among prefixes

• When converting from one prefix to another, remember this saying:– King Henry Died By Drinking

Chocolate Milk.

• When set up as such: – k h da _ d c m

• Now converting among prefixes is just a matter of pushing the decimal

 Problem Solving

• Dimensional Analysis- technique of converting between units.  Unit equalities show how different units are related (1g=100cm).  Conversion factors are written from the unit equalities.  The conversion factor is set up so that the bottom number cancels the given unit and a new unit is created.  – Example:  Convert 10 cm to inches. Conversion

factors (1m = 100 cm)   (1m = 39.37inches)

• Start with the given unit, then use your conversion factors to cancel units to arrive at the unit you want to convert to.

Density

• The ratio of mass to volume: – Mass ÷ Volume

• The SI unit for density is kg/m3.

– Ex. A sample of metal has a mass of 12.3g and a volume of 2.5 cm3. What is the density of this metal?

2.3 Using Scientific Measurements

• Making Measurements– When recording a measurement you will record

all the certain/known/exact digits and one uncertain (usually a rounded digit)

• Ex. The measurement should be read to the 1000 th’s place exactly, but you read 21.32584 g on your scale… you should record 21.3258 g. The 8 is the uncertain digit.

– ****REMEMBER- Always record the units you are referring to in the measurement!!!!!!!!!!

• How many ml are in this graduated cylinder?– Hint: look at

the meniscus.

2 reasons for uncertainty in measurement• 1. Instruments used for measuring are not

perfect/ without flaws

• 2. Measuring always involves some estimation.

• The type of estimation required depends on the instrument you are using.– Digital display: The last digit on the display is the

estimated digit. The estimation is done for you! If the digit flickers… record the digit that seems to be “preferred”.

– Using a scale: The only “certain” numbers are those marked on the scale…all other values in between the markings are the uncertain digits.

• Reliability in MeasurementMeasurements can be checked for precision and accuracy to determine their reliability.

–Precision- continuing to get the exact reading every time.

–Accuracy- getting the accepted value (the exact measurement)

• ?? Is it possible to be precise and not accurate? Accurate and not precise? Neither accurate nor precise? Both accurate and precise?

• Significant Digits– 1. Leading zeros are never significant.

– 2. Imbedded zeros are always significant.

– 3. Trailing zeros are significant only if the decimal point is specified.

Hint: Change the number to scientific notation. It is easier to see.

EXAMPLES:Example Number of

Significant Figures

Scientific Notation

0.00682 3 6.82 x 10-3 Leading zeros are

not significant.

1.072 4 1.072 (x 100) Imbedded zeros are always significant.

300 1 3 x 102 Trailing zeros are significant only if

the decimal point is specified.

300. 3 3.00 x 102

Addition & Subtraction

•The last digit retained is set by the first doubtful digit.

Addition Even though your calculator gives you the answer 8.0372, you must round off to 8.04. Your answer must only contain 1 doubtful number. Note that the doubtful digits are underlined.

Subtraction Subtraction is interesting when concerned with significant figures. Even though both numbers involved in the subtraction have 5 significant figures, the answer only has 3 significant figures when rounded correctly. Remember, the answer must only have 1

doubtful digit.

Multiplication or Division•

The answer contains no more significant figures than the least accurately known number.

Multiplication The answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures.

Division The answer must be rounded off to 3 significant figures, since 45.2 has only

3 significant figures.

Notes on Rounding

When rounding off numbers to a certain number of significant figures, do so to the nearest value. Round like normal.– ex: Round to 3 significant figures:

2.3467 x 104 (Answer: 2.35 x 104)

– ex: Round to 2 significant figures: 1.612 x 103 (Answer: 1.6 x 103)

EXCEPT…………..EXCEPT…………..

• What happens if there is a 5 with a 0 after it? There is a rule: – If the number before the 5 is odd, round up. – If the number before the 5 is even, let it be.

The justification for this is that in the course of a series of

many calculations, any rounding errors will be averaged out. • ex: Round to 2 sig figs: 2.350 x 102 (Answer: 2.4 x 102) • ex: Round to 2 sig figs: 2.450 x 102 (Answer: 2.4 x 102)

Of course, if we round to 2 significant figures: • 2.452 x 102, the answer is definitely 2.5 x 102 since

2.452 x 102 is closer to 2.5 x 102 than 2.4 x 102.

Scientific Notation • Chemists often work with numbers that are

extremely large or extremely small. – For example, there are

10,300,000,000,000,000,000,000 carbon atoms in a 1-carat diamond each of which has a mass of 0.000,000,000,000,000,000,000,020 grams. It is impossible to multiply these numbers with most calculators because they can't accept either number as it is written here.

• To do a calculation like this, it is necessary to express these numbers in scientific notation, as a number between 1 and 10 multiplied by 10 raised to some exponent.

Exponent Review

Some of the basics of exponential mathematics are given below.

• Any number raised to the zero power is equal to 1. 10= 1 100= 1

• Any number raised to the first power is equal to itself. 11 = 1 101 = 10

• Any number raised to the nth power is equal to the product of that number times itself n-1 times.

22 = 2 x 2 = 4 105 = 10 x 10 x 10 x 10 x 10 = 100,000• Dividing by a number raised to an exponent is the

same as multiplying by that number raised to an exponent of the opposite sign.

Converting to Scientific Notation

The following rule can be used to convert numbers into scientific notation: The exponent in scientific notation is equal to the number of times the decimal point must be moved to produce a number between 1 and 10.

Ex: In 1990 the population of Chicago was 6,070,000. To convert this number to scientific notation we move the decimal point to the left six times.– 6,070,000 = 6.070 x 106

• To convert 10,300,000,000,000,000,000,000 carbon atoms into scientific notation, we move the decimal point to the left 22 times.

10,300,000,000,000,000,000,000 = 1.03 x 1022

• To convert numbers smaller than 1 into scientific notation, we have to move the decimal point to the right. The decimal point in 0.000985, for example, must be moved to the right four times.

–0.000985 = 9.85 x 10-4

• The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant, as shown by the following examples. 2.4 x 1022 2 sig. figs

9.80 x 10-4 3 sig. figs

1.055 x 10-22 4 sig. figs

Percents and Percent Error

You can change fractions to percent by dividing the top number by the bottom number and multiplying by 100 =%

– Ex. There are 29 students in Mrs. G’s first hour, 17 of the students are girls.  What percent are girls?

• 17÷29 =.59 x 100 = 59%

• Percent Error calculates how much error you have between your answer and a commonly accepted value. The formula is:– % Error = measured value - accepted value X 100

Accepted value

• What if we calculated the density of water, in class, and many students reported values other than the accepted value of 1g/ml or 1g/cm3. Let’s say you calculated the density of water to be .9g/ml– % Error = 0.9 - 1   x 100 = 10% error           

1

Ratios• Units found by dividing one unit by another.  (The

speedometer in your car registers the ratio of miles/hour.) The most common ratio in chemistry is density (g/ml or g/dm3). Density is calculated by this formula:

density = mass/volume• Lets say you had an object that’s mass was 20g

and its volume was 10cm3.  How would you calculate the density?– Density = mass/volume = 20g/10cm3 = 2g/cm3

• If you are given the mass and the density can you calculate volume?– Yes!  Density = mass/volume ► volume = mass/density.

Graphing

PRESENTING SCIENTIFIC DATA: • An important part of your lab write-up is

the presentation of your data. You will commonly present data in tables and easy to read graphs.

• Line Graphs- best for continuous changes– Generally compare 2 variables- one,

Independent, the other, dependant. – Graphs made with an x-axis (the independent

variable) and a y-axis (the dependant variable)

Bar Graphs- to compare items/events

• Helps to make clearer how large or small the differences in individual values maybe.

Pie Charts- show parts of a whole

• Helps to show percentages (%) of a whole.