Chemistry 11, Unit 01 1 Lesson 01: The Scientific Method
01 Introduction
The scientific method is a process of inquiry which attempts to explain the natural phenomena in a manner which is… logical consistent systematic
The ultimate goal of the scientific method is to arrive at an explanation that is… well-tested well-documented well-supported by evidence
For the scientific method to be termed scientific, the method of inquiry must be based on evidence that is… empirical: knowledge acquired by observation or experimentation measurable: knowledge acquired by measurement
Chemistry 11, Unit 01 2 02 Terminology
Three terms often used to describe the scientific method are often confused… hypothesis law theory
Hypothesis
This is an educated guess based upon observation. It is a rational explanation of a single event or phenomenon based upon what is observed, but which has not been proven. Most hypotheses can be supported or refuted by experimentation or continued observation.
Law
This is 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.
Some scientific laws include… the law of gravity the law of thermodynamics Hook’s law of elasticity
Chemistry 11, Unit 01 3 Theory
A theory is more like a scientific law than a hypothesis. A theory is 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.
In general, both a scientific theory and a scientific law are accepted to be true by the scientific community as a whole. Both are used to make predictions of events. Both are used to advance technology.
The biggest difference between a law and a theory is that a theory is much more complex and dynamic… a law governs a single action, whereas a theory explains a whole series of related phenomena
Some scientific theories include… the theory of evolution the theory of relativity the quantum theory
Chemistry 11, Unit 01 4 03 Process
There are roughly six steps to the scientific method… making observations identify a problem proposing a hypothesis designing an experiment to test the hypothesis acquiring and analysis of data accepting or rejecting the hypothesis
Scientific Method Summary
Chemistry 11, Unit 01 5 04 Making Observations
You may think the hypothesis is the start of the scientific method, but you will have made some observations first, even if they were informal.
05 Identify a Problem
What you observe leads you to ask a question or identify a problem. What is the problem? What is the question that needs to be answered?
Chemistry 11, Unit 01 6 07 Proposing a Hypothesis
A hypothesis is a proposed explanation for the behaviour of observed phenomena.
08 Designing an Experiment to Test the Hypothesis
To prove whether or not a hypothesis is valid requires… testing or experimentation
When you design an experiment, you are essentially doing two things… controlling variables measuring variables
Chemistry 11, Unit 01 7 The three types of variables are... controlled variables: these are parts of the experiment that you try to keep constant throughout an experiment so that they won't interfere with your test independent variable: this is the variable you manipulate dependent variable: this is the variable you measure (it depends on the independent variable)
09 Acquiring and Analysis of Data
As far as the results of ain experiment are concerned, you will need to… record data present the data in the form of a chart or graph, if applicable analyse the data
Chemistry 11, Unit 01 8 10 Accepting or Rejecting the Hypothesis
At this stage two outcomes are possible... accept the hypothesis reject the hypothesis
If the hypothesis is accepted, communicate your conclusion(s) and explain it.
If the hypothesis is rejected, then you need to either adjust the original hypothesis or come up with a completely new one and start the process again.
Chemistry 11, Unit 01 9 Lesson 02 01: Scientific Notation
Introduction
Since numbers can be very large or very small when written, a way had to be devised such that many zeros were not needed. Scientific notation solves this problem…
Decimal Notation Scientific Notation 1000000000 1x109 1000000 1x106 1000 1x103 10 1x101 1 1x100 0.1 1x10-1 0.01 1x10-2 0.001 1x10-3 0.0001 1x10-4
Scientific notation is a way of writing numbers using exponents to show how large or small a number is in terms of powers of ten.
Scientific notation provides a place to hold the zeroes that come after a number or before a number. The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient.
The example below shows the equivalent values of decimal notation, fractional notation, and scientific notation.
Chemistry 11, Unit 01 10
Fractional, Decimal and Scientific Notation
1 1 1 10 100
100 10 1 1 1
Fractional
0.01 0.1 1 10 100
Decimal
10-2 10-1 100 101 102 Scientific
Displaying Numbers in Scientific Notation
Numbers displayed in scientific notation must be displayed in a particular format. They must always start with one digit, followed by a decimal, followed by any number of digits desired (depending on significant figures), followed by base ten power indicating the number of zeros present, either to the left or right of the decimal point.
Converting Decimal to Scientific Notation 0.0000012345 = 1.2345x10-6
Chemistry 11, Unit 01 11 Adding and Subtracting Numbers in Scientific Notation
Though calculators can do this for us, it is always important to see the math process behind the operation. The fundamental rule when adding and subtracting numbers in scientific notation (exponential notation) is... to be sure that the powers of ten for each number being added (or subtracted) is the same
Adding Numbers in Scientific Notation
4.55x1023 +3.77x10 0.455x1033 +3.77x10
0.455+3.77 x103 4.225x103
Subtracting Numbers in Scientific Notation
7.65x1043 -4.32x10 7.65x1044 -0.432x10
7.65-0.432 x104 7.218x104
Chemistry 11, Unit 01 12 Multiplying and Dividing in Scientific Notation
Though calculators can do this for us, it is always important to see the math process behind the operation. The process of multiplying and dividing numbers written in scientific notation involves focusing on the exponents themselves. In the process of multiplication... the exponents are added while in the process of division the exponents are subtracted.
Multiplying Numbers in Scientific Notation
3.0x1045 x6.0x10 3.0x6.0 1045 x10 18 109 18x109 1.8x1010
Dividing Numbers in Scientific Notation
8.0x1063 / 2.0x10 8.0/2.0 1063 /10 4.0x106-3 4.0x103
Chemistry 11, Unit 01 13 Practice with Scientific Notation
Write out the decimal equivalent for the following numbers that are in scientific notation. Also, write out the scientific notation equivalent for the following numbers that are in decimal form.
Remember to be careful with the number of significant figures you place in your final answers!
Convert to Decimal Notation Convert to Scientific Notation
7 100000000 10
-2 0.1 10
-5 0.0001 10
0 10 1
2 400 3x10
4 60000 7x10
3 750000 2.4x10
-3 0.005 6x10
-2 0.0034 900x10
-6 0.06457 4x10
Chemistry 11, Unit 01 14 More Practice with Scientific Notation
Simplify the following and leave your answers in scientific notation.
Multiplication and Division
1x1031 3x10
3x1043 2x10
5x10-5 11x10 4
2x10-4 4x10 3 8x106
4x103 3.6x108
1.2x104 4x103
8x105 9x1021
3x1019
Chemistry 11, Unit 01 15
Addition and Subtraction
4x1032 + 3x10
9x1024 + 1x10
8x1067 + 3.2x10
1.32x10-3 + 3.44x10 -4
3x10-6 - 5x10 -7
9x1012 - 8.1x10 9
2.2x10-4 - 3x10 2
Chemistry 11, Unit 01 16 Lesson 03: Measurement, Accuracy, Precision, Uncertainty and Significant Figures
01 Measurements
Science is based primarily on two things… experimentation observations
Observations are in turn based on the taking of measurements…
Chemistry 11, Unit 01 17 Finally, all measurements involve the following three components… magnitude (size) units (standard physical quantity) uncertainty (degree of possible variation)
94.5 g 0.1 g
magnitude and units uncertainty and units
There are many kinds of measurements but the most common measurements in chemistry involve… mass time volume
Chemistry 11, Unit 01 18 When taking measurements two things must be considered... accuracy is how close a measurement is to the correct value for that measurement and is dependent upon the person doing the measuring. precision of a measurement system refers to how close the agreement is between repeated measurements and is dependent upon the device being used to do the measuring. A precise measuring tool is one that can measure values in very small increments.
Chemistry 11, Unit 01 19 Example 01 A calibration weight has a mass of exactly 1.000000 g. A student uses 4 different balances to check the mass of the weight. The results of the weighings are shown below.
Mass using balance Mass using balance A = 0.999999 g C = 3.0 g Mass using balance Mass using balance B = 1.00 g D = 0.811592 g
Which of the balances give accurate weighings?
Which of the balances give precise weighings?
Which of the balances is both accurate and precise?
Chemistry 11, Unit 01 20 02 Expressing Measurements as Numerical Values
When we expressing measurements as numerical values, we can only list as many digits as was initially measured using our measuring device.
Measurements
measurements numerical values
The number of digits placed in a numerical value, or significant figures, determines the level of precision in a measuring device… the lesser the precision of the measuring tool, the lesser the number of significant figures in the measurement the greater the precision of the measuring tool, the greater the number of significant figures in the measurement
Low Precision Small Number of Significant Figures
3.0
High Precision Large Number of Significant Figures
3.0000000001
In any measurement, the number of significant figures is the number of digits believed to be correct or certain by the Chemistry 11, Unit 01 21 person doing the measuring and includes one estimated digit, the last digit
Estimated Digit in a Numerical Value
1 3.000000000
Example 02 How many certain digits (as opposed to uncertain) are contained in each of the following measurements? a. 45.3 s c. 1.85 L b. 125.70 g d. 2.12138 g
Chemistry 11, Unit 01 22 03 Accuracy, Precision, and Uncertainty
Uncertainty in measurements is related to accuracy and precision.
Uncertainty is a quantitative measure of how much your measured values deviate from a standard or expected value. IF measurements are accurate and precise, then the uncertainty of your values will be very low IF measurements are not accurate and precise, then the uncertainty of your values will be very high
As a general rule measurements should always be taken to one tenth of the smallest division being measured.
Uncertainty
Chemistry 11, Unit 01 23 The factors contributing to uncertainty in a measurement include… limitations of the measuring device the skill of the person making the measurement irregularities in the object being measured any other factors that affect the outcome (highly dependent on the situation)
Chemistry 11, Unit 01 24 04 Reading Scales
There are several steps you need to follow when you read a scale.
You need to determine the increments on the scale by… first, reading the major divisions second, read the minor divisions third, estimate between the lines for the last digit
Finally, after the above measurement has been made you need to… state the level of uncertainty in your measurement to the nearest tenth of the smallest division
Example 03
47 1 mL 36.5 0.1 mL 20.38 0.01 mL
Chemistry 11, Unit 01 25 05 Significant Figures and Calculations Involving Significant Figures
In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. An answer is no more precise that the least precise number used to get the answer.
There are three rules on determining how many significant figures are in a number. Make sure you know all three... non-zero digits are always significant zeros between two significant digits are significant final zero or trailing zeros in the decimal portion are significant
Chemistry 11, Unit 01 26 06 Significant Figures Rules
Rule 01: Non-zero digits are always significant.
Hopefully, this rule seems rather obvious. If you measure something and the device you use (ruler, thermometer, triple- beam balance, etc.) returns a number to you, then you have made a measurement decision and that act of measuring gives significance to that particular numeral (or digit) in the overall value you obtain.
26.38 4 significant figures 7.94 3 significant figures.
The problem comes with numbers like 0.00980 or 28.09.
Rule 02: Any zeros between two significant digits are significant.
Suppose you had a number like 406. By the first rule, the 4 and the 6 are significant. However, to make a measurement decision on the 4 (in the hundred's place) and the 6 (in the unit's place), you had to have made a decision on the ten's place. The measurement scale for this number would have hundreds and tens marked with an estimation made in the units place.
406 3 significant figures 20056 5 significant figures
Chemistry 11, Unit 01 27 Rule 03: A final zero or trailing zeros in the decimal portion are significant. This rule causes the most difficulty with students.
0.00500 3 significant figures 0.03040 4 significant figures 2.30 x 10-5 3 significant figures 4.500 x 1012 4 significant figures
Chemistry 11, Unit 01 28 07 Other Kinds of Zeros
Zero Type 01: Space holding zeros on numbers less than one are not significant. They are there to put the decimal point in its correct location. They do not involve measurement decisions. Upon writing the numbers in scientific notation (5.00x103 and 3.040x102), the non-significant zeros disappear.
0.00500 3 significant figures 0.03040 4 significant figures
Zero Type 02: The zero to the left of the decimal point on numbers less than one. When a number like 0.00500 is written, the very first zero (to the left of the decimal point) is put there by convention. Its sole function is to communicate unambiguously that the decimal point is a decimal point. If the number were written like .00500, there is a possibility that the decimal point might be mistaken for a period. Many students omit that zero. They should not.
0.00500 zero to the left of decimal is not significant
Zero Type 03: Trailing zeros in a whole number such as 200 is considered to have only one significant figure while 25000 has two. This is based on the way each number is written. When whole number are written as above, the zeros, by definition, did not require a measurement decision, thus they are not significant. However, it is entirely possible that 200 really does have two or three significant figures. If it does, it will be written in a different manner than above. Typically, scientific notation is used for this purpose. If 200 has two significant figures, then Chemistry 11, Unit 01 29 2.0x102 is used. If it has three, then 2.00x102 is used. If it had four, then 200.0 is sufficient (see rule 02). If you were doing an experiment, the context of the experiment and its measuring devices would tell you how many significant figures to report to people who read the report of your work.
200 1 significant figure 25000 2 significant figures 2.0x 2 significant figures 2.00x102 3 significant figures 200.0 4 significant figures
Chemistry 11, Unit 01 30 Example 04 How many significant figures does each of the following measurements have? 1.25 kg 1.283 cm 1255 kg 365.249 days 2000000 11 s years 150 m 17.25 L
Example 05 State the number of significant figures in each of the following… 3570 0.000572 17.505 0.00900 41.400 41.50x104 0.51 0.007160x105
Chemistry 11, Unit 01 31 08 Math with Significant Figures
Examples of Addition and Subtraction Even though your calculator gives you the answer 8.0372, you must round off to 8.04. Addition Your answer must only contain 1 doubtful number. Note that the doubtful digits are underlined. Subtraction is interesting when concerned with significant figures. Even though both numbers involved in the subtraction Subtraction have 5 significant figures, the answer only has 3 significant
figures when rounded correctly. Remember, the answer must only have 1 doubtful digit.
Examples of Multiplication and Division The answer must be rounded off to 2 significant Multiplication figures, since 1.6 only has 2 significant figures. The answer must be rounded off to 3 significant Division figures, since 45.2 has only 3 significant figures.
Chemistry 11, Unit 01 32 09 Note Regarding Exact Numbers
Exact numbers, such as the number of people in a room, have… an infinite number of significant figures
Exact numbers are counting up how many of something are present, they are not measurements made with instruments. Another example of this are defined numbers, such as 1 foot = 12 inches. There are exactly 12 inches in one foot.
Therefore, IF a number is exact, it does not affect the accuracy of a calculation nor the precision of the expression.
Some more examples… 100 years in a century. 2 molecules of hydrogen react with 1 molecule of oxygen to form 2 molecules of water.
Chemistry 11, Unit 01 33 Example 06 Perform the indicated operations and give the answer to the correct number of significant figures…
12.50x0.50
40.0/30.0000
51.3x3.940
0.51x1047 / 6x10
0.00043x0.005001
Example 07 Perform the indicated operations and give the answer to the correct number of significant figures…
178.90456 125.8055
4.55x1055 3.1x10
0.0000481 0.000817
7.819x1054 8.166x10
0.0589x1068 7.785x10
Chemistry 11, Unit 01 34 Example 08 Perform the indicated operations and give the answer to the correct number of significant figures…
7.95+0.583
4.15+1.582+0.0588-35.5 5.31x104
3.187x108 375.59x1.5
1252.7 9.4x102
Chemistry 11, Unit 01 35 Example 09 Perform the indicated operations and give the answer to the correct number of significant figures…
25.00x0.100 15.87x0.1036
0.865 0.800 x 1.593 9.04
0.382 0.4176
0.0159 0.0146
3.65 6.14 0.3354 0.1766
5.3x0.1056
0.1036 0.0978
9.34x0.07146 6.88x0.08115
Chemistry 11, Unit 01 36 Lesson 04: SI Units (Metric System)
01 Introduction
The metric system, is the most widely used system of units and measures around the world.
In spite of this there is widespread misuse of the system with incorrect names and incorrect symbols being used by even educated and trained professionals who should know better.
The metric system comprises… units: classified into base units and derived units prefixes: used to form decimal multiples or sub-multiples of the units
Chemistry 11, Unit 01 37 Base Units Physical Quantity Base Unit Symbol length metre m time second s mass kilogram kg volume litre L electric current ampere A temperature kelvin K luminous intensity candela cd amount of substance mole mol
Some Derived Units Physical Name of Symbol Expressed in Base Quantity Unit Units frequency hertz Hz 1/s force, weight newton N m kg/s² work, energy, joule J m² kg/s² heat pressure, stress pascal Pa kg/m s²
Chemistry 11, Unit 01 38 Some Units with Compound Names Physical Quantity Name of SI Unit Symbol area square metre m² volume cubic metre m³ speed, velocity metre per second m/s acceleration metre per second squared m/s² density kilogram per cubic metre kg/m³ moment of force newton metre Nm electric field strength volt per metre V/m specific heat capacity joule per kilogram kelvin J/kgK
Units Also Used Quantity Name Symbol time minute min time hour h time day d plane angle degree ° mass metric ton t energy electron volt eV speed kilometre per hour km/h area hectare ha temperature degree Celsius °C rotational frequency revolution per minute r/min
Chemistry 11, Unit 01 39 Prefixes yotta Y 1024 = 1,000,000,000,000,000,000,000,000 zetta Z 1021 = 1,000,000,000,000,000,000,000 exa E 1018 = 1,000,000,000,000,000,000 peta P 1015 = 1,000,000,000,000,000 tera T 1012 = 1,000,000,000,000 giga G 109 = 1,000,000,000 mega M 106 = 1,000,000 kilo k 103 = 1,000 hecto h 102 = 100 deca da 101 = 10 deci d 101 = 0.1 centi c 102 = 0.01 milli m 103 = 0.001 micro µ 106 = 0.000,001 nano n 109 = 0.000,000,001 pico p 1012 = 0,000,000,000,001 femto f 1015 = 0.000,000,000,000,001 atto a 1018 = 0.000,000,000,000,000,001 zepto z 1021 = 0.000,000,000,000,000,000,001 yocto y 1024 = 0.000,000,000,000,000,000,000,001
Chemistry 11, Unit 01 40 02 Correct Usage of the Metric Symbols
The following points emphasize some of the important aspects about the use of metric units and their symbols…
Upper Case and Lower Case
names: the names of metric units, whether alone or combined with a prefix, always start with a lower case letter (except at the beginning of a sentence) - e.g. metre, milligram, watt. symbols: the symbols for metric units are also written in lower case - except those that are named after persons (m for metre, but W for watt - the unit of power, named after the Scottish engineer, James Watt). Note that this rule applies even when the prefix symbol is in lower case, as in kW for kilowatt. The symbol for litre (L) is an exception. prefixes: symbols for prefixes meaning a million or more are written in capitals, and those meaning a thousand or less are written in lower case - thus, mL for millilitre, kW for kilowatt, MJ for megajoule (the unit of energy).
Attaching Prefixes to Base Metric Units Basic unit Symbol Measure of Examples nanometer (nm) meter m length centimeter (cm) microgram (g) gram g mass kilogram (kg) milliliter (mL) liter L volume decaliter (daL)
Chemistry 11, Unit 01 41 Pluralization
Symbols are never pluralized (25 kg not 25kgs).
Punctuation and Spacing
Do not put a period after a unit symbol (except at the end of a sentence). Where there is room, leave a space between the number and the unit (25 kg, 100 m, 37 ºC…).
Common Mistakes
The temperature was 25C. C is the symbol for coulomb (a unit of electrical charge). Should use correct symbol. Also no space between number and symbol. The temperature was 25 ºC. The speed limit is 50KPH. Non-standard abbreviation (language dependent). Should use international symbol and leave space after number. The speed limit is 50 km/h Cathedral 2Kms. Symbol should be lower case and not pluralised. Should leave space between number and symbol. Cathedral 2 km Price 90per kilo. “kilo” is a prefix meaning “1000”. Should use correct symbol “kg” and insert “/” to indicate “per”. Price 90/kg Contents 5 LTRS. LTRS is a clumsy, invented abbreviation. Should use symbol L (not pluralised). Contents 5 L.
Chemistry 11, Unit 01 42 Lesson 05: Metric Conversions
When you need to convert one metric unit to another, you may only have to move the decimal place. Although some conversions may be simple enough for this to work, many others are more complex so the chance of making a decimal error is very likely.
Writing out an equation that will allow you to methodically convert the unit is a good way to make sure that these errors don’t happen.
You need to set up an equation that will allow the initial unit to cancel out and produce the new unit. You do this by first making a fraction that relates the units.
Let’s try two examples to see exactly how this is done.
2500 millimeters to meters Chemistry 11, Unit 01 43
1m 2500mm 2500mm 2.5m 1000mm
67400 centimeters to kilometers
1m 67400cm 67400cm 674m 100cm
1km 674m 674m 0.674km 1000m
1m 1km 67400cm 67400cm 0.674km 100cm 1000m
Chemistry 11, Unit 01 44
Convert the Following
170.4 m to cm
58 dg to mg
600 L to kL
0.0923 km to mm
49 hg to g
210 cL to dL
4.51x103 L to mL
45700 cg to kg
24.6 kL to L
82.4 nm to m
Chemistry 11, Unit 01 45 Lesson 06: Unit Conversions
Dimensional analysis is a problem-solving method that uses the fact that any number or expression can be multiplied by the number one without changing its value. This is a useful technique. The only danger is that you may end up thinking that chemistry is simply a math problem, which it definitely is not.
Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in. For example, we know that…
1 inch = 2.54 centimeters
We can make two unit factors from this information…
1 inch 1 centimeter or 1 centimeter 1 inch
With this information we can solve some problems. Set up each problem by writing down what you need to find with a question mark. Then set it equal to the information that you are given. The problem is solved by multiplying the given data and its units by the appropriate unit factors so that only the desired units are present at the end.
02 Single Conversions Chemistry 11, Unit 01 46
How many centimeters are in 6.00 inches?
2.54 cm ? cm 6.00 in 15.2 cm 1 in
Express 24.0 cm in inches.
1 in ? in 24.0 cm 9.45 in 2.54 cm
03 Multiple Conversions Chemistry 11, Unit 01 47
You can also string many unit factors together.
How many seconds are in 2.0 years?
365 d 24 hr 60 min ? sec 2.0 y 1 y 1 d 1 hr 60 sec 7 6.3x10 sec 1 min
Convert 50.0 mL to liters.
1 L ? L 50.0 mL 0.0500 L 1000 mL
What is the density of mercury (13.6g/cm3 ) in units of kg/m3 ?
3 kg 13.6 g 100 cm ? D m3 1 cm 3 1 m 3
1 kg 43 1.36x10 kg/m 1000 g
Chemistry 11, Unit 01 48 Lesson 07: Graphing
Introduction
Graphs are diagrams that show the relationship between two or more variables, for visualising scientific data. Many students have difficulties with various aspects of graphing. This lesson is an attempt to clear up the confusion.
There are eight concepts students need to be familiar with... data tables variables variable range scaling numbering and labeling axes plotting data best fit lines describing graphs labelling
Chemistry 11, Unit 01 49 01 Data Tables
Observations from an experiment are usually organized into a data table. The independent variable (x) is always located on the left side of the data table and the dependent variable (y) is on the right.
Data trends are fairly easy to see in small data tables, like the one shown here, but are much harder to see in larger data tables.
Graphs are valuable because they make trends easier to see.
Does Water pH Affect Tadpoles? pH of Water Number of Tadpoles 8.0 45 7.5 69 7.0 78 6.5 88 6.0 43 5.5 23
Chemistry 11, Unit 01 50 02 Variables
The independent variable (x) always goes on the horizontal axis of a graph. The experimenter chooses this variable to be the standard by which change is measured during the experiment.
The dependent variable (y) always goes on the vertical axis of a graph. This variable changes with changes in the Independent Variable.
Does Water pH Affect Tadpoles? pH of Water Number of Tadpoles 8.0 45 7.5 69 7.0 78 6.5 88 6.0 43 5.5 23 Independent Variable Dependent Variable x y horizontal axis vertical axis
Chemistry 11, Unit 01 51 03 Variable Range
The numerical range of each variable must be calculated before the scale of the axis can be determined. Subtract the lowest data value from the high value. This will give you the range of numbers that must be represented on each axis…
Does Water pH Affect Tadpoles? pH of Water Number of Tadpoles 8.0 45 7.5 69 7.0 78 6.5 88 6.0 43 5.5 23 Independent Variable Range Dependent Variable Range 8.0-5.5=2.5 88-23=65
Chemistry 11, Unit 01 52 The reason for calculating the numerical range for each variable is to make sure that the plotted data fills as much of the resulting graph as possible.
Data that fills… most of a graph: is considered good less than most of a graph: is considered poor
Variable Range: Good and Bad Graphs
Chemistry 11, Unit 01 53 04 Scaling
Scale is the number value for each square on an axis. In choosing the most appropriate scale for a graph the following are important... data should cover as much of the grid as possible the scale of each axis should have an increment of 1x10n, 2x10n , or 5x10n (“n” being a positive or negative integer such as ...-2, -1, 0, 1, 2...)
To determine the scale you must know two things... the number of squares available along each axis of the graph grid the range of the variable to be represented along each axis
Chemistry 11, Unit 01 54 05 Numbering and Labelling Axes
This grid is being prepared for the data from the previous table. For the independent variable (horizontal axis), the number of squares (25) is divided by the pH range (2.5). This gives 10 squares per pH value. For the dependent variable (vertical axis), the range of tadpoles (65) is divided by the number of squares (35). This gives a number just under 2 - so we round up to 2 tadpoles per square.
Using the scale for each axis, write numbers along the axis - increasing from left to right and bottom to top. Notice that the scale does not begin with zero. The lowest data points are typically the beginning of the scale.
Title each axis with the name and units of the variable too.
Chemistry 11, Unit 01 55 06 Plotting Data
Locate each data point with a small dot on the graph.
Place the dependent variable data value by each dot - as long as it does not clutter the graph. If the data points are very close together or the values interfere with the graph line, do not add the values to the graph.
Chemistry 11, Unit 01 56 07 Best Fit Lines or Curves
Draw the line or curve that best fits the data points.
Most scientific graphs are not "connect-the-dot" graphs. The purpose of the graph line is to show the general trend of the data. The line does not necessarily have to touch every data point.
Chemistry 11, Unit 01 57 08 Using the Graph
Mathematical Relationships
Plotted data may take on various shapes depending on the relationship between the dependent and independent variables.
The terms used to describe the apparent relationship are categorized as… linear non-linear: exponential, quadratic, inverse, and periodic
In most cases data will be plotted in the first quadrant as most data will be positive. Quadrants are the names we give to each of the four regions of a graph…
Quadrants of a Graph
Chemistry 11, Unit 01 58 Linear Relationships
Linear Relationship
Linear relationships are the simplest of all the mathematical relationships.
Chemistry 11, Unit 01 59 Non-Linear Relationships
Non-linear relationships are much more diverse and include the following…
Exponential Relationships
Chemistry 11, Unit 01 60 Quadratic Relationships
Inverse Relationships
Chemistry 11, Unit 01 61 Periodic Relationships
Knowing the mathematical relationship that exists for plotted data allows for… interpolation: determination of points within the variable range (between data points) extrapolation: determination of points within the variable range (beyond the plotted data)
Chemistry 11, Unit 01 62 The mathematical relationship for the example at the beginning of this lesson is quadratic in nature...
Note: This relationship was derived using Microsoft Excel. Students would not be expected to derive this relationship by hand.
Chemistry 11, Unit 01 63 Other Information
Graphs can give us all sorts of information. Not only can we determine describe graphs mathematically by determining the equation that best describes our data but we can also determine things such as… slope
Chemistry 11, Unit 01 64 x and y intercept(s)
As we proceed through the course we will discover instances where determining the above quantities are useful.
Keep in mind, the quantities mentioned above can be determined two ways… from a graph from the equation describing a graph
Chemistry 11, Unit 01 65 Example 01
Determine the slope, x-intercept and y-intercept for the following graph…
Example 02
Determine the slope, x-intercept and y-intercept for the following equation…
y 2x 5
Chemistry 11, Unit 01 66 09 Title and Legend
Lastly, never forget to add a title and legend to your graph.
A graph title should clearly tell what the graph is about. While the top location may be the most likely choice, any open space inside the grid may be used - as long as it does not interfere with information on the graph. Do not put the title of a graph in the margin of the paper.
If a graph has more than one set of data, a legend must be included to identify the different lines. Like the title, a graph legend should be placed in an open space inside the grid - not in the margin of the paper. Since this graph only has one set of data, a key is not needed.
Chemistry 11, Unit 01 67 Lesson 08: Density
01 Density
A material's density is defined as its mass per unit volume. It is, essentially, a measurement of how tightly matter is crammed together. The principle of density was discovered by the Greek scientist Archimedes.
To calculate the density (usually represented by the Greek letter "rho" or ρ) of an object, take the mass (m) and divide by the volume (v)…
m ρ v
The metric unit for density is… kilograms per cubic metre (most common) grams per cubic centimetre (also used)
Chemistry 11, Unit 01 68 Densities of Some Materials Material Density kg/m3 Air (1 atm, 20 degrees C) 1.20 Aluminum 2,700 Benzene 900 Blood 1,600 Brass 8,600 Concrete 2,000 Copper 8,900 Ethanol 810 Glycerin 1,260 Gold 19,300 Ice 920 Iron 7,800 Lead 11,300 Mercury 13,600 Neutron star 1018 Platinum 21,400 Seawater (Saltwater) 1,030 Silver 10,500 Steel 7,800 Water (Freshwater) 1,000 White dwarf star 1010
Chemistry 11, Unit 01 69 02 Using Density
One of the most common uses of density is in how different materials interact when mixed together… lower density solids will float in higher density liquids higher density solids will sink in lower density liquids
Another important consequence of density is that it allows you to do calculations and solve for mass and volume, if given the other quantity. Since the density of common substances are known, this calculation is fairly straightforward…
Chemistry 11, Unit 01 70 Example 01
An unknown liquid has a mass of 30.67g and a volume of 52.3mL. What is the density of the liquid?
m 30.67g 1ml 3 ρ 0.586g/cm v 52.3ml 1cm3
Example 02
The density of ice is 0.917g/cm3 . How much volume does 25.3g of ice occupy? m ρ v 25.3g 0.917g / cm3 v 25.3g v 27.58 cm3 0.917g / cm3
Chemistry 11, Unit 01 71 03 Specific Gravity
A concept related to density is the specific gravity (relative density) of a material, which is the… ratio of the material's density to the density of water
An object with a… specific gravity less than 1 will float in water specific gravity greater than 1 means it will sink