Lesson 01: The Scientific Method. 01 Introduction

Transcription

1 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

2 Chemistry 11, Unit 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

3 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

4 Chemistry 11, Unit 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

5 Chemistry 11, Unit 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?

6 Chemistry 11, Unit 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

7 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

8 Chemistry 11, Unit 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.

9 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 x x x x x x x x x10 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 8 time to write out, while 10 is much more efficient. The example below shows the equivalent values of decimal notation, fractional notation, and scientific notation.

10 Scientific Decimal Fractional Chemistry 11, Unit Fractional, Decimal and Scientific Notation 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 = x10

11 Chemistry 11, Unit 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 x x x x x x Subtracting Numbers in Scientific Notation x x x x x x10 4 4

12 Chemistry 11, Unit 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 x10 x6.0x x6.010 x x x10 10 Dividing Numbers in Scientific Notation x10 / 2.0x /2.010 /10 4.0x x10 3

13 Chemistry 11, Unit 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 x x x x x x

14 Chemistry 11, Unit More Practice with Scientific Notation Simplify the following and leave your answers in scientific notation x10 3x x10 2x x10 11x x10 4x10 8x10 4x x10 1.2x10 4x10 8x10 9x10 3x Multiplication and Division

15 Chemistry 11, Unit x10 + 3x x10 + 1x x x x x x10-5x x10-8.1x x10-3x10 Addition and Subtraction

16 Chemistry 11, Unit 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

17 Chemistry 11, Unit 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

18 Chemistry 11, Unit 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.

19 Chemistry 11, Unit Example 01 A calibration weight has a mass of exactly 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 A = g Mass using balance B = 1.00 g Mass using balance C = 3.0 g Mass using balance D = g Which of the balances give accurate weighings? Which of the balances give precise weighings? Which of the balances is both accurate and precise?

20 Chemistry 11, Unit 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 In any measurement, the number of significant figures is the number of digits believed to be correct or certain by the

21 Chemistry 11, Unit person doing the measuring and includes one estimated digit, the last digit Estimated Digit in a Numerical Value Example 02 How many certain digits (as opposed to uncertain) are contained in each of the following measurements? a s c L b g d g

22 Chemistry 11, Unit 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

23 Chemistry 11, Unit 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)

24 Chemistry 11, Unit 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 ml ml ml

25 Chemistry 11, Unit 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

26 Chemistry 11, Unit 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, triplebeam 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 significant figures significant figures. The problem comes with numbers like or 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 significant figures significant figures

27 Chemistry 11, Unit Rule 03: A final zero or trailing zeros in the decimal portion are significant. This rule causes the most difficulty with students significant figures significant figures 2.30 x significant figures x significant figures

28 Chemistry 11, Unit 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 3 ( 5.00x10 and x10 ), the non-significant zeros disappear significant figures significant figures Zero Type 02: The zero to the left of the decimal point on numbers less than one. When a number like 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 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 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

29 Chemistry 11, Unit x10 is used. If it has three, then 2.00x10 is used. If it had four, then 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 significant figure significant figures 2.0x 2 significant figures x10 3 significant figures significant figures

30 Chemistry 11, Unit Example 04 How many significant figures does each of the following measurements have? 1.25 kg cm 1255 kg days 11 s years 150 m L Example 05 State the number of significant figures in each of the following x x10

31 Chemistry 11, Unit Math with Significant Figures Examples of Addition and Subtraction Even though your calculator gives you the answer , you must round off to 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.

32 Chemistry 11, Unit 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.

33 Chemistry 11, Unit Example 06 Perform the indicated operations and give the answer to the correct number of significant figures 12.50x / x x / 6x x Example 07 Perform the indicated operations and give the answer to the correct number of significant figures x10 3.1x x x x x10

34 Chemistry 11, Unit Example 08 Perform the indicated operations and give the answer to the correct number of significant figures x x x x10

35 Chemistry 11, Unit Example 09 Perform the indicated operations and give the answer to the correct number of significant figures 25.00x x x x x x

36 Chemistry 11, Unit 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

37 Chemistry 11, Unit 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 Quantity Name of Unit Symbol Expressed in Base 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

38 Chemistry 11, Unit 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

39 Chemistry 11, Unit Prefixes yotta Y = 1,000,000,000,000,000,000,000,000 zetta Z = 1,000,000,000,000,000,000,000 exa E = 1,000,000,000,000,000,000 peta P = 1,000,000,000,000,000 tera T = 1,000,000,000,000 giga G 9 10 = 1,000,000,000 mega M 6 10 = 1,000,000 kilo k 3 10 = 1,000 hecto h 2 10 = 100 deca da 1 10 = 10 deci d 1 10 = 0.1 centi c 2 10 = 0.01 milli m 3 10 = micro µ 6 10 = 0.000,001 nano n 9 10 = 0.000,000,001 pico p = 0,000,000,000,001 femto f = 0.000,000,000,000,001 atto a = 0.000,000,000,000,000,001 zepto z = 0.000,000,000,000,000,000,001 yocto y = 0.000,000,000,000,000,000,000,001

40 Chemistry 11, Unit 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 meter m length nanometer (nm) centimeter (cm) gram g mass microgram ( g) kilogram (kg) liter L volume milliliter (ml) decaliter (dal)

41 Chemistry 11, Unit 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 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.

42 Chemistry 11, Unit 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 millimeters to meters

43 Chemistry 11, Unit m 2500mm 2500mm 2.5m 1000mm centimeters to kilometers 1m 67400cm 67400cm 674m 100cm 1km 674m 674m 0.674km 1000m 1m 1km 67400cm 67400cm 0.674km 100cm 1000m

44 Chemistry 11, Unit Convert the Following m to cm 58 dg to mg 600 L to kl km to mm 49 hg to g 210 cl to dl x10 L to ml cg to kg 24.6 kl to L 82.4 nm to m

45 Chemistry 11, Unit Lesson 06: Unit Conversions 01 Dimensional Analysis 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 1inch 1centimeter 1centimeter or 1inch 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

46 Chemistry 11, Unit How many centimeters are in 6.00 inches? 2.54 cm? cm 1in 6.00 in 15.2 cm Express 24.0 cm in inches. 1in? in 2.54 cm 24.0 cm 9.45 in 03 Multiple Conversions

47 Chemistry 11, Unit 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. 1L? L 1000 ml 50.0 ml L What is the density of mercury ( 13.6g/cm ) in units of 3 kg/m? 3 kg 13.6 g 100 cm? D m 1 cm 1 m 1 kg 1.36x10 kg/m 1000 g 4 3 3

48 Chemistry 11, Unit 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

49 Chemistry 11, Unit 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

50 Chemistry 11, Unit 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 Independent Variable Dependent Variable x y horizontal axis vertical axis

51 Chemistry 11, Unit 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 Independent Variable Range Dependent Variable Range = =65

52 Chemistry 11, Unit 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

53 Chemistry 11, Unit 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 n n n 1x10, 2x10, or 5x10 ( 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

54 Chemistry 11, Unit 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.

55 Chemistry 11, Unit 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.

56 Chemistry 11, Unit 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.

57 Chemistry 11, Unit 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

58 Chemistry 11, Unit Linear Relationships Linear Relationship Linear relationships are the simplest of all the mathematical relationships.

59 Chemistry 11, Unit Non-Linear Relationships Non-linear relationships are much more diverse and include the following Exponential Relationships

60 Chemistry 11, Unit Quadratic Relationships Inverse Relationships

61 Chemistry 11, Unit 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)

62 Chemistry 11, Unit 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.

63 Chemistry 11, Unit 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

64 Chemistry 11, Unit 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

65 Chemistry 11, Unit 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

66 Chemistry 11, Unit 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.

67 Chemistry 11, Unit 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) ρ The metric unit for density is kilograms per cubic metre (most common) grams per cubic centimetre (also used) m v

68 Chemistry 11, Unit Densities of Some Materials Material Density 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 kg/m

69 Chemistry 11, Unit 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

70 Chemistry 11, Unit Example 01 An unknown liquid has a mass of 30.67g and a volume of 52.3mL. What is the density of the liquid? ρ m 30.67g 1ml 3 v 52.3ml 1cm Example g/cm 3 The density of ice is 0.917g/cm. How much volume does 25.3g of ice occupy? m ρ v g 0.917g / cm v 25.3g 3 v 27.58cm g / cm 3

71 Chemistry 11, Unit 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