Scientific Method: a logical approach to understanding or solving problems that needs solved.

Transcription

1 Chapter 2 Section 1 Section 2-1 Objectives Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Describe the differences between hypotheses, theories, and models. Scientific Method: a logical approach to understanding or solving problems that needs solved. The goal is to solve a problem or to better understand an observed event. The scientific method is a set of processes and scientists may repeat stages many times before there is sufficient evidence to formulate a theory. You can see in the diagram above that each stage represents a number of different activities. Aspects of the Scientific Method Observation is information that you obtain through your senses. Repeatable observations become known as facts. Generalizing/ Hypothesis: A hypothesis is a testable statement that serves as the basis for predictions and further experiments. Your hypothesis addresses questions raised by your observations. Your hypothesis states that one variable causes a change in another variable. Testing / Experimenting Controlled Experiment: an experiment in which only one variable, the manipulated variable, is deliberately changed; the responding variable is observed for changes, all other variables are kept constant (controlled). Theorizing: A theory is a broad generalization that explains believed facts or phenomena.

2 A scientific theory is a well-tested explanation for a set of observations or experimental results, supported in repeated experiments by scientists. Theories are never proved; they become stronger if the facts continue to support them. However, if an existing theory fails to explain new facts and discoveries, the theory must be revised or a new theory will replace it. A scientific law is a statement that summarizes a pattern found in nature. A scientific law describes an observed pattern in nature without attempting to explain it. Model: representation, of an object or event. Scientific models are used to make it easier to understand things that might be too difficult to observe directly. HW: Section Review Page 31 #1-5; Chapter Review: Page 59 #1-3 SECTION REVIEW Page What is the scientific method? 2. Which of the following are quantitative? a. the liquid floats on water b. the metal is malleable c. the liquid has a temperature of 55.6 C 3. How do hypotheses and theories differ? 4. How are models related to theories and hypotheses? 5. What are the components of the system in the graduated cylinder shown on page 38? FIGURE 2-7 (from page 38 in your text) Density is the ratio of mass to volume. Both water and copper shot float on mercury because mercury is more dense.

3 Chapter 2 Section 2 Chapter 2-2 Objectives 1. Distinguish between a quantity, a unit, and a measurement standard. 2. Name SI units for length, mass, time, volume, and density. 3. Distinguish between mass and weight. 4. Perform density calculations. 5. Transform a statement of equality to a conversion factor. Measurements are quantitative observations (information). Measurements represent quantities - how much, how big, how little, Measurements use specific units Units state the type of measurement made. Quantity states the number (how many) of those units. For example, the quantity represented by a teaspoon is volume. The teaspoon is a unit of measurement, while volume is a quantity. Scientists have agreed on a single measurement system: The SI (Le Système International d Unités). SI units are defined in terms of standards of measurement. SI has seven base units; other units are derived from these seven. Numbers are written in a form that is agreed upon internationally. The number seventy-five thousand is written , not 75,000, because the comma is used in other countries to represent a decimal point. In place of the comma a space is used to avoid confusion Some non-si units are still commonly used by chemists and are also used in this class. The standards are objects or natural phenomena that are of constant value, easy to preserve and reproduce, and practical in size. In the United States, the National Institute of Standards and Technology plays the main role in maintaining standards and setting style conventions. Measurement Quantity 2 parts how much and the unit How Much a number Unit: give the number content - what feature is being measure SI - worldwide set of standardized units Don t use commas, keep the space for them. Standards are very specific items or rules that are used to keep the value for everyone in the world the same Select Base Units See Table 2-1 page 34 for the entire list Quantity Unit Quantity symbol Unit name abbreviation Length l meter m Mass m kilogram kg Time t second s Temperature T Kelvin K Amount of matter n mole mol

4 Mass & Weight Mass is often confused with weight because people often express the weight of an object in grams, this is incorrect weight is measured in newtons a derived unit. Mass is determined by comparing the object to a set of standards that are part of the balance. Weight is a measure of the gravitational pull on mass, and depends on gravity. Mass is measured on instruments such as a balance and weight is typically measured on a spring scale. Length: The standard unit for length is the meter. To express long distances, the kilometer (km) is used. To express shorter distances, the centimeter is often used. Derived SI Units Many SI units are combinations of the Base units Combinations of SI base units form derived units. See Table 2-3 page 36. Volume is the amount of space occupied by an object. The derived SI unit of volume is cubic meters, m 3. Such a large unit is inconvenient for expressing the volume of materials in a chemistry laboratory. A smaller unit, the cubic centimeter, cm 3, is used. There are one hundred centimeters in a meter, so a cubic meter contains one million cm 3. Here is the math: 1m 3 X Density is the ratio of mass to volume, or density equals mass divided by volume. Conversion Factors A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. By multiplying by the conversion factor, you do not change the overall meaning of the quantity. A conversion factor is a ratio made from an equality which means the ratio is equal to one. Example: 1 m = 100 cm which means 100 cm = 1 1 m 100 cm X 100 cm X 100 cm = cm 3 1 m 1 m 1 m D = and we can Substitute this in the equation for volume in 1 m 3... =? cm 3 m V Mass is determined by comparing with a standard; Mass is determined on a balance. Weight is a measure of how much pull gravity puts on a particular mass; Weight is measured on a scale Length meters Volume is three lengths multiplied together, it must be derived (by multiplying the lengths together) all derived units are base units that are multiplied together or divided to get the unit Example of a derived unit density is mass divided by volume, volume is some set of numbers multiplied together. it is a ratio that is extrinsic, making it specific for an object. A conversion factor A ratio that is = 1

5 After substituting into 1m 3 X 100 cm X 100 cm X 100 cm = cm 3 1 m 1 m 1 m you get 1m 3 X 1 X 1 X 1 = cm 3 = 10 6 cm 3 Then your final answer is 1m 3 =10 6 cm 3 and now we have a new 10 6 cm 3 1m 3 conversion factor to 1 = = m cm 3 use Note: quantity sought = quantity given multiplied by the conversion factor Examples: page 39 sample problem (sp) 2-1; page 41 sp 2-2 HW: Practice Problems: Page 40 #1-3(AT THE TOP OF THE PAGE; page 42 #1-5 Chapter Review: Page 59 #12-15; 27-29; 32-34

6 Chapter 2 SECTION 3 Section 2-3 Objectives Distinguish between accuracy and precision. Determine the number of significant figures in measurements. Perform mathematical operations involving significant figures. Convert measurements into scientific notation. Distinguish between inversely and directly proportional relationships. Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way. Accuracy = Correctness of the measurement Precision=Closeness of all of the measurements are to each other % Error Significant Figures Determining Whether Zeros Are Significant Figures Rule (Examples) 1. Zeros between other nonzero digits are significant. a m has three significant figures. b s has five significant figures. 2. Zeros in front of nonzero digits are not significant. a kg has three significant figures. b ms has one significant figure. 3. Zeros that are at the end of a number and also to the right of the decimal are significant. a g has four significant figures. b kg has seven significant figures.

7 4. Zeros at the end of a number but to the left of a decimal are significant if they have been measured (the decimal point is shown); otherwise, they are not significant. In this class, they will be treated as not significant if no decimal point is used. a m; in this book it will be assumed that measurements like this have one significant figure, and so shall we. b. 20. m may contain one or two significant figures, but it will be assumed to have two significant figures, because of the decimal point at the end of the number. Calculating with Significant Figures Rule (Examples) Addition (subtraction) The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. In this case 1 digit to the right of the decimal. In the case of addition the decimal point is the boss. Multiplication (division) The final answer has the same number of significant figures as the measurement having the smallest number of significant figures. In the case of multiplication the decimal point is not in charge. Exact conversion factors are completely certain and do not limit the number of digits in a calculation. Integrated Chemistry - Chapter 2 Page 7 of 10

8 Rounding What to do round down round up When to do it whenever the digit following the last significant figure is a 0, 1, 2, 3, or 4: becomes 30.2 if the last significant figure is an even number and the next digit is a 5, with no other nonzero digits: becomes 32.2 and becomes 32.6 (Bankers rule) whenever the digit following the last significant figure is a 6, 7, 8, or 9: becomes 22.5 if the digit following the last significant figure is a 5 followed by a nonzero digit: becomes 54.8 if the last significant figure is an odd number and the next digit is a 5, with no other nonzero digits: becomes 54.8 and becomes 79.4 (Bankers rule) Bankers rule: if there is no number after the rounding digit and that digit is a five then if the number to be rounded is even it stays even; if it is odd it is rounded up to be even. Scientific Notation: A number written in scientific notation is of the form M 10 n, where M is greater than or equal to 1 but less than 10 and the n is an integer. This is a way to write a very large or vary small number easily. Sometimes scientific notation is used to specify exact Significant Figures The x 10 n is used to save from writing zeros. Examples: A large number: 7.25 trillion dollars = 7.25 x dollars A small number: one 4 trillionth of a meter 1 of a meter = m = 2.5 x m Additionally scientist will also use prefixes; the two values above could be expressed 7.25 x dollars = 7.25 teradollars; 2.5 x m = 0.25 picometers (prefixes are on page 35) 0.25 x m Scientific Notation used to specify exact Significant Figures 6.2 x 10 2 m = 620 m (by the rules both have 2 sig figs) But 6.00 x 10 2 m = 600 m do not have the same # of sig figs 6.00 x 10 2 m has 3; 600 has only 1 M must be = or > 1 but NOT 10. If M is > 9 we must adjust n and move the decimal point left If we move the decimal point one place we add one to n; 2 places add 2 If M < 1 move the decimal right and SUBTRACT from n Prefixes are numbers in disguise tera is x Scientific Notation gives exact significant digits Integrated Chemistry - Chapter 2 Page 8 of 10

9 When adding in scientific notation the power of ten must be the same for each number before lining up the decimal. 1.5 x m x m 15 x m x m to add the 15 x m x m = 20.2 x m Still need to fix 2 things: 20.2 is not 1 & < 10 and by the Significant Figure addition rule the 15 has nothing after the decimal. Fix the sig fig first: 20. x m Final step change the number to 2.0 x m Proportionality Two quantities are directly proportional to each other if dividing one by the other gives a constant value. When two variables like x and y are directly proportional to each other, the relationship is expressed as y x, which is read as y is proportional to x. The line equation is expressed as k = y/x; k is a constant value. In the example, it is the density of aluminum (k=d; y= m; x=v). Note, by averaging, the k value is 2.71 g/cm 3 Rewrite the expression as the line equation y = kx This may look familiar to you; it is the equation for a special case of a straight line, with the y intercept = 0. The y intercept is not always zero; for example: temperature comparisons. We can use the direct proportionality of temperature readings in both o C and o F to create a conversion factor for temperature between the two. Temperature 0 o C = 32 o F so the y intercept = 32; Water freezes at 0 o C = 32 o F; water boils at 100 o C = 212 o F Recall x is o C and y is o F, then slope is (y 2 y 1 ) /(x 2 x 1 ) Slope 212 o F 32 o F = 180 o F 100 o C 0 o C 100 o C = 1.8 o F/ o C Integrated Chemistry - Chapter 2 Page 9 of 10

10 To use the conversion equation you must let x be the Celsius reading; and y is Fahrenheit then y= (1.8 o F/ o C)*x + 32 o F If you rearrange this you will get x = (y - 32 o F) which means: x = (y - 32 o F)( o C) (1.8 o F/ o C) (1.8 o F) and y = (1.8 o F/ o C)(x) + 32 o F Examples: Convert 37 o C to o F Use y = (1.8 o F/ o C)(x) + 32 o F and let x = 37 o C y = (1.8 o F/ o C)(37 o C) + 32 o F = 66.6 o F + 32 o F = 98.6 o F Convert 68 o F to o C Let y = 68 o F Use x = (y - 32 o F)( o C) (1.8 o F) = (68 o F - 32 o F)( o C) (1.8 o F) Celsius to Fahrenheit o C o F T F = 1.8(C) + 32 T o F Fahrenheit to Celsius o F o C T C = (F 32) T o C 1.8 Celsius to Kelvin T K = C T K Kelvin to Celsius T C = K 273 T o C = (36 o F)( o C) (1.8 o F) = 20 o C Two quantities are inversely proportional to each other if their product is constant. y 1/x; the line equation has the form k = yx In this example k = PV HW: All Practice problems: Pages 45; 48; 50; & 54 (Yes I know they have the answers, show step by step how to get the answers for credit); and Section Review page 57 # 1 # 9 Integrated Chemistry - Chapter 2 Page 10 of 10