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Honors Chemistry Chapter 3 Notes – Scientific Measurement (Student edition) Chapter 3 problem set: 57-61, 64, 65, 70, 71, 76, 84, 86, 89, 92, 101, 106 Useful diagrams: 3.5, 3.6, 3.9, 3.13 3.1 Measurements and Their Uncertainty Measurement: a quantity that has both a and a . Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct. Scientific Notation: a given number is written as the product of two numbers: a coefficient and 10 raised to a power. Accuracy: is a measure of how close a measurement comes to the actual or true value of whatever is measured. Precision: is a measure of how close a series of measurements are to one another. Precise Accurate Accurate and Precise : Experiments don’t always give perfect results. Error is pretty much a given. Observed Value (Experimental Value): the True Value (Accepted Value, Theoretical Value): the – typically found in a resource. Absolute Error: the Percent Error value in the lab. value between the true and observed value. = The order is important. It implies direction. + or - shows the direction of the error. It indicates if values are either too high or too low. 1 Percent error should be treated as absolute value. Looking at the absolute error in terms of + or – can help you to better analyze your experiments. Example: 65 oC is the answer in your experiment. 66 oC is the theoretical value. Calculate the percent error. NIB - Uncertainty in Measurement: Two important points to remember regarding measurement: 1. Instruments can only measure so well. 2. We only need some measurements to be really exact. A person has a height of 5’ 11” inches, not 5.916666667 feet. When measuring, include all readable digits and one 0 cm 1 digit. 2 If the measurement is exactly half way between lines record it as If it is a little over, record If it is a little under, record Significant Figures (Digits) - “Sig Figs”: Significant Figures: includes all of the digits that are plus a last digit that is . , Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation. Example: say you collect a paycheck for a 40 hour week. How much difference is there between getting paid pi vs. 3.14 per hour? 40 x pi = $ 40 x 3.14 = $ 2 Rules for finding the # of sig figs: 1. All non-zeros are significant Examples: 2. Zeros between non-zeros are significant Examples: 3. All other zeros are significant only if.... a) they are to the right or left of decimal point and b) they are to the right of a sig fig - all other (not a and b) are simply place holders Examples: Let’s sing the sig fig song!!!! Sig figs apply to scientific notation as well: Examples: Calculating with Measurements ( Sig Fig Math ) In general, a calculated answer cannot be more accurate than the least accurate measurement from which it was calculated. Rules of Rounding: numbers greater than 5 (6-9) get rounded up numbers less than 5 (1-4) get rounded down for numbers ending on 5 (the “5” rule): if the preceding digit is odd, round up if the preceding digit is even, round down Round the following examples to 3 sig figs: 35.27 87.24 35.25 95.15 3 * The “5” rule only applies to a “dead even” 5. If any digit other than 0 follows a 5 to be rounded, then the number gets rounded up without regard to the previous digit. Round the following examples to 3 sig figs:35.25000000000000000000001 Rules for calculating with sig figs: 1. When multiplying or dividing, the answer should have the smaller # of sig figs in the original problem. Example: 2 x 4.001283 doesn’t equal 2 x 4.001283 = Example: 3.9577836 15 divided by 3.79 doesn’t equal 15 divided by 3.79 = 2. When adding or subtracting, round to the last common decimal place on the right. Example: 21.52 + 3.1 doesn’t equal 21.52 + 3.1 = Exact conversion factors do not limit the # of sig figs. The final answer should always end with the # of sig figs that started the problem. Let’s refer back to sig figs and percent error now… NIB - Use of +/- notation: Scientists sometimes use +/- notation to show how much uncertainty there is in a measurement. 46.85 mm +/- .03 mm This means that the answer could be as high as ___________ mm or as low as __________ mm. Of course, there is always implied uncertainty. If we say a building is 9 m high, we’re saying that it is between 8 and 10 m high. We say 9 because it’s closer to 9 than 8 and closer to 9 than 10. We report 9 +/- .5 m Measurement 900 90 9 9.0 9.00 900. 900.0 Implied Range +/+/+/+/+/+/+/- 4 3.2 International System of Units SI system: Le Systeme International d’Unites: 7 base units Quantity Length Mass Temperature Time Amount of Substance Luminous Intensity Electric Current SI Base Unit Meter Kilogram Kelvin Second Mole Candela Ampere Symbol m kg K s mol cd A SI Advantages: easily convertible using decimals. English system uses fractions. Prefixes to know: Prefix Giga Mega Kilo Deca Deci Centi Milli Micro Nano Pico Symbol Value G M K da d c m µ n p 0.000 000 001 0.000 001 0.001 0.1 10 100 1000 1,000,000 1,000,000,000 1,000,000,000,000 Base Unit Value 1 1 1 1 1 1 1 1 1 1 Units of Volume: Volume = length x width x height 1 cm3 = 1 mL 1 dm3 = 1 L Volume is a derived unit. Derived Units: a combination of units. Other derived units: area cm2 Density g/cm3 Speed m/s 5 Units of Temperature: Temperature is used to determine the direction of heat transfer. Temperature is measured in degrees Temperature (definition): Thermometer - works by thermal expansion - usually Hg or alcohol Temperature scales Celsius - devised by a Swedish astronomer - Anders Celsius - 1742 Kelvin - named for Lord Kelvin - English physicist absolute zero - temperature at which all molecular motion stops temperature = 0 K or -273.15 Co It’s never been reached, but we have gotten within 1/1,000,000,000 K. Conversion formulas K = Co + 273 **Fo = 9/5(Co) + 32 **Co = 5/9(Fo - 32) ** ask about the coolest rule ever Units of Energy: Energy: The capacity to do work or to produce heat. 1 Joule = 0.2390 calories 1 cal = 4.184 J 6 3.3 Conversion Problems General Rules for Problem Solving: 1. Read the problem - make a list of knowns and unknowns 2. Look up any needed information (conversion factors, etc.) 3. Work out a plan. 4. Do the math. 5. Check your work. Does the answer seem right? Did you record the correct number of sig figs? Does your answer have the proper unit? Conversion Factor: a ratio of equivalent measurements. Dimensional Analysis (Factor Label Method): a method of problem solving that treats units like algebraic factors. Basic Rules: 1. Put the known quantity over the number 1. 2. On the bottom of the next term, put the unit on top of the previous term. 3. On top of the current term put a unit that you are trying to get to. 4. On the top and bottom of the current term, put in numbers in order to create an equality. 5. If the unit on top is the unit of your final answer, multiply/divide and cancel units. If not, return to step # 2. 6. As far as sig figs are concerned, end with what you start with! Example: convert 3.0 ft to inches Example: convert 1.8 years to seconds Example: convert 2.50 ft to cm if 1 inch = 2.54 cm Example: convert 0.75 L to cm3 Example: convert 1,500,000,000 mm3 to m3 Example: convert 22 cm to dm 7 3.4 Density Density: the ratio of the of an object to its . D= Density is an intensive property that depends only on the a substance, not on the of the sample. The density of a substance generally of as its temperature increases. Careers in Chemistry: Analytical chemists focus on making quantitative measurements. They can work for a pharmaceutical company investigating the composition of medicines in drugs. They are creative thinkers and find solutions to problems. They can also be hired by biomedicine companies, biochemistry companies, and industrial manufacturers. Many of these jobs require a master’s degree or Ph. D. 8