Notes: Measurement and Calculation

Transcription

1 Name Chemistry-PAP Per. I. The Basics of Measurement Notes: Measurement and Calculation A. Measurement Most provide quantitative information, but because they are obtained experimentally, they are inexact. Measurements always contain a degree of uncertainty. Measurements have both (a number) and a. Ex. of magnitude of a measurement: Ex. of unit of a measurement: A measurement has a specific numerical value; a measurement does not. Ex.: The temperature reached 89.3 C is an example of a measurement. B. Units The test tube felt warm is an example of a measurement. A tells us what was measured. Units must always follow the numerical portion of a measurement. No Naked Numbers!!! There are two major unit systems used in the world today. One is the United States Customary System (USCS) used in the U.S. primarily for nonscientific purposes. Examples of USCS units include the and the. The other unit system is the Systeme Internationale (SI), which is used by most other countries and all scientists in the U.S. We will be using SI units in this class. SI units important in chemistry: Quantity SI Unit Name Unit Symbol length meter mass time temperature amount of substance kilogram second Kelvin mole The metric system is based on powers of ten. Metric system are used with SI units to represent quantities that are larger or smaller (by powers of 10) than the base units. 1

2 The Metric System: KING HENRY DIED BY DRINKING CHOCOLATE MILK giga mega kilo hecto deka BASE deci centi milli micro nano G M k h da --- d c m µ n or 1 The basics of metric relationships: To relate two metric units to each other, start by putting a 1 on the larger unit. Count the number of metric place moves to the desired unit. This is the same number of zeros you must add on to make the conversion, since the metric system is based on powers of 10. Ex. of a metric equality: 1 km = 1000 m = 10 3 m Practice: Write an equality for the following metric unit pairs: 1. m and cm 4. g and Mg 7. L and nl 2. m and dm 3. m and mm 5. g and Gg 6. g and dag 8. L and hl 9. L and µl units are combinations of simple units. They are produced by multiplying or dividing simple units. For example, a derived unit for volume is (from length x width x height). *, or the ratio of mass to volume for a substance, also uses a derived unit, commonly or for solids and liquids, or for gases. *Important note: a cubic centimeter (cm 3 ) is sometimes abbreviated as a cc in medical applications. A cubic centimeter is the same size volume as a milliliter. 1 cm 3 = 1 ml C. Using Scientific Measurements refers to the closeness of a measurement to the correct or accepted value. Accuracy = correctness refers to the closeness of repeated measurements to each other. Precision = reproducibility Examples of accuracy and precision: good precision & good accuracy poor accuracy but good precision moderate accuracy but poor precision poor precision & poor accuracy 2

3 is a calculation scientists use to compare an experimental result with a theoretical or accepted value. It is an assessment of accuracy and is a lab quality check. % error = Practice: 1. Calculate the percent error in a length measurement of 4.25 cm if the correct value is 4.08 cm. 2. The actual density of a material is 7.22 g/cm 3, A student measures the density of the same material as 7.30 g/cm 3. What is his percent error? II. Scientific Notation In scientific notation, numbers are written in the form M x 10 n where M = the ; < M < and n = the or power of. Examples: To convert to scientific notation: 1. Move the in the original number to the left or right so only one nonzero digit remains to the left of the decimal point. 2. Count the number of you moved the decimal point. This determines the exponent on 10. If you moved the decimal point to the left, n is. If you moved the decimal point to the right, n is. Ex. 1: Convert to scientific notation. Ex. 2: Convert to scientific notation. Practice 1. Convert to scientific notation 2. Convert to scientific notation 3. Convert to scientific notation To convert to standard decimal form: 1. If the exponent is positive, move the decimal that many places to the right. You may have to add zeros to fill in spaces. 2. If the exponents is negative, move the decimal that many places to the left. You may have to add zeros to fill in spaces. Ex. 1: Convert 5.78 x 10 5 to standard form. Ex. 2: Convert 5.78 x 10-5 to standard form. 3

4 REMEMBER that numbers larger than 10 should be represented with POSITIVE powers of 10, and numbers smaller than 1 should be represented with NEGATIVE powers of 10. What about numbers between 1 and 10? How would you represent 7 in scientific notation? Note: To put scientific notation in your calculator, you MUST use the EE or EXP button. NEVER put scientific notation in your calculator by typing x 10^!! Ex.: Using your calculator, determine 7.89 x / 6.02 x Practice 1. Using your calculator, determine the following: a) 3.56 x x = b) 5.64 x x = c) 3.78 x 10-7 / 6.34 x 10-5 = d) 7.89 x x 2 / 6.37 x = e) 15.6 / 6.02 x = III. Uncertainty in Measurement (Significant Figures) 1. Definition and Determination Significant figures ( sig figs ) are the in any measurement that are known with certainty plus one final digit that is estimated and. Rules for determining significant figures: 1. Any number that isn t a zero is always a sig fig. Ex.: 6.15 has 3 sig figs has 9 sig figs 2. Zeros that are between two non-zeros are always sig figs. Ex.: has 5 sig figs 3. Leading zeros are not sig figs. They only act as placeholders. Ex.: has 3 sig figs 0.02 has 1 sig fig 4. For values written in scientific notation, all digits in the coefficient (big # in front of power of 10) are the significant digits. Ex.: 4.50 x 10 7 has 3 sig figs 9.0 x 10 6 has 2 sig figs 5. Zeros that come at the end of a number are significant only if the number contains a decimal point. Ex.: 5200 has 2 sig figs has 6 sig figs 100. has 3 sig figs 100 has 1 sig fig 4

5 Note: Trailing zeros with no decimal point are ambiguous. We assume they are not significant, but it is preferred to write these numbers in scientific notation. This helps to eliminate confusion, especially if some of the zeros are significant. Example: 5000 with no significant zeros = 5 x with 1 significant zero = 5.0 x with 2 significant zeros = 5.00 x with 3 significant zeros = x 10 3 Further notes: Exact Numbers: Numbers that are obtained by counting rather than measuring are assumed to have infinite significant figures. Example: You count the number of eggs left in the carton and find it to be 8. This number has infinite significant figures because it is exact (no uncertainty). Definitions: Numbers that arise from definitions are also exact. For example, 1 meter = 100 centimeters. The 1 and the 100 have infinite significant figures. Ex.: Determine the number of significant figures in a) 404 b) 4.0 c) 40 d) e) 4.00 x 10 5 f) Rules for doing math with sig figs 1. When multiplying or dividing, round the answer so that it has the same number of TOTAL significant figures as the measurement with the least number of TOTAL significant figures (the least precise* measurement). Ex.: 12345/67 = 180 or 1.8 x 10 2 (2 sig figs because 67 has only 2 sig figs) 2. When adding or subtracting, round the answer so that it has the same number of DECIMAL PLACES as the measurement with the least number of DECIMAL PLACES (the least precise measurement). In other words, your answer cannot have any decimal places beyond the last decimal place common to all the numbers being added or subtracted. Ex.: = (to the tenths place) * The term precise in this context refers to the degree of exactness of the measurement. Ex.: Determine the volume of a cube that is 3.23 cm x cm x 2 cm, and round to correct SF. Ex.: Determine the sum of kg and 8.2 kg, and round to correct SF. 5

6 Practice: Determine the number of sig figs in the following answers: cm cm = /(12.2+5) = (mixed operations!) Rules for rounding to correct number of sig figs 1. Count from the left over to the correct number of sig figs. 2. If the number to the right of where you are ending is 4 or less; leave it alone and drop all the numbers after it. Note: You cannot change the place value of any significant figures this means all numbers must be left in the appropriate value column and you may need to fill in the rest with zeros. Ex.: rounded to 3 sig figs becomes If the number to the right of where you are ending is 5 or greater, add one to the end and drop numbers after that. Again, numbers need to keep their place value (tens, hundreds, etc.) column. Ex.: rounded to 5 sig figs becomes Ex.: Round the following numbers to 3 sig figs a) d) 51,358 b) e) c) f) 5,135, Sig figs in the lab When reading measurements from equipment in the lab, it is ESSENTIAL to include all known, plus a last digit. Look for the interval on the piece of equipment. This is the smallest division you can see marked off. You must estimate decimal place beyond the value of the interval on the equipment. Example: If a graduated cylinder has an interval of 1 ml, you must read the volume to the 0.1 ml. You are estimating the tenth s place. 6

7 Example: Measure the bristles on the toothbrush with each centimeter ruler below.. Ruler #1: interval value = ; measurement = Ruler #2: interval value = ; measurement = Notice how the degree of precision is different for each measurement, because the rulers have different intervals. Ruler #2 allows better precision than Ruler #1. Practice Read measurements F, A and H on the centimeter ruler below. Interval value = F = cm A = cm H = cm Do all measurements above go out to the same number of decimal places? They should! You used the same ruler to get all of the measurements, so the precision MUST be the same in each case. 7