Chapter 1. Matter and Measurement. Matter and Measurement page 1
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1 Chapter 1 Matter and Measurement Matter and Measurement page 1
2 Measurement Part 1: Significant Figures are used to communicate measurement uncertainty. Rules for Significant Figures (Sig Figs) Significant Figures The digits in a measurement known with certainty plus one estimated digit. Nonzero Digits The digits 1, 2, 3, 4, 5, 6, 7,8 & 9 are always significant. The Digit Zero Zeros may or may not be significant. Leading Zeros Zeros located at the beginning of a number are NEVER significant. Confined Zeros Zeros located between nonzero digits are ALWAYS significant. Trailing Zeros Zeros located at the end of a number are significant if the number has a decimal point or the zeros carry overbars Matter and Measurement page 2
3 Round each of the following numbers to the number of sig figs indicated in ( ). 6,478 (two) (two) 456,924 (three) (three) 4000 (two) Important Distinction! Zeros are important place holders to preserve the overall value of the measurement. Sig figs are about the accuracy and precision of the measurement. Round 689,532 to the indicated number of sig figs Four: Two: Round to the indicated number of sig figs Four: Two: Matter and Measurement page 3
4 Significant Figures in Calculations 1. For multiplication and division, the result is limited by the term with the smallest number of significant figures ft x 2.6 ft = 5.0 ml x 13.9 g = ml 2. For addition and subtraction, the result is limited by the term with the least precision. Look at what digit place has the uncertainty the hundreds, tens, ones, tenths, hundredths,...? 7.05 ft ft 63,200 g g Matter and Measurement page 4
5 Measurement Part 2: Scientific Notation Exponents a very brief review Exponents > 1 Exponents < 1 Matter and Measurement page 5
6 Converting from Decimal to Scientific Notation Learn to use your calculator to toggle back and forth between decimal and scientific notation. Learn how to enter numbers in scientific notation into your calculator. Convert the following numbers from decimal to scientific notation or vice versa x , x Matter and Measurement page 6
7 Mathematical Operations with Scientific Notation Multiplication Division Be Aware of the Order of Operations Practice Problems solve the following (2.340 x 10-3 ) x (2.6 x 10 6 ) = x 10 3 = (5.7 x 10 7 ) (2.61 x 10-2 ) 7.4 x 10-2 = (3.248 x 10 6 ) (6.50 x 10-3 ) Matter and Measurement page 7
8 Measurement Part 3: Converting Between Units Converting between Metric Units 2 Approaches 1) Unit Conversion Factors How many mg are in 0.53 g? 2) Shifting Decimals by adding/subtracting exponential terms How many dg are in 3,475,892 g? How many ml are in kl? Matter and Measurement page 8
9 Converting Between Metric and English Units - 3 important bridges What is the kilogram weight of a 210 lb patient? A typical member of the species Vibrio cholerae is 8.8 x 10-6 m long. How long is this in inches? Matter and Measurement page 9
10 Using Multiple Conversion Factors Horse racing uses the distance of furlongs. If a mile is defined as 8 furlongs, how many kilometers is a 22 furlong race? There are 42 gallons in one barrel of crude oil. How many ml of crude oil are contained in one barrel? Matter and Measurement page 10
11 Measurement Part 4: Dosage Calculations Dosage Calculations An antibiotic is prepared in 3.0 ml ampoules that contain 60.0 mg of drug. How many ml of the solution should be administered to a patient prescribed 45 mg per injection? Ivermectine is used to treat dogs that have intestinal parasites. The effective dosage of this drug is 1.5 g/kg of body weight. How much invermectine should be given to a 17 lb dog? Matter and Measurement page 11
12 The doctor ordered 20. mg/kg of a medication for a patient who weighs 36 lbs. The medication is available as 100. mg/ml. How many ml should be given to the patient? A young child is being treated for a severe ear infection. The pediatrician prescribes amoxicillin at a daily dose of 40 mg/kg to be given in three injections 8 hours apart. If the amoxicillin is supplied as a solution that contains 125 mg amoxicillin per 5 ml of liquid, then how many ml should the child receive in each injection? The child weighs 7.64 kg. Matter and Measurement page 12
13 Dosage of IV Solutions administering drugs gradually over time to allow for different metabolism rates Flow rate = dosage per unit time A medication is given intravenously at the rate of 250 drops per min. The medication s concentration is 450 ng/ L (450 ng/mcl). What is the weight, in grams, of the medication delivered to the patient in 24 hours? (15 drops = 1.0 ml) A patient is given intravenous morphine at a rate of 0.35 mg per hour. At this rate, how many minutes will it take to give the patient 1.5 mg of morphine? Matter and Measurement page 13
14 Measurement Part 5: Energy & Specific Heat Energy the capacity to do work Heat a form of energy Temperature a measure of the hotness or coldness of an object Heat vs Temperature The units for heat: Specific Heat (SH) The heat needed to raise 1.00 g of any substance by 1 C. The units of specific heat: Matter and Measurement page 14
15 Specific Heats for Some common Substances Substance SH (cal/g C) Substance SH (cal/g C) Water 1.00 Wood average 0.42 Ice 0.48 Glass average 0.22 Steam 0.48 Rock - average 0.20 Iron 0.11 Ethanol 0.59 Aluminum 0.22 Methanol 0.61 Copper Ether 0.56 Specific Heat calculations use the following equation: Calculate the number of calories of heat energy required to heat 25.0 g of copper from 23.0 C to 34.7 C. Matter and Measurement page 15
16 Calculate the final temperature after 175 cal of heat energy is added to 7.73 g of water at 43.2 C. What is the mass, in grams, of a piece of aluminum if its temperature changes from 30.0 C to 315 C when it absorbs 1770 cal? Matter and Measurement page 16
17 Measurement Part 6: Specific Gravity Specific gravity is the density of a substance relative to water ( 1.00 g/ml) The specific gravity of urine can be used diagnostically. Normal urine has a specific gravity between and Matter and Measurement page 17
18 Solids, Liquids, and Gases Part 1: Temperature Temperature a measure of the hotness or coldness of an object Fahrenheit ( F) Celsius ( C) Kelvin (K) bp of water body temp fp of water absolute zero When converting between temperature units we must consider 1) 2) F = 9/5 ( C) + 32 K = C The hottest temperate ever recorded in the US was 56.7 C in Death Valley, California. Convert this temperature into C and K. Matter and Measurement page 18
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