Chemistry Mathematics Measurement 3221.MATH.1; 3221.MATH.2

Learning Goals Write the names and abbreviations for the units used in measurements of length, volume, and mass Label measurements as accurate or precise Write a number in scientific notation Determine the number of significant figures in measured numbers Adjust calculated answers to the correct number of significant figures. Use numerical prefixes to do metric conversions through decimal placement.

Units of Measurement 2 parts to any measurement: number and unit Units are extremely important in reporting and working with scientific numbers and they must be included The number of digits in a measurement reflects a degree of precision: the more digits in the measurement, the more precise it is; fewer digits, less precision Why is this important?? Why must both parts of a measurement be included in order to be determined as correct??

The units make all the difference!!! Read the following: When my son was 7 he walked 3, and when he was 4 he threw his baseball 8 and said his school was 5 away. When my son was 7 months old he walked 3 steps, and when he was 4 years old he threw his ball 8 feet and said his school was 5 minutes away. The units make all the difference!!!

Uncertainty in Measurement Accuracy: how close a measurement is to the accepted value Precision: degree of “agreement” between several measurements of the same quantity A MEASUREMENT CAN ONLY BE AS PRECISE AS THE INSTRUMENT USED!!! How many divisions are on the ruler? How precise is the ruler? What is the most precise a measurement can be using this ruler? (answer: 2 decimal places—why??)

Accuracy and Precision Illustration What makes something accurate? Precise?

Two major systems: English system -used only in the United States -inches, yards, pounds 2. Metric system -International System (SI system) is the system of measurement for the scientific world -centimeters, meters, kilograms

Fundamental SI Units Quantity Symbol Unit name Unit abbreviation Length l Meter m Mass Kilogram kg Time t Second s Temperature T Kelvin K Amount of substance n Mole mol Electric current I Ampere A Luminous intensity Iv Candela cd

What do the units mean? Unit: predefined standard of measurement or basis of comparison Second: 60 s = 1 min 1 meter is slightly longer than 1 yard a 100 yd football field is only 91.4 m 1 kg = 2.205 lb Remember: mass is different than weight, which is affected by gravity

Prefixes in SI system Prefix Symbol Meaning Exponential Notation mega- 1,000,000 106 kilo- k 1,000 103 hecto- h 100 102 deka- da 10 101 ------ ----- 1 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- µ 0.000001 10-6 nano- n 0.000000001 10-9 What are mnemonics? Does anyone know a mnemonic for the SI prefixes? Mighty King Hector Died---Driving crazy mini-motorcycles nightly.

Prefix Multipliers Used with the standard units of the SI system, rather than having different “units” with which to make comparisons Multipliers change the value of the unit by powers of 10 Prefix multipliers allow us to express a wide range of measurements in units that are similar in size to the quantity we are measuring Choose the prefix that is most convenient for a particular measurement

Volume/ amt of substance Derived SI Units Quantity Symbol Unit name Abbreviation Derivation Area A Square meter m2 Length x width Volume V Cubic meter m3 Length x width x height Density D kg/ m3 Mass/volume Molar mass M kg/ mol Mass/amt of substance Molar volume Vm m3/ mol Volume/ amt of substance Energy E Joule J Force x length What is the definition of volume? Area? ANY UNIT OF LENGTH, WHEN CUBED (RAISED TO THE THIRD POWER), BECOMES A UNIT OF VOLUME 1 cm3 = 1 mL 1 dm3 = 1 L

Uncertainty in Measurements Measured numbers: numbers you obtain when you use a measuring tool to determine your height, weight, or temperature To report a measurement, first read the numerical value of the marked line. Finally, estimate between the smallest marked lines. When an estimate ends on a marked line, a zero is written for the estimated digit.

Significant Figures Scientific numbers are recorded so that every digit is certain except for last, which is estimated. 48.872 When recording measurements, only estimate ONE digit beyond the smallest division on the instrument being used!!

Reading Volume Meniscus: the curved portion at the top of a volume of liquid Most liquids have a concave meniscus, however mercury has a convex meniscus

Rules for determining significant figures: All nonzero digits are significant 1.05 0.0110 2. Interior zeros (zeros between 2 numbers) are significant 1.0208 50.1 3. Trailing zeros (zeros after a decimal point) are significant 5.10 3.00 4. Leading zeros ( zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 0.00005

Practice Problems 0.00789 2.0012 0.001 4.100 0.1000 2.65001 100.25

Solutions to Problems 0.00789 3 significant figures (0.00789) 2.0012 5 (2.0012) 0.001 1 (0.001) 4.100 4 (4.100) 0.1000 4 (0.1000) 2.65001 6 (2.65001) 100.25 5 (100.25)

Exact numbers Exact numbers have an unlimited number of significant figures 3 sources 1. accurate counting of discrete objects 3 atoms means 3.000000 atoms 2. defined quantities 100 cm = 1 m means 100.000 cm =1.00m 3. integral numbers that are part of an equation radius = diameter/ 2

Significant Figures in Calculations In multiplication or division, the result carries the same number of significant figures as the factor with the fewest significant figures In addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places

Scientific Notation Used to write cumbersome numbers in a compact manner 1.2 x 10-10 exponent (n) Decimal part exponential part To convert a number to scientific notation: 1. move the decimal point to obtain a number between 1 and 10. 2. multiply by 10 raised to the number of places you moved the decimal point -if decimal moved left: positive exponent -if decimal moved right: negative exponent

Practice

Percent Error NO MEASURED VALUE WILL EVER BE EXACT!! The percentage by which a measurement deviates from the accepted value NO MEASURED VALUE WILL EVER BE EXACT!! % Error = Accepted Answer - Experimental Answer x 100 Accepted Answer WORK EXAMPLE PROBLEMS!!!

Practice Problems 1. Samantha S. Sloppiness measured the volume of her soda before she drank it for her midmorning snack. She measured the volume of the 12 oz. bottle to be 14 oz. 2. Clyde Clumsy was directed to weigh a 500 g mass on the balance. After diligently goofing off for ten minutes, he quickly weighed the object and reported 458 g. 3. Pretty Patty Pestilence had casually recorded her grades for the nine weeks in her notebook. She concluded she had 250 points out of 300 for the grading period. However, Miraculous (chemistry teacher) determined she had 225 points out of 300 and awarded her a "C" for the grading period. 4. Drew D. Ditzy came to Miraculous with a problem. Drew was told to measure 50 cm of copper wire to use in an experiment. Since his ruler only measured to 45 cm he used this amount of wire and his experiment was a failure. 5. Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55 mph not 65 mph.