Measurement

The Quantitative Properties Basic Units of Measurement quantitative observations of an extensive property Measurements are comparisons between what is to be measured and a defined established size (reference point) Two parts: an amount and a unit. For example: 3.6 Liters 3.6 is the amount, Liters is the unit. The property is volume, since Liters measure volume

The Quantitative Properties - Mass Measures the amount of matter present Measured with a BALANCE Basic unit: gram (g)

The Quantitative Properties - Length Measures a straight line distance from one point to another Measured with a RULER Basic unit: meter (m)

The Quantitative Properties - Volume Measures the amount of space a piece of matter occupies. 3 dimensional Measured with a GRADUATED CYLINDER or a RULER Basic unit (if measured with a graduated cylinder) is LITER (L) and if measured with a ruler (L x W x H) a CUBIC METER (cm3)

The Quantitative Properties - Pressure Measures amount of force exerted by a gas colliding with another object Measured with a BAROMETER or MANOMETER Basic units include: ATMOSPHERE (atm), MILLIMETERS OF MERCURY (mm Hg), and POUNDS PER SQUARE INCH (psi)

The Quantitative Properties - Moles Describes number of atoms (element) or molecules (compound) needed to measure a mass in grams Formula (or molar) mass in grams = 1 mole 6.02 x 1023 atoms or molecules = 1 mole 22.4 L of any gas at standard temp and pressure (STP) = 1 mole

The Quantitative Properties - Heat Form of energy (thermal) Heat always moves from where it is to where it isn’t. The amount of heat moving is what we detect and turn into temperature Basic units: JOULE (J) and CALORIE (cal) Food calorie (C) = 1000 cal

The Quantitative Properties - Temperature Indicates moving heat, heat intensity Measures average kinetic energy (KE) of molecules Measured with a THERMOMETER Scale names and Basic units: CELCIUS (ºC) and KELVIN (K) (also Fahrenheit [ºF] which we don’t really use in science) Absolute Zero: The temperature at which all molecule motion stops (so everything becomes a solid)

98.6°F 37°C 310°K Normal Body Temp

Converting between Temperature Scales Know ºC, want K: ºC + 273 = K Know K, want ºC: K – 273 = ºC Between ºC and ºF: 1.8(ºC) = ºF – 32 (1.8 x ºC) + 32 = ºF ºC = (ºF – 32) 1.8

Density Mass per volume Describes how tightly packed particles are Water’s density changes with temperature but defined as 1.00 g/mL or 1.00 g/cm3 If an object’s density > water’s density, the object sinks when put in water If an object’s density < water’s density, the object floats when put in water Density units can be: g/mL or g/cm3 or g/L Specific gravity – compares density of one object to that of water (or another liquid)

D = density M = mass V = volume V = M M = D x V D Density (units) = Specific Gravity (no units – it’s a comparison)

Density Practice Problems Calculate to the correct sig figs. Don’t forget the correct units! Density Practice Problems Find the density of a piece of concrete if 6.120 kg has a volume of 9.0 L. Find the density of a block that has a mass of 108 grams and measures 2.0 cm x 2.0 cm x 9.0 cm. If the element Bismuth (Bi) has a density of 9.80 g/cm3, what is the mass of 3.74 cm3? Magnesium (Mg) has a density of 1.74 g/mL. What is the volume of 56.6 g? An object with a mass of 18.73 g is placed in 15.5 mL of water. The water rises to 19.0 mL. What is the object’s density?

Accuracy, Precision, and Percent Error “Measure twice, cut once.” A. Accuracy How close to the correct answer a measurement is B. Precision The closeness of a set of measurements made using the same technique 2 lab groups have similar data on the same object

C. Percent Error Calculated % difference between your answer and the accepted (actual, theoretical, or “correct”) answer How good a job you did - the smaller the % error, the better the accuracy (-)% errors mean your answer is smaller than the accepted (+)% errors mean your answer is larger than the accepted Formula for calculating % error: Experimental - actual x 100 actual Usually rounded to nearest 0.1% (to 1 decimal place) Experimental = your results Actual = accepted, theoretical, or “correct” answer

Significant Digits In any measurement: All the certain, precisely determined digits Uncertain, estimated digit

Significant Digit Rules All non zero digits are significant Zeroes are tricky: Trapped zeroes are always significant (ex. 707) Atlantic (absent decimal points): zeroes on the end are not significant; they’re placeholders (ex. 320) Pacific (present decimal points): zeroes immediately following the decimal point are not significant; they’re placeholders (ex. .000842) In numbers with decimal points, zeroes at the end are significant (ex. 5.912000)

Calculations and Significant Digit Rules Addition and Subtraction Round answers to fewest decimal places in the calculation Measurement with fewest decimal places is least precise data Calculated answer can’t be better than least precise data 12.3 mm + 6.25 mm 18.55  rounds to 18.6 mm (1 decimal place)

Calculations and Significant Digit Rules Multiplication and Division Round answers to the number of significant figures in the given Conversions are exact numbers (definitions), not data so they’re not used to determine sig figs. 108.3 cal x 4.18 J = 452.694  452.7 J 1 1 cal Given has 4 sig figs

Metric System Universal Establishes a common and comparable way of measuring Based on powers of 10 - measurements get bigger or smaller by 10s Prefixes used to indicate whether indicated measurement is getting bigger by 10s (by multiplying) or smaller by 10s (by dividing) Works for all types of extensive properties

Prefix Symbol Meaning METRIC PREFIXES Tera T 1 000 000 000 000 x bigger than basic unit Giga G 1 000 000 000 x bigger than basic unit Mega M 1 000 000 x bigger than basic unit Kilo k 1 000 x bigger than basic unit Hecto h 100 x bigger than basic unit Deka da or dk 10 x bigger than basic unit Basic unit L, m, g, J, cal, mole and others Deci d 10 x smaller than basic unit Centi c 100 x smaller than basic unit Milli m 1 000 x smaller than basic unit Micro µ 1 000 000 x smaller than basic unit Nano n 1 000 000 000 x smaller than basic unit Pico p 1 000 000 000 000 x smaller than basic unit

LARGE M Go down X k LARGE Basic unit d c Go up ÷ small m  small

UNIT ANALYSIS CHANGING (CONVERTING) ONE UNIT INTO ANOTHER WHAT YOU KNOW WHERE YOU START WHAT YOU’RE GIVEN WHAT YOU WANT WHERE YOU END WHAT IS UNKNOWN CONVERSIONS HOW 2 UNITS ARE EQUAL X =

CONVERSIONS Conversions tell how 2 units are equal. Ex. 1 foot = 12 inches Conversions can be written 2 ways Like dominoes, conversions can be played either way. The way you play the conversion is to help a unit CANCEL! 12 inches 1 foot or 12 inches 1 foot

1.64 feet = ? inches Unknown Know 1.64 feet 1 x = = Multiply across the tops and divide by the bottoms