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)

Normal Body Temp

98.6°F 37°C 310°K

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 =Mass

Volume

M = D x VV = M

Density (units) = Specific Gravity (no units – it’s a comparison)

D

D = density M = mass V = volume

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?

Calculate to the correct sig figs. Don’t forget the correct units!

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 DigitsIn any measurement:

• All the certain, precisely determined digits

• Uncertain, estimated digit

Significant Digit Rules

• All non zero digits are significant• Zeroes are tricky:1. Trapped zeroes are always significant (ex. 707)2. Atlantic (absent decimal points): zeroes on the end

are not significant; they’re placeholders (ex. 320)3. Pacific (present decimal points): zeroes immediately

following the decimal point are not significant; they’re placeholders (ex. .000842)

4. 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

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

METRIC

PREFIXES

M

k

d

c

m

Go down X

Go up ÷

Basic

unit

LARGE

small

LARGE

small

UNIT ANALYSIS• CHANGING (CONVERTING) ONE UNIT

INTO ANOTHER

WHAT YOU KNOW

WHERE YOU START

WHAT YOU’RE GIVEN

X

CONVERSIONS

HOW 2 UNITS ARE EQUAL

=

WHAT YOU WANT

WHERE YOU END

WHAT IS UNKNOWN

CONVERSIONSConversions tell how 2 units are equal. Ex. 1 foot = 12 inches

Conversions can be written 2 ways

1 foot

12 inches

or

12 inches

1 foot

Like dominoes, conversions can be played either way.

The way you play the conversion is to help a unit CANCEL!

1.64 feet = ? inches

Know Unknown

1.64 feet

1x =

Multiply across the tops and divide by the bottoms

=