measurement. the quantitative properties basic units of measurement quantitative observations of an...
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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
=