Presentation Ch. 2 CHM 160
User Manual:
Open the PDF directly: View PDF .
Page Count: 48
© 2015 Pearson Education, Inc.
Chapter 2: Measurement, Problem
Solving, and the Mole Concept
2.1: The Metric Mix-up: A
$125 Million Unit Error
1998 –Mars Climate Orbiter
•Onboard Computers
programmed in metric
•Ground engineers working
in English units
•Corrections to trajectory
4.45 times too small
• Orbiter burned up in Mars’
atmosphere
© 2015 Pearson Education, Inc.
The Standard Units of Measurement
•Scientists have agreed on a set of international standard
units for comparing all our measurements called the SI
units
✓Système International = International System
© 2015 Pearson Education, Inc.
Temperature
•Measure of the average amount of kinetic energy caused by
motion of the particles
✓higher temperature = larger average kinetic energy
•Heat flows from the matter that has ___________________
__________________________________________________
✓heat flows from hot object to cold
✓heat is exchanged through molecular collisions between
the two materials
© 2015 Pearson Education, Inc.
4
Temperature Scales
•Fahrenheit scale, °F
✓used in the U.S.
•Celsius scale, °C
✓used in all other countries
•Kelvin scale, K
✓absolute scale
➢no negative numbers
✓_____________________
_______________________
_______________________
✓0 K = absolute zero
© 2015 Pearson Education, Inc.
Common Prefix Multipliers in the
SI System
© 2015 Pearson Education, Inc.
Volume
•Measure of the amount of space occupied
•SI unit = cubic meter (m3)
•Commonly measure solid volume in cubic
centimeters (cm3)
•Commonly measure liquid or gas volume
in milliliters (mL)
✓1 L is slightly larger than 1 quart
✓1 L = 1 dm3= 1000 mL = 103mL
✓1 mL = 0.001 L = 10−3 L
✓1 mL = 1 cm3
© 2015 Pearson Education, Inc.
Measurement
and Significant Figures
© 2015 Pearson Education, Inc.
What Is a Measurement?
•Quantitative observation
•Comparison to an agreed
standard
•Every measurement has a
number and a unit
•The unit tells you what standard
you are comparing your object to
•The number tells you
•what multiple of the standard
the object measures
•the uncertainty in the
measurement
© 2015 Pearson Education, Inc.
Reliability of Measurements:
Precision and Accuracy
•Uncertainty comes from limitations of the instruments used for
comparison, the experimental design, the experimenter, and
nature’s random behavior
•To understand how reliable a measurement is, we need to
understand the limitations of the measurement
•Accuracy
_________________________________________________
_________________________________________________
_________________________________________________
•Precision is an indication of how close repeated
measurements are to each other
✓how reproducible a measurement is
© 2015 Pearson Education, Inc.
Precision and Accuracy
•Measurements are said to be
•precise if they are consistent with one another;
•accurate only if they are close to the actual value.
•Scientific measurements are reported so that _________
_______________________________________________
Consider the following reported value of 5.213:
•The first three digits are certain; the last digit is estimated.
5.213
Known with certainty
Estimated value
© 2015 Pearson Education, Inc.
© 2015 Pearson Education, Inc.
Precision and Accuracy
Example 2.1
Reporting the Correct
Number of Digits.
The graduated cylinder
shown here has
markings every 0.1 mL.
Report the volume
(which is read at the
bottom of the meniscus)
to the correct number of
digits.
© 2015 Pearson Education, Inc.
Precision and Accuracy: An Illustration
Problem
Consider the results of three students who repeatedly
weighed a lead block known to have a true mass of 10.00 g.
© 2015 Pearson Education, Inc.
Precision and Accuracy: An Illustration
Problem
Consider the results of three students who repeatedly
weighed a lead block known to have a true mass of 10.00 g.
From the above data, what can you conclude about each of
the students’ recorded data?
© 2015 Pearson Education, Inc.
Precision and Accuracy: An Illustration
Problem
Lead block known to have a true mass of 10.00 g
•Student A’s results are both _______________ (not close to the true value)
and ____________________ (not consistent with one another).
–Random error
___________________________________________________________
___________________________________________________________
•Student B’s results are _____________ (close to one another in value) but
_______________________.
–Systematic error
___________________________________________________________
___________________________________________________________
•Student C’s results display little systematic error or random error—they are
both ___________________ and _________________.
© 2015 Pearson Education, Inc.
Significant Figures
•Significant figures deal with writing numbers to reflect
precision of their ___________________________.
•The precision of a measurement depends on the
instrument used to make the measurement.
•The preservation of this precision during calculations can
be accomplished by using significant figures.
•The greater the number of significant figures, the greater
the certainty of the measurement.
© 2015 Pearson Education, Inc.
Significant Figures
•The non-place-holding digits in a
reported measurement are called
significant figures
✓some zeros in a written number are only
there to help you locate the decimal point
•Significant figures tell us the range of
values to expect for repeated
measurements
✓the more significant figures there are in a
measurement, the smaller the range of
values is
12.3 cm
has 3sig. figs.
and its range is
12.2 to 12.4 cm
12.30 cm
has 4sig. figs.
and its range is
12.29 to 12.31 cm
© 2015 Pearson Education, Inc.
Rules of Significant Figures
1. Nonzero digits are always significant.
96 2 significant digits
61.4 3 significant digits
2. Zeros that are “sandwiched” between nonzero digits are significant.
5.02 3 significant digits
6004 4 significant digits
3. Zeros used as placeholders are NOT significant.
7000 1 significant digit
0.00783 3 significant digits
4. One or more final zeros used after the decimal point are significant.
4.7200 5 significant digits
0.250 3 significant digits
© 2015 Pearson Education, Inc.
Using Significant Figures in Mathematical
Operations:
Multiplication and Division:
The answer has the same number of significant figures as the least precise
factor in the calculations.
3.05 x 1.3 = 3.965 = 4.0 correct ans
3 sig figs 2 sig figs answer in calc w/ 2 sig figs
9.247 g (4 sig figs) = .684962= 0.685 g correct ans
13.5 cm3(3 sig figs) (ans in calc) cm3w/ 3 sig figs
© 2015 Pearson Education, Inc.
Review
How many significant figures are in each of the following?
0.04450 m
5.0003 km
10 dm = 1 m
1.000 × 105s
0.00002 mm
10,000 m
© 2015 Pearson Education, Inc.
Exact Numbers
•Exact numbers have an unlimited number of
significant figures.
•Exact counting of discrete objects
•Integral numbers that are part of an equation
•Defined quantities
•Some conversion factors are defined quantities,
while others are not.
© 2015 Pearson Education, Inc.
Intensive and Extensive Properties
•Extensive properties are properties whose value depends
on amount of the substance
✓extensive properties cannot be used to identify what
type of matter something is
➢if you are given a large glass containing 100 g of a clear,
colorless liquid and a small glass containing 25 g of a clear,
colorless liquid, are both liquids the same stuff?
•Intensive properties are properties whose value is
independent of the amount of the substance
✓intensive properties are often used to identify the type of
matter
➢samples with identical intensive properties are usually the same
material
© 2015 Pearson Education, Inc.
Density
Density is a physical property: the ratio of mass to volume
–is an intensive property
•The physical properties of mass and volume that determine a
substance’s density are EXTENSIVE.
–Units of Density
•Solids = g/cm3Liquids = g/mL Gases = g/L
✓1 cm3= 1 mL
•Volume of a solid can be determined by water displacement
•Density : solids > liquids >>> gases
✓except ice is less dense than liquid water!
Density = mass
volume Density (d) = m
V
© 2015 Pearson Education, Inc.
Density
•For equal volumes, denser object
has larger mass
•For equal masses, denser object
has smaller volume
•Heating an object generally causes
it to expand, therefore the density
changes with temperature
© 2015 Pearson Education, Inc.
Calculations and Solving Chemical Problems
•Many problems in science involve using
relationships to convert one unit of measurement
to another
–unit conversion problems.
•Using units as a guide to solving problems is
–dimensional analysis.
•Units should always be included in calculations;
they are multiplied, divided, and canceled like any
other algebraic quantity.
© 2015 Pearson Education, Inc.
Dimensional Analysis
•A unit equation is a statement of two equivalent
quantities, such as
2.54 cm = 1 in.
•A conversion factor is a unit equation written in fraction
form with the units we are converting from on the
bottom and the units we are converting to on the top.
or
•Conversion factors are relationships between two units
✓may be exact or measured
© 2015 Pearson Education, Inc.
Problem Solving and
Dimensional Analysis
•Arrange conversion factors so the starting unit cancels
✓arrange conversion factors so the starting unit is on the bottom
of the first conversion factor
•May string conversion factors
✓so you do not need to know every relationship, as long as you
can find something else the starting and desired units are
related to
© 2015 Pearson Education, Inc.
Dimensional Analysis
Units Raised to a Power:
•When building conversion factors for units raised to a
power, remember to raise both the number and the unit
to the power. For example, to convert from square inches
to square centimeters, we construct the conversion factor
as follows:
© 2015 Pearson Education, Inc.
Problem Solving: Dimensional Analysis
Example:
The engineers involved in the Mars
Climate Orbiter disaster entered the
trajectory corrections in units of
pound·second. Which conversion
factor should they have multiplied
their values by to conver them to the
correcdt uniots of newton.second?
(1 pound·second = 4.45
newton·second)
© 2015 Pearson Education, Inc.
Problem-Solving Strategy
•Identify the starting point (the given information).
–Sort out information given in the problem.
•Identify the endpoint (what we must find).
–What is the problem asking you to solve for? What units does the
answer need?
•Devise a way to use the given information to get the answer.
•Solve:
–Most chemistry problems you will solve in this course are unit
conversion problems.
–Using units as a guide to solving problems (dimensional analysis)
•Units should always be included in calculations; they are multiplied,
divided, and canceled like any other algebraic quantity.
•Check whether the numerical value and its units make sense.
© 2015 Pearson Education, Inc.
1. Sort into
a. Given
b. Find
2. Strategize: Devise a conceptual
plan from the given units, using the
appropriate conversion factors and
ending with the desired units.
3. Solve: Begin with the given
quantity. Multiply by the
appropriate conversion factors,
canceling units to arrive at the find
quantity. Round to correct number
of significant figures.
4. Check: Correct units? Does the
answer make sense?
Example 2.3: Convert 1.76 yards to centimeters.
Note: 1.094 yd = 1m and 1 cm = 10-2 m
© 2015 Pearson Education, Inc.
1. Sort
2. Strategize
3. Solve
4. Check
© 2015 Pearson Education, Inc.
1. Sort
2. Strategize
3. Solve
4. Check
© 2015 Pearson Education, Inc.
1. Sort
2. Strategize
3. Solve
4. Check
© 2015 Pearson Education, Inc.
1. Sort
2. Strategize
3. Solve
4. Check
© 2015 Pearson Education, Inc.
Moles
© 2015 Pearson Education, Inc.
Counting Atoms by Moles
•If we can find the mass of a particular
number of atoms, we can use this
information to convert the mass of an
element sample into the number of atoms
in the sample
•Amole (mol) of anything contains
6.02214 × 1023 of those things.
–Examples:
•1 mol of marbles corresponds to
6.02214 × 1023 marbles.
•1 mol of sand grains corresponds
to 6.02214 × 1023 sand grains.
•This number is Avogadro’s number.
© 2015 Pearson Education, Inc.
Chemical Packages - The Mole
•Mole = number of particles equal to the number
of atoms in 12 g of C-12
✓1 atom of C-12 weighs exactly 12 amu
✓1 mole of C-12 weighs exactly 12 g
•The number of particles in 1 mole is called
Avogadro’s Number = 6.0221421 x 1023
✓1 mole of C atoms weighs 12.01 g and has
6.022 x 1023 atoms
➢the average mass of a C atom is 12.01 amu
© 2015 Pearson Education, Inc.
Mole Conversions:
Atoms to Moles or Moles to Atoms
•Converting between number of moles and number of
atoms is similar to converting between dozens of eggs
and number of eggs.
•For atoms, you use the conversion factor
1 mol atoms = 6.022 × 1023 atoms.
•The conversion factors take the following forms:
© 2015 Pearson Education, Inc.
Practice —A silver ring contains 1.1 x 1022 silver
atoms. How many moles of silver are in the ring?
40Tro: Chemistry: A Molecular Approach, 2/e
© 2015 Pearson Education, Inc.
Converting between Mass and Amount
(Number of Moles)
•To count atoms by weighing them, we need
one other conversion factor—the mass of 1 mol
of atoms.
•The mass of 1 mol of atoms of an element is the
molar mass.
•An element’s molar mass in grams per mole is
numerically equal to the element’s atomic mass
in atomic mass units (amu).
•The lighter the atom, the less a mole weighs
•The lighter the atom, the more atoms there are in
1 g
© 2015 Pearson Education, Inc. 42
Mole and Mass Relationships
1 mole
sulfur
32.06 g
1 mole
carbon
12.01 g
Tro: Chemistry: A Molecular Approach, 2/e
© 2015 Pearson Education, Inc.
Converting between Mass and Moles
•The molar mass of any element is the conversion factor
between the mass (in grams) of that element and the
amount (in moles) of that element.
•Example:
12.01 g C atoms = 1 mol C atoms
or
12.01 g C atoms/1 mol C atoms
or
1 mol C atoms/12.01 g C atoms
© 2015 Pearson Education, Inc. 44
© 2015 Pearson Education, Inc.
Mass to Moles to Number of Particles:
The Conceptual Plan
For an element,
For a molecule (compound),
Mass of
molecule
(grams)
Number
of molecules
Moles of
molecules
Divide by atomic
mass
Multiply by
Avogadro’s number
Mass of
element
(grams)
Moles of
element
Number
of atoms
Divide by molar
mass
Multiply by
Avogadro’s number
© 2015 Pearson Education, Inc.
Number of Particles to Moles to Mass:
The Conceptual Plan
For an element,
For a molecule (compound),
Mass of
molecule
(grams)
Number
of molecules
Moles of
molecules
Multiply by atomic
mass
Divide by
Avogadro’s number
Mass of
element
(grams)
Moles of
element
Number
of atoms
Multiply by molar
mass
Divide by
Avogadro’s number
© 2015 Pearson Education, Inc.
Practice —Calculate the moles of sulfur in
57.8 g of sulfur
47
© 2015 Pearson Education, Inc.
Practice —How many aluminum atoms are in
a can weighing 16.2 g?
48